Ultimate Pre-Algebra
*6.1 Test* You worked 15 hour and earned $195, how much did you earn per hour
$13 an hour
12.3) Measures of an interior angle inside a polygon
((n-2) • 180)/n n = amount of sides the shape has This formula finds the measurement of one angle inside a shap
*9.5 Test* Find the distance between (-5, 6 ) and (3, 8)
(-1, 7)
*8.8 Test* y = -x + 4 y = 2x +1
(1,3)
*8.4 Test* Find the slope of the line through (-3, 6) and (-1, 2)
(2-6)/(-1- -3) = -2
12.3) Sum of the measures of the interior angles of a convex shape
(n-2) • 180 n = amount of sides the shape has This formula adds up all the angles inside a shape
*1.8 Test* If you go left 4 units and up 2 units what is the coordinate point if you started from 0
(x,y) X goes left and right and y goes up and down Left 4 is -4 Up 2 is 2 The coordinate point is (-4, 2)
*5.4 Test* -4/5 • 25/42
-10/21
1.6) Subtract -9 - 4
-13
*9.4 Test* Order the numbers -2.5, √6, 17/8, 1.8, and -√2 from least to greatest
-2.5, -√2, 1.8, 17/8, √6
1.7) Divide -20 / 5
-4
*1.5 Test* Find the sum -42 + (-17)
-42 + (-17) = -59
1.6) Subtract 4 - 10
-6
1.7) Multiply -7*9
-63
*5.5 Test* 2/3 / -6/7
-7/9
1.4) Order these numbers from least to greatest -8, 5, -4, 2, 0, 6
-8, -4, 0, 2, 5, 6
1.5) Add -54 + (-28)
-82
*3.6 Test* -8y + 5 < 29
-8y + 5 < 29 Subtract 5 to both sides -8y < 24 Divide -8 to both sides y > -3
7.3) Write 53.5% as a decimal
.535
1.7) Multiply -8 * 0
0, any number times 0 is 0
1.7) Divide 0 / -9
0, the quotient of 0 and a number is 0 (you cant divide by 0 though which would look like 2/0)
*1.2 Test* Evaluate 0.4^3
0.4 • 0.4 • 0.4 = 0.064
4.1) Write all the factors of 30
1 and 30, 2 and 15, 3 and 10, 5 and 6
1.2) 5^0
1, anything to the 0 power is 1
6.4) Properties of similar figures
1. Corresponding angles of similar figures are congruent 2. Ratios of the lengths of corresponding sides of a similar figure are equal Ex. The ratio of the left side of a figure to the left side of the similar figure is the same as the ratio of the right side of a figure to the right side of a similar figure Ex. If the left side of a small triangle is 3 and the left side of a similar figure is 6 then the ratio is 1:2 The ratio to the right side of the small triangle to the right side of the similar figure would also have to be 1:2
*11.1 Test* Look at: http://prntscr.com/oqnioh What's the frequency of cherry trees between 75 and 80 feet
10
4.6) Write 900 as a power of 10
10^2 = 100 9•100 = 900 so you can write 900 as 9 • 10^2
4.6) What is 4 • 10^4
10^4 = 10,000 (4 zeroes because it is the the power of 4) 4 • 10,000 = 40,000
*7.2 Test* 117 is 65% of what number
117/b = 65/100 180 = b
9.1) Find the square root of 144
12 12•12 = 144
*7.6 Test* You buy a cellphone 20% off the original price, if the original price is $129, how much did you buy it for
129 • (100%-20%) 129 • (80%) 129 • (.8) 103.2
*12.1 Test* If angle 1 and 2 are supplementary and angle 1 is 46 degrees what is angle 2
134
*3.3 Test* 13n - 45 = 36 + 4n
13n - 45 = 36 + 4n Subtract 4n to both sides 9n - 45 = 36 Add 45 to both sides 9n = 81 Divide by 9 on both sides n = 9
1.1) Find the product 4.5 * 3.2
14.4
5.2) 2 3/4 + 1 3/4
2 3/4 into a mixed number = 11/4 1 3/4 into a mixed number = 7/4 Add them together to get 18/4 then reduce to 4 2/4 -> 4 1/2
4.3) Equivalent Fractions
2/4 is equivalent to 1/2 because 2/4 reduces to 1/2
*11.9 Test* A bag has 5 green, 6 red, and 9 blue marbles. You randomly draw one marble then draw another without replacing the first. What is the probability you draw a red then a green marble
20 marbles total 6 red and 5 green There are 20 marbles when you draw a red so 6/20 There are only 19 marbles left when you draw a green so 5/19 6/20 • 5/19 = 3/38 converted to a decimal then percentage is about 7.9%
1.5) Add 38 + (-17)
21
*11.6 Test* 7P3
210
5.1) Show that the number is rational by writing it as a quotient of two integers (write the number as a fraction to show it is rational) 5 3/4
23/4 Remember to turn a mixed number ( 5 3/4) into an improper fraction (23/4) you multiply the denominator (4) by the leading whole number (5) and then add the numerator (3) and keep the denominator the same 5*4+3 = 23 -> 23/4
*4.1 Test* Factor 240 into prime numbers (prime factorization of 240)
240 can be split into 12 • 20 12 can be split into 3•4 which can be split into 3 • 2 • 2 20 can be split into 4 • 5 which can be split into 2 • 2 • 5 So now you have 5 • 3 • 2 • 2 •2 •2 All prime numbers
*10.8 Test* Find the volume of the pyramid Square base with length of 5 Height of 3
25
*10.4 Test* Find the area of the circle if the radius is 9
254
*6.8 Test* In a game you are to choose a 2 letter code from the 26 capital letters find the possible codes
26 • 26 = 676
4.1) Factor 28xy^3
28 can be broken down into the prime numbers 2, 2, and 7 (because 2•2•7 = 28) Then you get 2•2•7•x•y^3 then you need to split up the y into 2•2•7•x•y•y•y
4.6) Write 1/16 without using a fraction and using exponents
2^(-4) Because the negative exponent carries the 2^(-4) down and becomes 1/(2^4) and 2^4 is 16 so it becomes 1/16
4.1) Factor 6ab
2•3•a•b
9.1) Evaluate 2√(a+b^2) when a = 11 and b = 5
2√(11+5^2) 2√(11+25) 2√(36) 2(6) 12
1.7) Divide -30 / -10
3
*9.1 Test* What are the square roots of 9
3 and -3
*6.7 Test* Find the probability that you roll a 3 or a 6 when rolling a die
3 and a 6 are 2 of the 6 options on a die 2/6 -> 1/3 probability
1.2) 30^1
30, anything to the power of 1 is itself
7.1) Write 30% as a fraction
30/100 (can be reduced to 3/10)
*11.5 Test* If a school has 1000 students and a survey asks 375 if they like the color blue and 30 say yes then estimate the number of students in the entire school that like blue
30/375 = 0.08 = 8%, if 8% of the surveyed likes blue then you can make a broad assumption that 8% of the school likes blue in that case you find 8% of 1000 by multiplying 1000 by 0.08 and getting 80 students
*7.4 Test* What percent of 70 is 31.5
31.5 = x • 70 x = .45 .45 -> 45%
1.6) Find the change in temperature 32F to -10F
32F to -10F goes down into the negatives, to get 32 to -10 it has to go down 32 to reach 0 and then go down 10 more to reach -10 so it goes down -42 total
1.7) Multiply -3*-12
36
11.6) 3!
3•2•1 = 6
2.2) Use the distributive property to simplify x(3 + x)
3•x = 3x and x•x = x^2 x(3 + x) = 3x + x^2
*10.2 Test* How many sides does a quadrilateral have
4
9.1) Find the square root of 16
4 4•4 = 16
1.4) Absolute Value |-4|
4 (the absolute value of any number is positive)
3.4) Say 4 ≥ x in words
4 is greater than or equal to x
*8.7 Test* f(x) = 4x - 5 What is the value when x = -3
4(-3) -5 -17
*3.2 Test* 4(3r - 9) = 36
4(3r-9) = 36 Multiply the 4 to both the 3r and -9 12r - 36 Add 36 to both sides 12r = 72 Divide by 12 on both sides r = 6
10.3) Find the area of a trapezoid if it has bases 4cm and 9cm with a height of 2.5cm
4+9 = 13 13•2.5 = 32.5 32.5 • 1/2 = 16.25 Note: Multiplying by 1/2 is the same as dividing by 2
*4.7 Test* Write 41,800,000 in scientific notation
4.18 x 10^7
*4.3 Test * Write 60/75 in simplest form
4/5
*6.4 Test* If side A-B of one triangle is 40 and the same side of another triangle is 48 find the ratio of their lengths
40/48 -> 5/6 Means the first triangle is 5/6 the size of the bigger triangle
7.3) Write .42 as a percentage
42%
*10.5 Test* Find the surface area of the prism if the length and width of the base are both 12 and the height is 5
420
*7.1 Test* Write 44% as a fraction
44/100 -> 11/25
7.3) Write 4.432 as a percentage
443.2% You move the decimal over two spots and since there is still a number behind 443 you add a decimal then that number (in this case 2) and add the percentage sign
*3.1 Test* 45 = 10 + 1.25v
45 = 10 +1.25v Subtract 10 on both sides 35 = 1.25v Divide by 1.25 on both sides 28 = v
*4.2 Test* Find the greatest common factor between 18, 45, and 90
45 can be split up into 3 • 3 • 5 18 can be split up into 2 • 3 • 3 90 can be split up into 2 • 3 • 3 • 5 They all have 3 as the highest number in common so that's the answer
*7.7 Test* Suppose you deposit $440 into an account that earns 5% simple annual interest, find the balance after 3 years
460
*11.7 Test* 12C4
495
1.1) 4•d where d = 10
4•d is the same as 4•d, d =10 so now it changes to 4•10 = 40
1.4) Absolute Value |5|
5
2.1) Find the perimeter of a triangle if the sides are 5, 6, 10
5 + 6 + 10 = 21
*2.2 Test* Do 5(204) by splitting 204 up so its easier to multiply
5(204) -> 5(200+4) Now you can solve as 5(200) + 5(4) = 1020
2.1) Find the perimeter of a rectangle with the length of 5 and the width of 3
5+5+3+3 = 16
*7.5 Test* Find the percent of decrease from 55 to 33
55-33 = 22 22/55 = .4 = 40%
1.2) 5^3
5•5•5 = 125
*1.7 Test* -42 / -7
6
*2.7 Test* 9.74 + (-3.31)
6.43
*5.2 Test* 1/12 + 5/12
6/12 -> 1/2
*7.3 Test* Write 0.6 as a percent
60%
7.1) Write 65% as a fraction
65/100 (can be reduced to 13/20)
*9.6 Test* Find the hypotenuse of a 45 45 90 triangle if the 45 degree sides are equal to 6
6√2
*1.6 Test* Find the difference 7 - -15
7 - -15 = 7 + 15 = 22
*10.3 Test* Find the area of the trapezoid if the height is 1.5, the top is 3, and the bottom is 7
7.5
1.1.) Find the sum 3.2 + 4.7
7.9
5.1) Show that the number is rational by writing it as a quotient of two integers (write the number as a fraction to show it is rational) 7
7/1
8.4) What is the slope of a ramp that has a rise of 7 and a run of 10
7/10
8.4) What is the slope of a ramp that has a rise of 7 and a run of 5
7/5
*5.3 Test* 77/18 - 62/9
77/18 - 124/18 -47/18 -2 11/8
11.5) Out of 5000 randomly selected households, 780 were watching a certain program. Find the percentage of households that was watching that program
780/5000 = 0.156 now convert it to a percentage and get 15.6% of households watching the program
9.1) Find the square root of 64
8 8•8 = 64
*1.3 Test* 800 - 7(2+3)^2
800 - 7(2+3)^2 800 - 7(5)^2 800 - 7(25) 800 - 175 625
7.1) Writing percents
85/100 = 85% 8/10 = 80% A percent is how close the top number is to the bottom number in a fraction, if the bottom number is 100 then you can just write the top number and add a % sign. Notice how 8/10 = 80% because you can add a 0 to the top and bottom number and get 80/100 which is 80%
*4.6 Test* Write 8^0•b^-5 using positive exponents
8^0 = 1 b^-5 = 1/b^5 1 • 1/b^5 = 1/b^5
*9.3 Test* Find the longest side of the triangle if one side = 8 and the other side is 14
8^2 + 14^2 = c^2 c = 2√65
6.1) Reduce 9 to 12 to simplest form
9 to 12 is a ratio, 3 can fit into both 9 and 12 (3 is the GCF of 9 and 12). 3 fits into 9 3 times, 3 fits into 12 4 times So you get 3:4
8.4) What is the slope of a ramp that has a run of 3 and a rise of 9
9/3
2.3) Simplify variable expressions 5x+4x+7
9x+7
10.5) Net
A 2D representation of a 3d figure, what it would look like if it was folded out and all the faces were shown at once
9.6) 45, 45, 90 triangle
A 45, 45, 90 triangle is a special triangle with the angles being measured at 45, 45, and 90 degrees The hypotenuse of this special right triangle is one of the leg's lengths multiplied by √2 You can still use the Pythagorean theorem for this as its a right triangle but sometimes its quicker to use this method because often times you don't need to do much work to figure out the answer Ex. What is the hypotenuse of a 45 45 90 degree triangle if the legs both add up to 20 Since the legs both add up to 20 and they are the same length in this case (because they have the same 45 degree angle to make it) you know each leg has a length of 10 The hypotenuse is just 10√2 because you know its a special right triangle
10.3) Area of a Trapezoid
A = 1/2•(b1 + b2)•h b1 = base 1 b2 = base 2 It does not matter which is which h = height
2.1) Area of a triangle
A = 1/2•b•h (Area = 1/2 • base • height)
2.1) Find the area of a triangle with a height of 8 and a length of 14
A = 1/2•b•h for a triangle 1/2 • 8 • 14 = 56
10.3) Area of a parallelogram
A = b•h
2.1) Area of a rectangle
A = lw (Area = length • width)
2.1) Find the area of the rectangle if the length is 7 and the width is 5
A = lw for a rectangle 5•7 = 35
2.7) If the area of a rectangle is 75.52 and one of the sides is 11.8 what is the other side
A = l•w You know one value (11.8) but don't know the other so substitute x for it 11.8 • x = 75.52 Divide 11.8 to both sides since 11.8 is being multiplied to x then you get x = 6.4
7.7) Find the compound interest balance if p = $800, r = 5%, t = 3 years
A = p(1+r)^t 5% as a decimal is 0.05 1 + 0.05 = 1.05 Now you have A = p(0.05)^t t = 3 and (1.05)^3 = 1.157625 now you have p(1.157625) p = $800 800 * 1.157625 = $926.10
7.7) Compound interest formula
A = p(1+r)^t A = balance after interesting P = principle (starting amount) r = rate (as a decimal) t = time in years
1.2) Area of a square
A = s^2
10.4) Area of a circle
A = πr^2
10.4) Find the area of a circle if the diameter is 10
A = πr^2 We have the diameter and know its double the radius so we take half the diameter (5) and we use that for r r^2 or 5^2 = 25 now we have 25π and that is about 78.5
12.4) Transformation
A change made to the location or to the size of a figure
3.4) Would you use an open or a closed circle to graph an inequality with ≥ on a number line
A closed circle because it is "or equal to", you would use an open circle if it was just >
5.1) Inductive reasoning
A conclusion made on several examples
11.6) Factorial
A factorial is multiplying a number by each number below it, a factorial can be written with an exclamation mark after the number such as 4! 4! = 4•3•2•1
6.7) Fair game
A fair game is a game in which all players are equally likely to win
4.3) Simplest form of a fraction
A fraction is in simplest form if it cant be reduced anymore
8.6) Scatter Plot
A graph where values dont have to be exactly in a straight line
12.2) Transversal
A line that intersects two or more lines at different points is transversal. Transversal line: http://prntscr.com/oqm2m8
8.6) Line of best fit / Best fitting line
A line that lies as close as possible to the data points (doesn't have to touch all of them just as close to touching all of them as possible)
7.6) Markup
A markup is the price added to an item by a seller If it costs the seller $5 to obtain an item they can sell it for $10 (200% markup)
9.1) Perfect Square
A number is a perfect square if you are able to take the square root of it and not get a decimal number 25 is a perfect square because 5•5 works for it, 10 is not a perfect square because you cant multiply two whole numbers to reach it
9.4) Irrational number
A number that can not be written as a fraction, the decimal form of an irrational number keeps on going and doesn't repeat Think π (pi) 3.14159.... it doesn't repeat and it doesn't end so it is irrational The square root of any whole number that is not a perfect square is irrational (like the square root of 19)
4.1) Composite number
A number that is not a prime number
2.3) Constant Term
A number that wont change (no variable attached to it) the 7 in 5x + 7
4.1) Monomial
A number, a variable, or a product of a number and one or more variables raise to whole number powers. There is no addition or subtraction in a monomial 7x, 25mn^2, 24y^3z^2 To factor a monomial write the monomial in prime numbers and variables
10.2) Rhombus
A parallelogram with 4 congruent sides
10.2) Rectangle
A parallelogram with 4 right angles
10.2) Square
A parallelogram with 4 right angles and 4 congruent sides
10.2) Parallelogram
A quadrilateral with both pairs of opposite sides parallel
10.2) Trapezoid
A quadrilateral with exactly 1 pair of parallel sides
9.2) Simplest Form
A radical is in simplest form when 1. The number under the radical isn't a perfect square 2. There are no fractions under the radical sign 3. A radical sign is not in the denominator of any fraction
11.1) Interval
A range of data Like Ages 11 - 15 is an interval reaching from age 11 to age 15
6.1) Rates
A rate is a ratio of two quantities measured using different units
8.1) Function
A relation where one input as only one output For example: If I look at the last question where Domain: 0, 2, 5, 6 Range: 1, 3, 8, 10 You see it is a function because the inputs(domain) don't have the same outputs (range), if one input as the same output as another it is not a function
11.4) Systematic sample
A rule is used to select members of a population
11.4) Biased sample
A sample which excludes important members of a population and may change the data
6.6) Scale
A scale is the relationship between the actual lengths of an object to the lengths of a similar object
10.2) Quadrilateral
A shape with 4 sides
5.1) Conjecture
A statement thought to be true that is not yet shown to be true
12.5) Reflection
A transformation in which a figure is reflected across a certain line
12.6) Rotation
A transformation in which a figure is rotated around a fixed point
12.6) Dilation
A transformation in which a figure stretches or shrinks around a point
12.4) Translation
A transformation where each point of a figure moves the same distance and the same direction
9.3) Equiangular Triangle
A triangle with 3 congruent angles (all the angles are the same) In this case the angle measurements must be 60 degrees because there are 3 angles in a triangle and they must add up to 180 degrees 60+60+60 = 180
9.3) Right triangle
A triangle with a right angle inside Right angle = 90 degrees
9.3) Acute triangle
A triangle with all acute angles Acute angles = angles < 90 degrees
9.3) Obtuse triangle
A triangle with an obtuse angle Obtuse angle = angle > 90 degrees
6.1) Unit Rates
A unit rate is a rate that has a denominator of 1, often expressed using the word "per" which means "for every"
4.1) Prime number
A whole number that is greater than 1 and the only way to multiply two whole numbers to get it is 1 • itself 7 is a prime number because you cant multiply to get 7 other than 7•1 First few prime numbers are 2,3,5,7,11,13
*10.6 Test* Find the surface area of the cone if the slant height is 41 and the radius is 9
About 1414
*10.7 Test* Find the volume of the cylinder if the diameter is 20 and the height is 24
About 7539.8
3.1) -2 = t/3 - 11
Add 11 to both sides to get 9 = t/3 then multiply 3 to both sides to get 27 = t
2.1) Commutative Property of Addition
Add numbers in any order 2 + 3 is the same as 3 + 2 a + b = b + a
2.4) Find x The perimeter of a figure is 35 with the sides measured at 9, 8, 5, 9, x
Add up all the sides 9+8+5+9+x = 31+x You know that it should add up to 35 31+x = 35 Get x by itself by subtracting 31 on both sides since it is being added to x then you are left with x = 4
2.5) Addition Property of Equality
Adding the same number to each side of an equation produces and equation with the same value 50 = 50 If I were to add 10 to both sides I get 60 = 60 which is still true
2.1) Perimeter
Adding up the length of all the sides
7.7) Balance after simple interest
After doing the equation I = PxRxT add P to it to find the balance after the interest
10.1) Equilateral Triangles
All sides are equal
10.2) Regular Polygon
All sides have the same length
10.2) Quadrilateral Tips
All the angles in a quadrilateral add up to 360 degrees
10.1) Find all the angles of the triangle if one side = 60 and the other two sides each equal 2x
All the angles should add up to 180 so 60 + 2x + 2x = 180 60 + 4x = 180 4x = 120 x = 30 The angles are each 2x and x = 30 so 2•30 = 60 All the sides are equal to 60
2.1) Find the perimeter of a square if a side is 5
All the sides on a square are equal and there are 4 sides - > 5+5+5+5 = 20
7.5) Percent of Change
Amount increased or decreased divided by the original amount
11.6) Permutation
An arrangement of objects in which order is important
8.7) Function notation
An equation using a variable (often f) like f(x) in place of y to denote that the equation is a function f(x) = 2x+3 is in function notation y = 2x+3 is not in function notation
8.2) Linear equation
An equation when graphed is a straight line
8.2) Equation in two variables
An equation with two variables such as 3x + y = 10 A solution to an equation in two variables is an ordered pair (x,y)
9.1) Radical Expression
An expression that involves a √ sign, evaluate whatever is inside the radical before you take the square root √(3+6) since the 3+6 is inside the √ you first do 3+6 and get 9 then you have √9 and now you can solve it to get 3 √ is also called the radical
8.9) Solution to a linear inequality
An ordered pair (like (5,3)) is the solution to a linear inequality
8.8) Solution of a linear system
An ordered pair that is a solution to the equations in a system of linear equations
11.2) Outlier
An outlier is a data value whose distance from the upper of lower quartile range is more than 1.5 times the interquartile range
12.1) Interior Angles
Angles inside a shape
12.1) Exterior Angles
Angles outside a shape
2.1) Identity Property of Addition
Any number + 0 is equal to the same number -6 + 0 = -6 a + 0 = a
2.1) Identity Property of Multiplication
Any number • 1 is equal to the same number 4 • 1 = 4 a • 1 = a
1.4) Integers
Any positive or negative number (not including decimals)
11.5) Subjects
Are people or objects being measured in a study
1.2) Find the area of a square with a side of 3 inches
Area of a square is s^2 with s representing a side. Replace the length of the side into s and you get 3^2 = 9. Add inches squared to the end of your answer for your units (it is squared (2) since you multiplied 2 times) -> 9 in^2
10.8) Find the volume of the square pyramid with a base of 14 and a height of 10
Area of the base is 14•14 because its a square and that equals 196 1/3 • 196 • 10 = 653.3333
10.1) Isosceles Triangle
At least 2 congruent sides
11.3) Mean Absolute Deviation
Average of how much data values differs from the mean
1.6) Mean
Average of numbers Add up all the numbers and divide by the total number of numbers to find the average
10.6) Regular Pyramid
Base is a regular polygon All of the lateral faces of the pyramid are congruent isosceles triangles
4.1)Factor 15n^3
Break 15 down into 5 and 3 then break down n^3 into n•n•n to get 5•3•n•n•n
9.2) √(24s^2)
Break it up like the last problem You can break it up like (√4)(√6)(√s^2) √4 = 2 √(s^2) = s √6 = √6 2s√6
10.4) Find the circumference of a circle if the diameter is 20
C = πd 20π is about 62.8
10.4) Circumference of a circle
C = πd C = circumference d = diameter Diameter is the length straight through a circle Or you could use the formula C = 2πr R = radius, its half the diameter so 2πr is like saying 2 • r which is just d and then its back to πd Circumference can also be called the perimeter because it is the length around the circle
7.4) What is 120% of 50
Change 120% to a decimal (1.2) and then multiply it to 50 to get 60
7.4) What is 30% of 200
Change 30% into a decimal -> .30, and multiply it to 200 and that equals 60
7.4) What number is 60% of 10
Change 60% into a decimal (.6) and then multiply it by 10 to get 6
5.5) 2/9 / 3/7
Change division to multiplication and flip the 2nd fraction 2/9 • 7/3 now treat it like a multiplication problem and multiply straight across 14/27
2.1) Associative Property of Multiplication
Changing the grouping of numbers does not change the product (3•2) • 4 is the same as (3•4) • 2 (a•b) • c = (a•c) • b
2.1) Associative Property of Addition
Changing the grouping of numbers does not change the sum (3+4) +7 is the same as (3+7) + 4 (a+b) + c = (a+c) + b
10.2) Polygon
Closed figure and the sides don't intersect each other
8.1) Relation
Comparing the domain and ranges of a data set
9.8) Find the cos of the angle 60 degrees if the hypotenuse is 10, the opposite side is 6, and the adjacent side is 4
Cos 60 = 4/10 Cos 60 = 2/5
9.8) Cosine Ratio
Cosine or cos = side adjacent to the angle / hypotenuse
12.4) Tessellation
Covering a graph with a repeated pattern of one or more shapes
11.1) Stem-and-leaf plot
Data display that organizes data based on their digits. Each data value is separated into a *stem* (leading digits) and a *leaf* (the last digit)
11.3) Categorical Data
Data that consists of names, labels, or any other nonnumerical (non number) value such as types of animals
11.3) Numerical Data
Data that consists of numbers such as weights of animals
8.4) Find the slope between the points (1,2) and (4,5)
Difference of y coordinates = 5 - 2 = 3 Difference of x coordinates = 4 - 1 = 3 3/3 = 1 The slope is 1
10.3) Height of a parallelogram
Distance between the top and bottom of the parallelogram
10.3) Height of a trapezoid
Distance between the top and bottom of the trapezoid (the top being the top parallel line and the bottom being the bottom parallel line)
3.6) 13(2a+1)
Distribute 13 to both 2a and 1 to get 26a + 13
3.3) A statement can have no solution like 5(2x+1) = 10x
Distribute 5 to both the 2x and 1 and get 10x + 5 = 10x move the 10x by themselves by subtraction but they end up canceling each other out like 5 = 0 so there is no solution since 5 does not equal 0 and the variables went away
3.2) 2m+0.5(m-4) = 9
Distribute the 0.5 to both the m and -4 to get 2m + (0.5m - 2) = 9 then combine like terms to get 2.5m - 2 = 9 then add 2 to both sides to get 2.5m = 11 then divide by 2.5 on both sides to get m = 4.4
3.3) A statement can have any number that works as the solution 6x+2 = 2(3x+1)
Distribute the 2 to both the 3x and 1 and get 6x+2 = 6x+2 since the equation is the exact same on both sides then any number will work as the solution
*5.1 Test* Write the fraction as a decimal -39/1000
Divide -39 by 1000 -0.039
3.2) -5(2w+1) = 25
Divide both sides by -5 and you get (2w+1) = -5 then subtract 1 to both sides to get 2w = -6 then divide by 2 and get w = - 3
2.4) Solve 12p = 60
Divide by 12 on both sides because 12 is being multiplied to p then you get p = 5
2.6) Division Property of Equality
Dividing each side of an equation by the same nonzero number produces an equation with the same value 30 = 30 If I were to divide 3 to both sides I get 10 = 10 which is still true
3.5) Division Property of Inequality
Dividing each side of an inequality by a negative number reverses the inequality sign 4 > 2 then divide -1 to both sides and get -4 < -2
7.1) 5/8 write the fraction as a decimal
Do long division 5 divided by 8 http://prntscr.com/onk7dj
2.6) -3 = z/(6+11)
Do parenthesis first (6+11) = 17 Now you have -3 = z/(17) Multiply 17 on both sides since z is being divided by 17 then you get -51 = z
1.3) Evaluate the expression (18+12)/(7-2)
Do the parenthesis first (30)/(5), now divide to get 6
8.1) Identify the domain and range of this relation (0,1), (2,3), (5,8), (6,10)
Domain: 0, 2, 5, 6 Range: 1, 3, 8, 10
*8.9 Test* Graph y > x - 3
Dotted line because it is just a > sign and not a > or equal to sign and shaded above the line because the sign is >
8.1) Input
Each number in the domain
8.1) Output
Each number in the range
11.4) Population
Entire group you want information about when collecting data
11.8) Disjoint events/Mutually exclusive events
Events that have no outcomes in common
11.8) Overlapping events
Events that have one or more outcomes in common
11.4) Random sample
Every member of a population has an equal chance of being selected
6.7) What is the probability of choosing an e from the word experimental if you picked a letter at random
Experimental has 3 e's with 12 letters total So the probability is 3/12 which can be reduced to 1/4
12.3) Exterior angles tip
Exterior angles add up to 180 degrees If an interior angle is 87 degrees then the exterior angle to that interior angle is 93 because 87 + 93 = 180
10.5) Lateral faces
Faces that are not bases of a figure (bases are the top and bottom of the figure)
4.4) 2/4 + 2/3
Find the LCM of the denominators (3 and 4) which is 12. To get a denominator of 12 for 2/4 multiply both the top and bottom of the fraction by 3 to get 6/12 To get a denominator of 12 for 2/3 multiply both the top and the bottom of the fraction by 4 to get 8/12 Then just add straight across 8/12 + 6/12 = 14/12 which simplifies to 1 2/12 -> 1 1/6
7.5) Find the percent of decrease from 512 to 320
First do 512 - 320 and get 192, that is the amount decreased. Now you divide it by the original amount (512) 192/512 = 3/8% So there was a 3/8% decrease
1.3) Evaluate the expression 28 - 49 / 7
First do division first 49/7 = 7 Now you have 28 - 7 which is 21
11.9) Probability of independent events
For two independent events the probability that both events occur is the product of the probabilities of the event Looks like P(A and B) = P(A)•P(B)
12.6) Angle of rotation
Formed by rays drawn from the center of rotation through corresponding points on an original figure and its image
4.2) Greatest common factor
GCF for short, the biggest factor between two numbers
3.6) 45 + 4v < 9v
Get the v by itself so subtract 4v from both sides and get 45 < 5v then divide by 5 on both sides and get 9 < v
3.3) 4x = 2x + 6
Get the x terms by themselves so move the 2x over to the 4x by subtraction and now you have 4x - 2x = 2x - 2x + 6 which simplifies to 2x = 6 then divide by 2 on both sides to get x = 3
*12.4 Test* Describe what happens to (x,y) if it changes to (x+5, y-4)
Goes to the right 5 and down 4
8.5) Graph the equation y = -2/3x + 4
Graph: http://prntscr.com/op79w3
11.2) Upper Extreme
Greatest data value in a set
11.1) Frequency Table
Groups sets of data to how frequencies
10.6) Slant height of a pyramid
Height of any of the triangular faces of a pyramid The height that is slanted up
*11.3 Test* What type of data display is this? http://prntscr.com/oqnkrl
Histogram
8.4) Slope
How steep a line is The ratio of the line's vertical change (called rise) to it's horizontal change (called run) rise/run
7.7) Simple Interest
I = PxRxT I = Interest added P = principal (starting amount) R = interest rate (as a decimal) T = time in years
1.8) Name the quadrants and where they are
II : I III : IV (X axis is horizontal (left and right) line while y line is vertical (up and down))
11.9) Probability of Dependent Events
If A and B Are dependent events then P(A and B) = P(A)•P(B given A)
11.8) Probability of disjoint events
If A and B are disjoint events then P(A or B) = P(A) + P(B)
11.8) Probability of overlapping events
If A and B are overlapping events then P(A or B) = P(A) + P(B) - P(A and B)
12.6) Rotational Symmetry
If a rotation of 180 degrees or less around its center produces an image that is exactly the same it has rotational symmetry
9.2) Quotient property of square roots
If a square root is over an entire fraction like √(11/4) then you can write the fraction as √11/√4 which is √11/2
7.1) Use equivalent rations to solve the proportion a/3 = 14/21
If a/3 is equal to 21 then whatever you do to 21 to get to 3 you would do to 14 to find a. You can divide 21 by 7 to get it to 3, so you would divide 14 by 7 to find a and that is 2
4.6) Negative exponents
If an exponent is negative then it carries the number on the opposite side of the fraction and then the exponent becomes positive 3^(-4) = 1/(3^4) Also works if there is a negative exponent under the fraction and it goes to the top and becomes positive
8.9) Tips on graphing linear inequalities
If it is < or > then make the graph a dotted line, if it is <= (≤) or >= (≥) then make it a solid line. If it is > or ≥ then shade the area above the line in If it is < or ≤ then shade the area below the line in
6.8) Multiplication Principle
If one event can occur in m ways and a second event can occur in n ways then the number of ways they occur together is m•n If this doesn't make sense it'll make more sense in the next problems)
11.9) Dependent events
If the occurrence of one event does affect the probability of the occurrence of the other event
11.9) Independent events
If the occurrence of one event does not affect the probability of the occurrence of the other event
10.2) Concave Polygon
If the polygon goes inwards like a cave its concave Example: http://prntscr.com/opnu4d
8.1) Vertical Line Test
If the relation is graphed out you can test if it is a function by seeing when you put a vertical line on the graph if it touches more than one point. If it touches more than one point then it is not a function
6.1) Write the equivalent rate 5cm/1min = x cm/ 1 h
If there are 5cm per every min (5cm/1 min) and there are 60 minutes in 1 hour then there must be 60•5cm in 1 hour 60•5 = 300
6.8) Addition Principle
If two events have no outcomes in common and if one of the events can happen in m ways and the other in n ways then either of the events can occur in m+n ways You use addition if the questions asks the "probability of something or the probability of something else happening"
8.5) Slopes of two parallel lines
If two lines are parallel to each other they have the same slope
8.5) Slopes of two perpendicular lines
If two lines are perpendicular to each other the slopes are negative reciprocals to each other Ex. The negative reciprocal of 4/5 is -5/4
4.5) Quotient of Powers Property
If you want to divide numbers with exponents with the same base then subtract their exponents (6^8)/(6^5) = 6^3 This only works because 6 is the same on both this will not work if you try and divide (6^8)/(4^5)
4.5) Product of Powers Property
If you want to multiply numbers with exponents with the same base then add their exponents 4^3 • 4^5 = 4^8 This only works because the 4 is the same on both this will not work if you try and multiply 4^3 • 3^5
4.7) Dividing numbers with scientific notation
If you were to divide numbers with scientific notation like (4.8 • 10^(-7))/(6•10^6) you would group them like 4.8/6 and 10^(-7)/10^6 4.8/6 = 0.8 10^(-7) / 10^6 = 10^(-13) (remember the rule of dividing with exponents if they have the same base) Now you have 0.8 • 10^(-13) but notice how you have no number in front of the decimal (0 doesn't count) you should have another number there for scientific notation so you have to move the decimal so 0.8 becomes 8 then subtract an exponent (subtract because you moved a decimal to the right) to 10^(-13) to get 8 • 10^(-14)
4.7) Multiplying numbers with scientific notation
If you were to multiply numbers with scientific notation like (3.5 • 10^10) • (5.4 • 10^8) you would group them like (3.5 • 5.4) and (10^10 • 10^8) 3.5 • 5.4 = 18.9 10^10 • 10^8 = 10^18 (remember the rule of multiplying with exponents if they have the same base) Now you have 18.9 • 10^18 but notice how you have two numbers in front of the decimal (1 and 8) you should have only one for scientific notation so you have to move the decimal like 1.89 then add an exponent (add because you moved the decimal to the left) to 10^18 to get 1.89 • 10^19
*12.7 Test* Describe what happens to a shape with coordinates (x,y) when it changes to (2x, 2y)
It grows twice the size because all the x values are multiplied by 2 and all the y values are multiplied by 2
7.2) What percent is 4 of 7
It wants you to convert 4/7 to a percentage, for this you can multiply 4/7 by 100 and get 400/7. You can reduce that to 57 1/7, so your answer is 4 is 57 1/7% of 7
4.4) Least Common Multiple
LCM for short, the least common multiple if two numbers is the lowest number that both of the numbers can go into 8 can go into 8, 16, 24, 32, 40, 48 12 can go into 12, 24, 36, 48 The lowest number they both go into is 24 so the LCM of 8 and 12 is 24
4.4) Least Common Denominator
LCM of the denominators in a fraction
11.2) Lower extreme
Least data value in a set
10.3) Base of a parallelogram
Length of any one of its sides
10.3) Base of a trapezoid
Length of one of the parallel sides
8.9) Linear Inequality
Like an equation but with greater than or less than symbols in place of the equal sign y > 4x
9.5) Find the midpoint between the points (3,8) and (-9,-4)
M = ( (x1+x2)/2 , (y1+y2)/2 ) x1 = 3 x2 = -9 y1 = 8 y2 = -4 3+(-9) = -6/2 = -3 8 + (-4) = 4/2 = 2 (-3,2)
8.2) Graph y = 2x - 1
Make a table of coordinates by plugging in numbers Try the numbers -2, -1, 0, 1, 2 y = 2(-2) - 1 -> y = -4 - 1 -> y = -5 (when x = -2, y = -5) y = 2(-1) - 1 -> y = -2 - 1 -> y = -3 (when x = -1, y = -3) y = 2(0) - 1 -> y = 0 - 1 -> y = -1 (when x = 0, y = -1) y = 2(1) - 1 -> y = 2 - 1 -> y = 1 (when x = 1, y = 1) y = 2(2) - 1 -> y = 4 - 1 -> y = 3 (when x = 2, y = 3) Now you have the ordered pairs (-2, 5) (-1, -3) (0, -1) (1,1) (2,3) You can graph those where the first number is the x and the second number is the y Picture of the graph: http://prntscr.com/op6w2p
Find the Mean, Median, Mode, and Range of -11, -9, -6, 0, 2, 18, 20, 36, 37, 46, 47, 51
Mean: Add up all the numbers then divide by total number of numbers. The sum is 231, then divide by 12 and get 19.25 as the mean Median: All the numbers are already ordered form least to greatest but there are two number sin the middle (18 and 20). Add them up and divide by 2 (18+20)/2 = 38/2 = 19 Mode: There is no value in the data set that occurs more than once so the data set has no mode Range: The highest number is 51 and the lowest is -11. The difference of 51 and -11 -> 51 - -11 = 51 +11 = 62
6.4) Congruent
Means equal, same shape and size when talking about figures
11.8) P(A)
Means probability of event A happening P(A or B) means probability of either A or B happening
11.4) Self-selected sample
Members of the population can select themselves by volunteering
Mode
Most often occurring number, there is no mode if a no number appears more than once, one mode if only one number repeats more than all others or multiple modes if there are multiple numbers that are repeated the same amount of times
7.1) Write 0.004643 as a percentage
Move the decimal two places right and get .4643%
7.1) Write 5.6 as a percentage
Move the decimal two places right and get 560%
7.1) Write 0.85 as a percentage
Move the decimal two places right and get 85%
7.1) Write 86 as a percentage
Move the decimal two places right and get 8600%
3.5) d/(-11) < 6
Multiply -11 to both sides since d is being divided by -11 and reverse the sign because it is being multiplied by a negative d > -66
7.6) If a shirt costs $12 what would the new price be if a 40% markup is added
Multiply 140% to $12 because 140% is 40% more than the original 100% price. Change 140% to a decimal and get 1.4 Multiply 1.4 to $12 and get $16.8
3.5) b/7 > 7
Multiply 7 to both sides since b is being divided by 7 b > 49
2.4) Solve x/30 = 3
Multiply by 30 on both sides since 30 is being divided into x then you get x = 90
6.3) Another way to solve complex proportions Solve 48/28 = x/63
Multiply like an x 48 gets multiplied to 63 28 gets multiplied to x 48•63 = 3024 28•x = 28x Now you get 3024=28x Divide 28 on both sides and get 108 = x
6.3) 90/y = 27/12
Multiply like an x 90 gets multiplied to 12 y gets multiplied to 27 90•12 = 1080 y • 27 = 27y Now you get 1080 = 27y Divide 27 on both sides and get y = 40
2.1) Commutative Property of Multiplication
Multiply numbers in any order 3•4 is the same as 4•3 a•b = b•a
5.4) 3/5 * 4/7
Multiply straight across 3•4 and 5•7 to get 12/35
2.6) Multiplication Property of Equality
Multiplying each side of an equation by the same nonzero number produces and equivalent equation 20 = 20 If I were to multiply 5 to both sides I get 100 = 100 which is still true
3.5) Multiplication Property of Inequality
Multiplying each side of an inequality by a negative number reverses the inequality sign 3 < 4 then multiply -1 one to both sides go to -3 > -4
1.6) Subtract 5 - (-2)
Negative negative becomes positive 5 + 2 = 7
10.1) Scalene Triangle
No congruent sides
Congrats
Now go watch Khan Academy videos
6.7) Odds in favor
Number of favorable outcomes divided by number of unfavorable outcomes
6.7) Odds against
Number of unfavorable outcomes divided by number of favorable outcomes
*1.4 Test* Order -2, 3, 0, 2, -3 on a number line and order from least to greatest
On a number line the numbers to the left of the 0 are negative and the numbers to the right of the 0 are positive Least to greatest: -3, -2, 0, 2, 3
12.4) Describing transformations
On a point (x,y) a change in the x is moving left or right and a change in the y is moving up or down (x+2, y) means moving to the right 2 and keeping the y the same (x-2, y) means moving to the left 2 and keeping the y the same (x,y+3) means moving up 3 and keeping the x the same (x,y-3) means moving down 3 and keeping the x the same (x-3, y+4) means moving left 3 and going up 4
11.1.) Histogram
One bar for each interval
4.3) Write an equivalent fraction to 8/12
One equivalent to fraction to 8/12 is 2/3
11.4) Convenience sample
Only members of the population who are easily accessible are selected
*11.8 Test* What is the probability you will role a multiple of 3 (event A) or an even number (event B)
P(A) = 2/6 P(B) 3/6 2/6 • 3/6 = 6/36 -> 1/6 P(A and B) = 1/6 Probability of overlapping events P(A or B) = P(A) + P(B) - P(A and B) = 2/6 + 3/6 - 1/6 = 4/6 -> 2/3
1.3) Order of Operations
PEMDAS Parenthesis Exponents Multiplication or Division Addition or Subtraction (Solve left to right, if subtraction comes before addition in solving left to right then do it first since addition and subtraction carry the same importance. If division comes before multiplication in solving left to right then do it first for the same reason)
11.4) Sample
Part of the population
*12.3 Test* Find the measure of the interior angles of a pentagon
Pentagon = 5 sides (5-2) • 180 then divide by 5 = 108
2.3) Find the perimeter of a triangle with the sides measured at 2x+1, x, x+5
Perimeter is adding all the sides 2x+1 + x = 3x+1 3x+1 + x+5 = 4x+6
9.5) Distance formula
Picture of the distance formula: http://prntscr.com/opmx79 The distance formula is used to find the distance between two points on a graph d = √((x2-x1)^2 + (y2-y1)^2) d = distance x2 = 2nd x coordinate value x1 = 1st x coordinate value y2 = second y coordinate value y1 = 1st y coordinate value Distance can not be negative
9.5) Midpoint Formula
Picture of the midpoint formula: http://prntscr.com/opna9b M = ( (x1+x2)/2 , (y1+y2)/2 ) M = midpoint x1, = first x coordinate x2 = second x coordinate y1 = first y coordinate y2 = second y coordinate The answer comes as an ordered pair like (3,4)
*8.2 Test* Is (2,8) a solution of -3x + y =6
Plug 2 in for x and 8 in for y You end up with 2 = 6 which is not true so this isn't a solution
8.2) Tell whether the order pair (1, -3) is a solution to 2x-y = 5
Plug in the ordered pair (1, -3) into 2x-y = 5 2(1) - (-3) = 5 2 - (-3) = 5 2 + 3 = 5 5 = 5 Since 5 = 5 then the ordered pair is a solution to this equation
10.2) Convex Polygon
Polygons that are not concave
6.7) Probability of an event
Probability of an event, written as P(event) is the number of favorable outcomes divided by the number of possible outcomes
6.7) Experimental Probability
Probability of an event, written as P(event) is the number of successes/number of trials
11.4) Biased questions
Questions that encourage someone to respond in a particular way, these should be avoided to get accurate data
12.6) Scale factor
Ratio of a side length of the image to the side length of the original figure
5.1) Rational Numbers vs Irrational Numbers
Rational numbers: 7/8, 1/3, 0.97, 0.21212121212121..., square root of 9 Irrational numbers: pi, square root of 8, 0.3030030003...., square root of 2/5
9.4) Real numbers
Real numbers consists of all real numbers and all imaginary numbers
5.1) Deductive reasoning
Reasoning based on rules, definitions, or properties (an example of a conjecture)
*12.6 Test* Describe what happens to (x,y) when it changes to (x,-y)
Reflects across x axis
*12.5 Test* Describe what happens to (x,y) when it changes to (-x,y)
Reflects across y axis
10.5) Surface Area of a Cylinder
S = 2B + Ch B = base area C = base circumference h = height or S = 2πr^2 + 2πrh r = radius of base h = height
10.5) Surface Area of a Prism
S = 2B + Ph S = surface area B = base area P = perimeter of base h = height
10.5) Find the surface area of a prism if the base has lengths of 5 and 6 and the height is 7
S = 2B + Ph To find B (base area) we multiply 5 and 6 and get 30, that is the area of the base The formula is 2B so 30 • 2 = 60 Now we have S = 60 + Ph The perimeter of the base is all the side lengths of the base added up (5 + 5 + 6 + 6, 4 sides because its a prism and the opposite sides are equal) and get 22 • h which is 22 • 7 which is 154 S = 60 + 154 S = 214
10.5) Find the surface area of a cylinder with a diameter of 2.5 and a height of 5
S = 2πr^2 + 2πrh Radius = diameter/2 Radius = 2.5/2 Radius = 1.25 2π(1.25)^2 + 2π(1.25)(5) 2π(1.5625) + 2π(6.25) 3.125π + 12.5π 15.625π About equal to 49.1
10.6) Surface Area of a regular pyramid
S = B + 1/2Pl B = base area P = base perimeter l = slant height
10.6) Surface area of a cone
S = B + πrl r = radius of base l = slant height or S = πr^2 + πrl
10.6) Find the surface area of a cone if the radius is 8 and the slant height is 15
S = πr^2 + πrl πr^2 = π8^2 = 64π πrl = π(8)(15) = 120π S = 64π + 120π = 184π S = 184π is about 578
11.7) Combination
Selection of objects where the order chosen is not important
*11.4 Test* A website operator posts a link to a survey and people can ignore it or participate, what type of sampling method is used
Self-selected
2.1) Convert oz to grams if 1 oz = 28.35g 25oz to grams
Set up a multiplication problem, put the number you have (25) over 1 like 25/1 Then multiply by the conversion rate, you are told 28.35g are in 1 oz so the other fraction will be using 28.35 and 1. Put what you want on top of the fraction (you want grams so put 28.35 since that is what you are given) and put what you already have on the bottom (you already have oz so put the 1 for oz on the bottom of the fraction) like 28.35/1 Then you get 25/1 • 28.35/1 Then it multiplies to 708.75
2.1) Convert inches to feet if 12 inches are in a foot 26 inches to feet
Set up a multiplication problem, put the number you have (26) over 1 like 26/1 Then multiply by the conversion rate, you are told 12 inches are in 1 foot so the other fraction will be using 12 and 1. Put what you want on top of the fraction (you want feet so put 1 since that is what you are given) and put what you already have on the bottom (you already have inches so put the 12 for inches on the bottom of the fraction) like 1/12 Then you get 26/1 • 1/12 Then it multiplies to 26/12 = 2.166667
9.1) Square root
Shown by the symbol √ It's asking what number multiplied to itself equals the number under the √ symbol √9 = 3 because 3•3 = 9
11.5) Two-way table
Shows the observed frequencies for two categories of data collected from the same subjects
6.4) Corresponding parts
Sides or angles that have the same relative position The corresponding part of the left side of a triangle would be the left side of another triangle
9.8) Find the sin of the angle 20 degrees if the hypotenuse is 5 and the opposite side is 4 and the adjacent side is 3
Sin 20 = 4/5
9.1) Approximate the square root of 10 to the nearest whole number
Since 10 is not a perfect square we cant get an exact number without a calculator, we can approximate that it is between 3 and 4 because 3•3 = 9 4•4 = 16 It's closer to 9 than it is to 16 so the approximate square root rounded to the nearest whole number is 3 for the square root of 10
5.6) Solve (2/9)x = 12
Since 2/9 is being multiplied to x then you divide by 2/9 on both sides to get x = 12 / (2/9) then you do division 12 • 9/2 -> 108/2 -> 54 x = 54
1.1) Write a variable expression The product of 4 and a number
Since a number is not specific it can be represented by a variable (x) and since product means the answer to a multiplication problem we can write the product of 4 and any number as 4x (Take note that the variable x comes after 4 like it did in the question)
1.1) Write a variable expression The quotient of a number and 3
Since a number is not specific it can be represented by a variable (x) and since quotient means the answer to a division problem we can write this as x/3 (Take note that the variable x comes before 3 like it did in the question)
1.1) Write a variable expression The difference of a number and 1
Since a number is not specific it can be represented by a variable (x) and since the difference means an answer to a subtraction problem we can write it as x-1 (Take note that the variable x comes before 1 like it did in the question)
1.1) Write a variable expression The sum of 5 and a number
Since a number is not specific it can be represented by a variable (x) and since the sum means an answer to an addition problem we can write it as 5+x (Take note that the variable x comes after 5 like it did in the question)
9.8) Sine Ratio
Sine or sin = side opposite of the angle / hypotenuse
*8.5 Test* Identify the slope and y intercept of the line 24x + 4y = 80
Slope = -6 y intercept = 20
7.4) If k = 20, what is (k-15)% of 100
Solve k - 15 which is 5, now you have to find 5% of 100. Change 5% into a decimal (0.05) and then multiply it to 100 and get 5.
1.7) Simplify 10 / 2 * 5
Solve left to right keeping PEMDAS in mind 10/2 is 5 and 5*5 = 25 (Don't do 2*5 first because you solve left to right and multiplication and division have the same importance)
1.3) Solve 50•2000+7•64100+6•106700+198900
Split it up into order of operations 50•2000+7•64100+6•106700+198900 (50•2000) + (7•64100) + (6•106700) + 198900 (100000) + (448700) + (640200) + 198900 1387800
8.3) Find the y intercept of 3x - 2y = 6
Substitute 0 in for x and solve for y 3(0) - 2y = 6 -2y = 6 y = -3
8.3) Find the x intercept of 3x - 2y = 6
Substitute 0 in for y and solve for x 3x - 2(0) = 6 3x = 6 x = 2
1.4) Evaluate when x = -4 5 - x
Substitute the -4 in for x 5 - (-4), a negative negative becomes a positive 5 + 4 = 9
1.4) Evaluate when y = -5 17 - |y|
Substitute the -5 in for y 17 - |-5| -> 17- 5 -> 12
1.3) Evaluate the expression when x = 4 and y = 2 x^2 + y
Substitute the numbers in for the variables x and y 4^2+2 -> 16+2 = 18
3.1) 4x + 1 = 5
Subtract 1 on both sides to get 4x = 4 then divide 4 on both sides to get x = 1
2.7) x + 3.8 = 5.2
Subtract 3.8 on both sides since 3,8 is being added to x then you get x = 1.4
5.7) (1/2)x + 7/10 = 4/5
Subtract 7/10 to both sides 4/5 - 7/10 the LCD is 10, to get 4/5 to 10 you multiply the top and bottom by 2 8/10 - 7/10 = 1/10 Now you have (1/2)x = 1/10 now divide by 1/2 on both sides 1/10 divided by 1/2 is 1/10 • 2/1 = 2/10 -> 1/5 x = 1/5
3.1) 3n + 8 = 2
Subtract 8 on both sides to get 3n = -6 then divide 3 on both sides to get n = -2
3.3) Rewrite the equation in terms of x (get x by itself) a + bx = c
Subtract a to both sides to get bx = c - a then divide by b on both sides and get x = (c-a)/b
5.3) 4 3/8 - (-1 2/3)
Subtracting a negative number is adding a positive so it becomes 4 3/8 + 1 2/3 4 3/8 -> 35/8 1 2/3 -> 5/3 You cant add them yet because you need common denominators, the LCD of them both is 24 To get 35/8 to 24 multiply the top and bottom by 3 and get 105/24 To get 5/3 to 24 multiply the top and bottom by 8 and get 40/24 Then you can add straight across and get 145/24 You can reduce to 6 1/24
2.5) Subtraction Property of Equality
Subtracting the same number from each side of an equation produces an equation with the same value 34 =34 If I were to subtract 4 from each side I get 30 = 30 which is still true
10.5) Lateral area
Sum of the areas of the lateral faces (the surface area not including the base areas)
11.4) Census
Survey of an entire population
9.1) Solve the equation a^2 = 9
Take the square root of both sides √(a^2) = √9 √(a^2) is just a (because a*a = a^2) Now you have a = √9 And the √9 is 3 So a = 3 (But really a = ±3 because it could be a positive or negative 3)
9.7) Tangent Ratio
Tangent or tan or an angle = side opposite of the angle / side adjacent (next to) the angle The side adjacent to the angle is not the hypotenuse its a the leg of the triangle
*2.3* Test Identify terms, like terms, coefficients, and constants of the expression 7n-5-3n+2
Terms: 7n,-5, 3n, 2 Like Terms: 7n and -3n, -5 and 2 Coefficients: 7, -3 Constants: -5, 2
8.8) Tell whether or not (4,2) is a solution to both equations y = -5x + 22 y = 8x - 30
Test the coordinate (4,2) in both equations The 4 is the x and the 2 is the y 2 = -5(4) + 22 2 = -20 + 22 2 = 2 It works for the first equation so now we try the second 2 = 8(4) - 30 2 = 32 - 30 2 = 2 Since it works for both equations then the ordered pair (4,2) is a solution to this system of linear equations
4.6) Simplify 1/2^(-3)
The -3 exponent carries the 2 up and it becomes 2^3 then 2^3 is 2•2•2 = 8
9.3) Pythagorean Theorem Tip
The Pythagorean theorem only works for right triangles, if your work doesn't make sense after you do the Pythagorean theorem it might not be a right triangle at all To test if a triangle is a right triangle with only the sides plug all the sides into the Pythagorean theorem Try: 3, 5, 7 7 is c because it is the longest side and 3 can be a or b and 5 can be a or b doesn't matter 3^2 + 5^2 = 7^2 9 + 25 = 49 34 ≠ 49 so the triangle is not a right triangle (≠) means not equal to
11.3) Absolute deviation
The absolute deviation of a value in a data set is the absolute value of the difference between the value and the mean of the data set
10.6) Find the surface area of the regular pyramid if the base is a square with a length of 10 and the slant height is 13
The area of a square is s^2 B = 10^2 = 100 The perimeter of a square is all the sides added up and since all the sides of a square are equal then then P = 10 + 10 + 10 + 10 = 40 S = 100 + 1/2(40)(13) S = 100 + 20(13) S = 100 + 260 S = 360
10.8) Find the volume of the cone if the radius is 3.5 and the height is 9
The base area of a cone is the area of the circle base πr^2 -> π(3.5)^2 = 12.25π 12.25π • 9 = 110.25π 1/3 • 110.25π = around 15.45
Range
The difference between the highest and lowest numbers
4.2) Find the GCF of 12 and 30
The factors of 12 are 1,2,3,4,6,12 The factors of 30 are 1,2,3,5,6,10,15,30 The greatest common factor that is in both of these is 6
12.6) Center of rotation
The fixed point a figure is rotated around
12.6) Center of dialation
The fixed point that a figure stretches or shrinks on
11.7) 7C4
The formula is nPr / r! nPr = 7P4 7•6•5•4•3•2•1/3•2•1 -> 7•6•5•4 = 840 840/r! -> 840/4! = 840/(4•3•2•1) = 840/24 = 35
12.5) Line of reflection
The line that a figure is reflected over to make a reflection
11.2) Lower quartile
The median (middle when lined up least to greatest) of the lower half of a data set
11.2) Upper quartile
The median (middle when lined up least to greatest) of the upper half of a data set
Median
The middle of the numbers when they are lined up from least to greatest, if there are two middle numbers then you find the average of them (add them up and divide by 2)
6.8) If a student has 3 sweaters and 3 pairs of paints then how many different outfit combinations are possible
The multiplication principle says we can just multiply the numbers to see how many different ways something can happen. 3•3 = 9
12.4) Image
The new figure formed after a transformation has occured
2.3) Coefficient
The number in front of a variable The 5 in 5x
11.1) Frequency
The number of data values in a spot
6.8) Find the probability of getting a sum of 3 or 5 when rolling two dice
The numbers 1,2,3,4,5,6 are on a die You can get a sum of 3 by rolling a 1 and 2 (that's the only way) You can get a sum of 5 by rolling a 2 and a 3, and a 1 and a 4 (those are the only ways). The total number of possible outcomes for two dice is 36 (you do 6*6 because of the multiplication principle) To get a sum of 3 there are two ways (you can get a 1 on dice#1 and a 2 on dice#2 or a 2 on dice#1 and a 1 on dice#2) so there is a 2/36 chance To get a sum of 5 there are 4 different ways (you can get a 2 on dice#1 and a 3 on dice#2 or a 3 on dice#1 and a 2 on dice#2 or a 1 on dice#1 and a 4 on dice#2 or a 4 on dice#1 and a 1 on dice#2) so there is a 4/36 chance for getting a 5 The question asks the probability of getting a sum of 3 or 5 (keyword is or, that means add because of the addition principle) so you add the probabilities of getting a 3 and 5 together 2/36 + 4/36 = 6/36 which can be reduced to 1/6
4.1) Factors
The numbers multiplied together to reach a number 2 and 5 are factors of 10 since you do 2•5 to get to 10
6.7) Favorable outcomes
The outcomes you want in a probability The favorable outcomes for rolling an odd number on a die are 1,3, and 5 (there are 3 favorable outcomes)
8.3) X-intercept
The point where a line crosses the x axis and y = 0 Like (4,0)
8.3) Y-intercept
The point where a line crosses the y axes and x = 0 Like (0,5)
11.4) Stratified sample
The population is divided into distinct groups, members are selected from each group
6.7) Possible outcomes
The possible outcomes of rolling a number on a die are 1,2,3,4,5,6 (6 total)
5.6) Multiplicative Inverse Property
The product of a number and its inverse is equal to 1 (the inverse of 1/3 is 3/1, 4/3 is 3/4 etc) 3/5 • 5/3 = 1
11.5) Margin of error
The range of error, if there is a 5% margin of error on the value 20% then that means that even though the data says 20% it can be 5% above or below that value (15% or 25%)
9.6) Triangle tips
The shortest angle is opposite of the shortest side and the biggest angle is opposite of the largest side and if the angles are the same then the sides are equal
9.3) Hypotenuse
The side opposite of the right angle (90 degree angle) in a triangle. It is also the longest side on a triangle
9.3) Sum of the Measure of the Angles of A triangle
The sum of all the 3 angles in a triangle is equal to 180 degrees
12.1) Supplementary Angles
The sum of the angles add up to 180 degrees
12.1) Complementary Angles
The sum of the angles add up to 90 degrees
10.5) Surface Area
The surface area of a 3D figure is the sum of the area of all the sides of the figure A cube has 6 faces so the surface area would be the area of all the faces added up
11.6) Permutation Formula
The symbol for permutations is nPr n = represents a number on the left side of the P (the bigger number) r = represents a number on the right side of p (the smaller number) The formula to solve permutations is n! /( (n-r)! )
9.3) Legs
The two other sides of a triangle that form the right angle
4.7) Scientific Notation
The way of writing numbers as powers of 10
1.8) Which quadrant would (-5, 3) go in
The x coordinate is first so go left -5 and then go up 3 on the y coordinate which lands you in quadrant II
8.1) Domain
The x values in a data set
8.1) Range
The y values in a data set
6.8) If you want to make a 4 digit password with only numbers how many different ways are there
There are 10 numbers you can use (0,1,2,3,4,5,6,,7,8,9) for each digit There are 4 digits so you do 10•10•10•10 = 10,000 different combinations
4.6) Write 0.0005 as a power of 10
There are 4 zeroes so 10^4 but it is a decimal number so make the exponent negative 10^(-4) and then you have a 5 so the answer is 5 • 10^(-4)
4.7) Write 324, 000, 000 in scientific notation
There are 6 zeroes and 2 numbers before the very first number so 10^8 The number in front is 3.24 (3 is the leading number then put a decimal and add the ret) So the answer is 3.24 • 10^8
4.7) Write 120,000,000 in scientific notation
There are 7 zeroes and 1 number before the number in front so 10^8 Write the 1 and 2 in this number as 1.2 1.2 • 10^8 If there is more than one number in the front like this one (1 and 2) then put the number that's farthest in front (1) then put a decimal and then put the other numbers on (1.2) If the number was like 123,400 then you would use 1.234 as the number
4.6) Write 900,000,000 as a power of 10
There are 8 zeroes in this number and a 9 So the answer is 9 • 10^8
4.6) Write 0.3 as a power of 10
There is 1 zero and a 3 Since there is 1 zero you can do 10^1 but it is a decimal so change the exponent to be negative and get 10^(-1) Now you get 3 * 10^(-1)
7.5) Find the percent change from 28 to 35
There is a difference of 7 from 28 to 35. Now 7 has to be divided by the original amount (28) 7/28 = .25 There was a 25% increase to get 28 to 35
8.5) Identify the slope and y-intercept of y = x - 4
This equation is in slope intercept form, in that form the number in front of the x is the slope, in this case it is just a 1 so (1x is the same as x) the slope is 1 In slope intercept form the number after the mx is the y intercept in this case it is -4
7.6) If a bracelet costs $15 after the markup, what was the original price if the markup is 120%
This is very similar to the previous problems where we find the percent change between two numbers except we don't have the original number but we have the percent change. We see that 120% is a 20% increase from the original 100% price so to find the original price we would just need to do a 20% decrease To do that we would need to multiply $15 by 80% (It is 20% down from 100% which is a 20% decrease) Change 80% to a decimal = .8 Multiply .8 to 15 and get 12
9.4) Approximate √7 to the nearest tenth
To approximate a square root to the nearest 10th we do something similar to approximating a square root to the nearest whole number To start off we actually approximate to the nearest whole number that is less than the value in the radical 2•2 = 4 3•3 = 9 7 is closer to 3•3 but it goes over and we want the nearest tenth so we go to the next closest and that is 2 Now we can test by multiplying the numbers between 2 and 3 It is closer to 3 than it is to 2 so we can start with 2.5 2.5•2.5 = 6.25 2.6•2.6 = 6.76 2.7•2.7 = 7.29 2.6 is the closet to 7 so that is the answer
*4.4 Test* Which fraction is greater 5/36 or 17/90
To compare fractions you want them with the same base, 36 and 90 both go into 180 together so we can make that the common denominator To get 36 to 180 you multiply by 5 so multiply the top and bottom by 5 5•5 = 25 and 36•5 = 180 so the its now 25/180 To get 90 to 180 you multiply by 2 so multiply the top and bottom by 2 17•2 = 34 and 90•2=180 so its now 34/180 34/180 is greater than 25/180 so 17/90 is greater than 5/36
1.1) Write a variable expression to represent the phrase The number of inches in x feet
To find the number of inches in x amount of feet you need to multiply x (feet) by 12 inches because there is 12 inches every foot. So the answer is x*12 This is a variable expression because it works with any number of feet, just replace x with the number of feet and you can find the amount of inches
8.3) Finding intercepts
To find the x intercept of a line, substitute 0 in for y and solve for x To find the y intercept of a line, substitute 0 in for x and solve for y
6.2) Find x x/2 = 20/10
To get 10 to 2 you divide by 5 So to get 20 to whatever x is you would also need to divide by 5 So x must be 20/5 = 4
6.2) Find x 5/6 = x/18
To get 6 to 18 you would have to multiply by 3 So to get 5 to whatever x is you would also need to multiply by 3 So x must be 5•3 = 15
6.2) Find x 2/7 = x/21
To get 7 to 21 you multiply by 3 So to get 2 to whatever x is you would also need to multiply by 3 So x must be 2•3 = 6
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12.2) Alternate exterior angles
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12.2) Corresponding angles
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6.2) Proportion
Two equal ratios are a proportion 2/3 = 8/12
11.8) Complementary events
Two events are complementary if they are disjoint events and one event or the other must occur P(not A) = 1 - P(A) not A would be the complementary event
6.4) Similar Figures
Two figures are similar if they have the same shape but not necessarily the same size The symbol ~ means two figures are similar
8.4) Parallel lines
Two lines that are in the same area and never cross no matter how far they go out The symbol || means a line is parallel to another
8.4) Skew lines
Two lines that don't lie in the same area and do not intersect
8.8) System of linear equations
Two or more linear systems with the same variables y = 2x+ 1 y = -3x + 2 Together these two linear equations make up a system of linear equations If you were to graph these two lines the point where they intersect is the solution to both of them
11.2) Box-and-whisker plot
Type of data display that organizes data values into 4 groups (Watch a video on how to make this type of plot)
11.2) Interquartile range
Upper quartile minus lower quartile
7.7) If a $15,000 bond earns 4% simple interest every year how much interest will it earn after 2 years
Using the formula we have I = PxRxT Before you multiply 4% make sure to convert it to a decimal (0.04) 15,000 x 0.04 x 2 = 1200
7.7) If a $15,000 bond earns 4% simple interest every year what will be the balance after 2 years
Using the formula we have I = PxRxT Before you multiply 4% make sure to convert it to a decimal (0.04) 15,000 x 0.04 x 2 = 1200 Now you find the new balance we add the $1200 of interest to the $15,000 and get $16,200 as the new balance with interest
10.8) Volume of a pyramid or a cone
V = 1/3Bh V = Volume B = Base area h = height
10.7) Find the volume of a prism if the base is a rectangle with a length of 8 and a width of 13, and the height of the prism is 6
V = Bh The base is a rectangle with Length = 8 Width = 13 To find the area of the rectangle we do 8*13 and get 104 Then we do the Base area (104) • height (6) and get 312 as the volume of the prism
10.7) Volume of a Prism
V = Bh V = volume B = base area h = height
10.7) Volume of a Cylinder
V = Bh V = volume B = base area h = height or V = πr^2 • h
1.2) Volume of a cube
V = s^3
10.7) What's the volume of a cylinder if the diameter if 18 and the height is 4
V = πr^2 • h If the diameter is 18 the radius is 9 π9^2 = 81π 81π • 4 = around 1017.9
1.2) Find the volume of a cube with a side of 4 inches
Volume of a cube is s^3 with s representing a side Replace the length of the side into s and you get 4^3 = 64. Add inches cubed to the end of your answer for your units (it is cubed (3) since you multiplied 3 times) -> 64 in^3
9.3) Find the unknown angle of the right triangle of one of the angles is equal to 40 degrees
We know it is a right triangle so one of the angles is 90 degrees, we also know one of the angles is 40 degrees and that all 3 must add up to 180 degrees 90 + 40 = 130 degrees The last angle must be 50 degrees because 130 + 50 = 180
11.2) Find the outliers if there are any 109, 113, 119, 121, 124, 125, 128, 134, 134, 136, 198
We need the upper quartile, lower quartile, and the interquartile range to find any outliers To find the upper and lower quartile we need to find where half of the data set is, there are 11 terms so the halfway point is 6 because it is 5 away from 11 (the top) and 5 away from 1 (the bottom) The upper quartile is the median of the upper half 128, 134, 134, 136, 198 the median is 134 (its in the middle) so the upper quartile is 134 The lower quartile is the median of the lower half of the data set, 109, 113, 119, 121, 124 the median is 119 (its in the middle) so the lower quartile is 119 The interquartile range is the upper quartile range minus the lower quartile range so 134 - 119 = 15 An outlier is any number that is above or below the upper and lower quartile ranges when the interquartile range times 1.5 is added to them. The interquartile range times 1.5 = 15 times 1.5 = 22.5 So the upper quartile range with the added interquartile range times 1.5 = 159.5 The lower quartile range with the subtracted 22.5 = 96.5 So any number above 159.5 is an outlier and any number below 96.5 is an outlier There is only one outlier in this data set and its 198 because it is above the value of 159.5
8.2) Function form
When an equation is in terms of y (y = x + 2) An equation is not in function form if the y is grouped with other terms like 2x + 5y = 7
8.4) Perpendicular lines
When two lines intersect and form a right angle (90 degrees) The symbol ⊥ means a line is perpendicular to another
12.1) Vertical Angles
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6.1) Equivalent Ratios
When two ratios have the same value 3:4 compared to 6:8 6:8 is still like 3:4, both can be reduced to 3:4
12.5) Describing transformations
With the point (x,y) (-x,y) means reflection on the y axis (you multiply the x values by -1 and that makes it reflect across the y axis) (x,-y) means reflection on the x axis (you multiply the y values by -1 and that makes it reflect across the x axis)
4.2) 2/9 + 5/9
You can add the 2 and 5 together because the fractions both have 9 on the bottom so you get 7/9
*4.5 Test* Find the product 5^8 * 5^3
You can add the exponents because they have the same base 5^11
9.2) √20/√15
You can change √20/√15 into √(20/15) and then reduce the fraction to √(4/3) Now you can change it back to √4/√3 and then get 2/√3 but it is still not done because a radical is in the bottom of a fraction. You can fix this by multiplying the top and bottom by √3 (the denominator) We can do this because multiplying the fraction by √3/√3 reduces to 1 and is like multiplying it by 1, when you multiply a fraction by 1 it doesn't change the value, in this case we aren't changing the value we are just moving the radical from outside the denominator while keeping the value the same 2/√3 • √3/√3 = 2•√3 = 2√3 √3•√3 = √9 = 3 2√3/3
7.1) Write 4/5 as a percentage
You can divide 4 by 5 and get .80 which written as a percentage is 80% or you can see that 4/5 doubled is 8/10 (which is like 80/100) so you can write 80%
*2.1 Test* -5(19)(20)
You can multiply in any order (-5)(20) = -100 (-100)(19) = -1900
9.8) Sin, Cos, Tan Tip
You can remember how to find Sin, Cos, and Tan by remembering the acronym SohCahToa It means Sin = opposite/hypotenuse Cos = adjacent/hypotenuse Tan = opposite/adjacent
6.5) A cactus is 5 feet tall and casts a shadow that is 1.5 feet long. How tall is a nearby cactus that casts a shadow that is 8 feet long.
You can set up a proportion 5/1.5 = x/8 You can set it any way you like just make sure if you put the actual height of the cactus (5) on top then the actual height of the other cactus (x because we don't know) is also on top of the other fraction. Multiply like an x 5•8 = 40 x•15 = 15x 40 = 15x Divide by 15 on both sides x = 2.6667
9.2) √180
You can simplify this by breaking it up into two radicals √180 is also like saying (√36)(√5) because 36•5 = 180 (We use 36 because it is the greatest number that is a perfect square while also fitting into 180 evenly) √36 = 6 √5 = √5 6√5
6.1) Writing Ratios
You can write ratios in 3 different ways a to b a:b a/b
11.6) You have 4 posters on the wall, you want to arrange one poster on each wall, how many different ways can you do this
You have 4 options for the first poster spot, 3 options for the second spot, 2 options for the third spot, and 1 option for the last spot So you can solve this like 4•3•2•1 (which is just 4!) = 24
*8.1 Test* Graph (-2, -2)
Your dot should be to the left 2 and down 2 in the III quadrant
*9.8 Test* sin 40 = a/15
a is about = 9.6
2.2) Distributive Property
a(b + c) = a•b + a•c
9.3) Find the unknown length of the triangle if one of the legs = 20 and the hypotenuse = 25
a^2 + b^2 = c^2 We have one leg of the triangle, we can plug it in for a or b it doesn't matter and we have the hypotenuse we plug in for c 20^2 + b^2 = 25^2 400 + b^2 = 625 Subtract 400 on both sides to get b^2 by itself b^2 = 225 Take the square root of both sides √b^2 = b √225 = 15.9687194 ≈ 16 b ≈ 16 (≈) means approximately equal to Note that the side length cant be a negative number even though you could multiply a negative by a negative to reach a positive number because a length can't be negative
9.3) Pythagorean Theorem
a^2 + b^2 = c^2 a and b are the two legs of the triangle c is the hypotenuse of the triangle
12.1) If angle 1 = 63 degrees and angle 2 = 27 degrees are they complementary or supplementary angles
complementary angles because they add up to 90 degrees
8.4) Slope of a line
difference of y coordinates divided by the difference in x coordinates
8.7) If f(x) = -7x - 11 What is the value of f(-4)
f(x) = -7x - 11 f(-4) -7(-4) - 11 -7(-4) = 28 f(-4) = 28 - 11 28 - 11 = 17 f(-4) = 17
8.7) If f(x) = 4 What is the value if x = 3
f(x) = 4 f(3) = 4 For any value of x the answer will always be 4 in this case
8.7) If f(x) = 5x + 3 What is the value if x = 9
f(x) = 5x+3 f(9) = 5(9)+3 f(9) = 45+3 f(9) = 48
6.3) Basic Geometry Concepts
http://prntscr.com/onj8br Picture of book explaining geometry terms
8.4) Slope directions
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*12.2 Test* Name the angle pairs (4) http://prntscr.com/oqnpq6
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9.6) A 30 60 90 triangle's shortest leg is 8 units what are the measurements of the other leg and the hypotenuse
hypotenuse = 2 • short leg hypotenuse = 2 • 8 = 16 long leg = shortest leg • √3 long leg = 8 • √3 = 8√3
9.6) 30, 60, 90 triangle
hypotenuse = 2 • short leg long leg = short leg • √3
*9.7 Test* tan 20 = m/48
m is about = 17.5
11.6) If a fair has 10 contestants how many different ways can first, second, and third place be awarded
n = 10 because its the bigger number, the number of contestants r = 3 because there are 3 places that can be won (first second and third) 10P3 -> using the formula you get 10! / (10-3)! 10! / 7! That is 10•9•8•7•6•5•4•3•2•1 / 7•6•5•4•3•2•1 Since there are repeats in the fraction (7•6•5•4•3•2•1 is in the both top and bottom) they cancel out and you are left with 10•9•8 = 720 different ways
11.7) Combination formula
nCr The formula for nCr = nPr / r!
*2.6 Test* Solve r/-13 = -5
r/-13 = -5 Multiply -13 to both side and get r = 65
*5.6 Test* 4/5•t = -8/11
t = -10/11
*3.5 Test* t/-8 < 5
t/-8 < 5 Multiply -8 on both sides and get t > -40 The < changes to > because you multiplied by a negative (happens whenever you multiply or divide by a negative number)
9.7) Find the tangent of the angle 30 degrees if the opposite length is 40 and the adjacent length is 10
tan 30 = 40/10 tan 30 = 4
*3.4 Test* x + 13 < 20 Solve then graph
x + 13 < 20 Subtract 13 on both sides x < 7 Since it is just a < sign and not a less than or equal to sign it is an open dot on 7 and the arrow points left because it is everything less than 7
*5.7 Test* -8/9x + 1/6 = 49/54
x = -5/6
*6.6 Test* 1cm/20km = 7cm/x km
x = 140
*8.3 Test* Find the intercepts of the line 9x +3y = 27
x = 3 y = 9
*2.4 Test* Solve using mental math x+7 = 11
x = 4
*6.2 Test* x/9 = 15/27
x = 5
*6.5 Test* 6/x = 14/21
x = 9
3.4) Say x < 3 in words
x is less than 3
*2.5 Test* Solve x+19=6
x+19=6 Subtract 19 on both sides x = -13
9.5) Find the distance between the two points (6,3) and (5,7)
x2 = 5 x1 = 6 y2 = 7 y1 = 3 √((5-6)^2 + (7-3)^2) √((-1)^2 + (4)^2) √(1 + 16) √17
*1.1 Test* If x = 12 and y = 3 What is xy
xy = 12•3 = 36
1.2) X^4
x•x•x•x
*8.6 Test* Write an equation of the line parallel to the line y = -3x +4 and passes through (0,7)
y = -3x + 7 works because the slope needs to be the same if its parallel (-3 is the slope because its the number in front of the x in y = mx + b form) and it passes through (0,7) because when you plug in 0 for x in and 7 for y you get 7=7
*10.1 Test* Find y if the other two angles in a triangle are 50 degrees and 40 degrees
y = 90 degrees
*6.3 Test* 8/20 = 38/y
y = 95
8.6) Write an equation where the slope is 3 and the y intercept is 5
y = mx + b M = slope b = y intercept y = 3x + 5
8.6) Write an equation where the y intercept is -3 and the slope is 1/2
y = mx + b m = slope b = y- intercept y = 1/2x - 3
8.5) Slope Intercept form
y = mx+b m = slope b = y intercept
9.2) Product Property of Square Roots
√(ab) = √a • √b (a has to be greater than or equal to 0 and b has to be greater than or equal to 0 because you cant take a square root of a negative number) √9 • √7 = 3√7 √9 goes to 3 and √7 is already simplified because it is not a perfect square so that is why you get 3√7
*9.2 Test* Simplify √112
√112 = √(16•7) √16 • √7 4√7
9.1)Square root tip
√9 is 3 and -3 because 3•3 = 9 -3•-3 = 9 The +- symbol (±) means plus or minus/positive or negative If I say ±√100 the answer is ±10 If I say -√100 the answer is -10