Math(5169) #2
How to change fractional exponents to radicals: 3^1/3=
^3√3
explain why one graph may be a function when the other one is not
a graph is a function when every value of x is paired with only one value of y. the graph on the left is a function; the graph on the right is not.
Prime numbers
a number which can only be divided by itself and 1
Relation
a relationship between sets of values. In math is often between x values (inputs) and y values (outputs)
Function
a special type of relation where each input has only one output
associative property of multiplication
changing the grouping () of the factors does not change the product
With addition and multiplication, it does not matter what order the numbers are written, you still get the same result.
communitive property
An operation is ____________ if changing the order of terms does not change the outcome
commutative (a + b = b + a)
A number without a variable. It is called a ______ because its value does not change (it stays ______).
constant (in the expression 2x + 4y -5, there is one constant: -5)
a set of values that can take any value within an interval
continuous (all variables between 1 and 10)
distance formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Triangular Prism Volume
1/2*b*h*length
translate the verbal expression into a mathematical one: a third of an unknown number
1/3n or (n/3)
volume of a cone
1/3πr²h
rectangular prism area
2(wl+hl+hw)
translate the verbal expression into a mathematical one: the quantity of
(. ) put in perinthesis
2(x-2)(3x-5) =
1) 2(x-2)(3x-5) 2) Multiply the outer 2 to (x-2) to get 2x-4) Now i have (x-4)(3x-5) 2) Use the foil method Now I have 6x^2 - 22x + 20
given points (-4,t) (0,3) (6,0), what is the value of t?
1) find the slope using the intercepts 3-0/ 0-6 = 3/-6 = -1/2 2) write the slope-intercept form y= -1/2 + 3 (it is 3, because the y-intercept moves in i 2) substitute -4 into the equation to find the value of t. y= -1/2x + 3 ---> -1/2(-4) + 3. Therefore, the value of t when x=-4 is 5.
The sum of three consecutive integers is 19 less than four times the smallest integer. What is the value of the middle integer?
23. If three intergers are consecutive, their values can be represented as x, x+1, and x+2, where x is the value of the smallest interger. The equation x + x + 1 + x + 2 = 4x-19 represents the given condition. The equation can be simplified to 3x + 3 = 4x -19, and the solution of the equation is x=22. Therefore, the value of the middle interger is x+1 = 22 + 1 = 23
How do you find the median, mean, mode, and range on calculator?
2nd > stat > L1- input all of the numbers median: 2nd > stat > math > mean > enter L1> enter. Median: same just click mode Mode: click stat > sort A > enter L1> done. go back to list.
Perimeter of a circle
2πr
surface area of a sphere formula
4 x π x r2
Volume of a sphere formula
4/3 x π x r3
Tessellation
A repeating pattern of plane figures that completely cover a plane with no gaps or overlaps
A sequence that has the same common difference between terms. Give formula
Arithmetic Sequence Tn = a1 + d (n-1) tn= nth term a1= first term d= common difference n=term number
a polynomial with two terms
Binomial (6y+3)
how to find the radius when circumference is only given
C = 2πR isolate the radius
congruent
Having the same size and shape
irrational number
IR=Not Ratio nal ex: Pi: 3.141592....... the numbers go on forever and do not repeat themselves
identity property of addition
If you add zero to a number, the sum is the same as that number.
skew lines
Lines that do not intersect and are not coplanar
polynomial with one term
Monomial (2x^2)
The simplest function within a specific family
Parent function (y=x is the parent function for linear equations)
An expression with one or more term; terms may include exponents that may only be whole numbers and may not be whole numbers and may not include division by a variable.
Polynomial (4x-5)
An equation where the highest exponent of the variable is 2
Quadratic equation (y=x2+3x−15)
an inequality that includes a quadratic expression
Quadratic inequality (quadratic = polynomial with a degree of 2. y=x^2) ex: x^2-3x <10
cone surface area
SA=πrs (s= slant height)
if two different shapes (rectange and triangle) are made up of the same triangles, how will the area compare to the perimeter?
The area will be the same the perimeter will be less with the rectangle than the triangle
instantaneous rate of change
The exact rate of change at one instant of time. Found using a derivative of a function at a specific point.
How many different scenarios: The number of different committees of 3 people that can be formed from a group of 7 people.
The first member of the committee can be chosen from the 7 people in 7 ways, the second in 6 ways, and the third in 5 ways. But, the committee that is selected would be the same as those in which the same three people were selected but in a different order. there are 3 x 2 x1 ways to arrange the committee selected into the different orders in which they could have been selected. The number of different committees is therefore 7x6x5 / 3x2x1= 35
How to find the instantanous rate of change on a graph?
The slope of the tangent line (the straight line that "just touches" the curve at that point) represents the instantaneous rate of change at any given point.
a polynomial with three terms
Trinomial (3x2+5x−4)
complementary angles
Two angles whose sum is 90 degrees
complementary angle
Two angles whose sum is 90 degrees (when chilis comps things off it feels like 90 degrees)
SSS postulate
Two triangles are congruent if all three sets of corresponding sides are congruent.
Vertical line test
Use this to determine whether or not the relation is a function. pass a vertical line through all the points of the graph, and if the vertical line passes through more than one point of the graph and the same time, the relation is NOT a function.
translate the verbal expression into a mathematical one: the product of:
X (multiplicaiton)
The distance a number is from zero; always a positive number
absolute value (∣−9∣=9 and |9|=9∣9∣=9)
The distance less than (<) or less than or equal to (≤) the distance from the value to zero OR the distance greater than (>) or greater than or equal to (≥) the distance from the value to zero.
absolute value inequality (∣x∣>3)
a/b + c/d=
ad + bc / bd -bd is the common denominator to use. bd is a multiple of both b and d 1) multiply a/b by d/d to get ad/bd. 2) multiply c/d by d/d to get bc/bd. therefore, your answer is ad+bc/ bd
Rational numbers
any number than can be represented as the ratio (RATIOnal) of any integer (a whole number)
rational number
any number that can be written and comes to a stop (unlike 3.333333 which continues on forever)
An operation is ___________ if regrouping the terms does not change the outcome
associative ((a+b)+c=a+(b+c))
associative vs communitive property
associative says you can re-group numbers (associates are friendly- they can regroup) communicative says you can move numbers around.
An number in front of a group of terms will multiply all terms in the grouping individually
distributive property (a(b+c)=ab+ac)
The set of all possible input values, or x-values, that satisfy a function.
domain
a functional relationship is when
each input (person) can only be in one output (place) at any given time.
equidistant
equally distant
apothem
extends from the center of the polygon to the midpoint of a side (it would be radius if it were extending to a corner)
values that are multiplied to get another number
factors (Some factors of 12 are 3 and 4 because 3 \times 4 = 123×4=12)
find the slope intercept form of 3x - 4y = 12
form: y= mx + b 3x - 4y = 12 2) 4y = 3x - 12 3) y = 3/4x -3 we can determine that the slope is 3/4
A sequence whose terms are generated by multiplying each term by the same common ratio.
geometric sequence Tn= A1 R^n-1 tn= nth term a1= first term r= common ratio n= term number
how would you find the height of a tree when a 6' tall person stands 40' from a tree and casts an afternoon shadow of 10'?
h/6 = 50/10 height of tree/height of person = shadow length of tree/shadow length person
A fraction where the numerator is larger than the denominator
improper fraction (6/2)
A statement that 2 expressions are not equal.
inequality
convex interior angle sizes
less than 180 degrees
An expression that does not contain any exponents
linear expression
A whole number with a fraction
mixed number (3 1/2)
concave interior angle sizes
more than 180 degrees
how do you simplify (5^2x-3)^-2
multiply the outside exponents to the inside exponents
How do you find the weighted average?
multiply the percentage ex: (.22)(9 cal/g) + (0.26)(4 Cal/g) + (0.52)(4 cal/gram) = 5.4 Cal/g
what does a rectangular pyramid look like?
one base in addition to the number of triangular faces that are equal to the number of sides of the base.
a nonfunctional relationship is when
one input has more than one output
Lines that intersect at a right (90º) angle. They have slopes that are opposite reciprocals, meaning their signs (positive or negative) are opposite and their fractions are flipped.
perpendicular lines
Set A consists of all integers that are prime numbers. Set B consists of all 2-digit positive integers that are less than 70 and have a units digit of 7. How many integers are members of both set A and set B ?
prime numbers= a number that can only be divided by itself and 1. intergers= a whole number that is not a fraction. the members of the set B, the 2-digit positive numbers are less than 70 and have units digit of 7 are: 17, 27, 37, 47, 57, and 67. of these numbers 17, 37, 47, and 67 are prime numbers. so 4 numbers are members of both set A and set B.
The symbol used to indicate a root.
radical sign (√)
The average rate of change of an interval is the slope of the _____ line between the endpoints of the interval.
secant (ex: 4≤x≤8- the endpoint is 8. therefore, it is labeled correctly in the picture)
what do you do when you are dividing quotients with negative exponents? ex: 5^-4 divided by. 5^-2
subtract the exponents when dividing exponential numbers with the same base. 5^-4 / 5^-2 = 5^-4-(-2) = 5^-2 = (1/5)(1/5)= 1/25
if a graph has a solid line and is shaded above that line, what does that mean?
that the inequality is "greater than (above) or equal to (solid line)"
quotient
the answer to a division problem
product
the answer to a multiplication problem
How many different scenarios: the number of different orders in which 5 people can finish a race if they each complete the race in a different amount of time.
the first person to finish the race can be chosen in 5 different ways, the second in 4 different ways, the third in 3, the fourth in 2, and the last in 1. giving 5 x 4 x 3 x 2 x 1= 120 orders.
How many different scenarios: The number of ways in which 2 different prizes can be awarded among 9 people if no one person can receive both prizes
the first prize could be awarded to any of the 9 people and the second prize could be awarded to any of the remaining 8 people who did not recieve the first prize. giving a total of 9 x 8 = 72 different ways
secant line
the line through two points on a curve
prism vs pyramid
the net for a prism has to bases in addition to a number of rectangular faces that are equal to the number of sides to one base. the net for a pyramid has one base in addition to a number of triangular faces that are equal to the number of sides of the base.
Range (in function)
the set of all possible output values (or y values) of a function.
Independent variable is often represented with what?
the variable x
Dependent variable is often represented with what?
the variable y
how do you find the x and y intercept of y= 3/4 - 3?
to find the x-intercept, let y = 0 and solve for x. 3x - 4(0) = 12 3x= 12 x=4. thus, the x-intercept is 4 the y intercept is "b": -3
what does a triangular pyramid look like?
triangle as the base, triangle as the sides
What does a rectangular prism look like?
two bases in addition to a number of rectangular faces that are equal to the number of sides of the base.
what does a triangular prism look like?
two bases in addition to a number of rectangular faces.
A letter or non-numeric symbol that represents an unknown value.
variable (in the expression 2x + 4y -5, there are 2 variables: x and y)
the absolute value of a number a,
written |a|, is always non-negative and can be thought of as the distance a is from 0 on the number line
slope formula
y2-y1/ x2-x1
Quadratic equation in standard form
y= ax^2 + bx + c (a,b,c are coefficients a= width and direction c= y-intercept)
quadratic
y=x^2 (polynomial with a degree of 2)
cylinder volume
πr²h
How to change fractional exponents to radicals: 3^1/2=
√3