WEST-E MATH 304
A pair of shoes is on sale for $96. If the shoes are on sale for 20% off, what was the original price?
$120 (set up proportion)
Simplify the following (3^3*4^-1)/(a^-7*b^2*c^-9)
(27a^7*c^9)/(4b^2)
When factored completely, the expression 3x^3−5x^2−48x+ 80 is equivalent to
(x+ 4)(x−4)(3x−5)
(xy)^a =
(x^a)(y^a)
Integers
,...,-2, -1, 0, 1 , 2, ....
If the area of the first triangle is 14, and the area of the second triangle is 350, what is the scale factor?
5 Explanation Since this is area we cannot simply divide 350 by 14 as area involves two dimensions multiplied together. To get our answer we have to divide then take the square root of that answer. 350 / 14 = 25 √25 = 5 Our scale factor is 5.
Find the resultant of 3i+4j 2i-6j
5i-2j
How many different-looking six-letter arrangements can be made using the letters of the word"TATTOO"?
6P6/3!2! = 60
A student measured the volume of water in a graduated cylinder to be 37 mL, but the actual volume of the water was 40 mL. What was the percent error in this measurement?
7.5% % error = |(37 - 40)|/40 = 7.5%
Suppose Nathan went to the store and bought 18 doughnuts for $25. The doughnuts are creme filled and jelly filled. Suppose the creme filled doughnuts are $2 each and the jelly filled doughnuts are $1 each, and we want to know how many of each doughnut Nathan bought. In using the guess, check, and revise method, we initially guess that he got 9 creme filled doughnuts. If this is our guess, how many jelly filled doughnuts are we guessing that he got?
9 We are given that he bought 18 doughnuts all together. Thus, since we are guessing that he bought 9 creme filled doughnuts, it must be the case that we are guessing he also bought 9 jelly filled doughnuts, because 9 + 9 = 18.
Simplify (9x^2y^6)^-(1/2)
9^(-.5)x^-1 y^-3 = (1/(3xy^3))
X^(a/b) =
= b,rt(X^a)
Scalar
A physical quantity that has magnitude only.
Vector
A quantity that has magnitude and direction
The measure of an interior angle of a regular polygon is 120◦. How many sides does the polygon have?
Ai=( (n-2)*180 )/n n=6
Real Numbers
All rational and irrational numbers
How do you solve an inverse matrix?
Turn it into the identity matrix.
Dot Product (a*b)
a*b= axby + ayby
The word that describes how close a measurement is to the true or accepted value is _____
accuracy
Determinant Formula [a b c d]
ad - bc
discriminant equals
b^2-4ac
conditional statement
if p, then q
inductive reasoning
specific to general
a determinant can only be calculated on a __________ matrix.
square
Change in area is the area __________.
squared
Fahrenheit to Celsius
C=(F-32)/1.8
Associative Property
Changing the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication
What is always logically equivalent to the inverse?
Converse
Rational Numbers
...,-1, -1/2 , 0, 1/2, 1, ...
Whole Numbers
0, 1, 2, 3, 4, ....
Natural Numbers
1, 2, 3, 4, ...
Find the tenth term in the expansion of (x + 3)^12
12C9 (x)^(12-9)(3)^9 = (220)x^3(19683) = 4330260x^3
In a certain high school, a survey revealed the mean amount of bottled water consumed by students each day was 153 bottles with a standard deviation of 22 bottles. Assuming the survey represented a normal distribution, what is the range of the number of bottled waters that approximately 68.2% of the students drink?
131-175
If we apply a scale factor of 4 to the triangular prism below, what will the volume of the new prism be? Base: 2 Base Height: 3 Height: 7
1344 multiply the area of the original prism by 4 ∗ 4 ∗ 4 or 64 21 ∗ 64 = 1344
A painting costs $225. If the sale price is $191.25, what is the percent discount?
15% (set up a proportion)
GCF of 10 and 22.
2
The sum of3√6a^4b^2 and 3√162a^4b^2, expressed in simplest radical form,
4a3√6ab^2
4x^1/3 written rationally
4cubert(x)
If we apply a scale factor of 3 to a cube where each side is 2 inches long, what will the volume of the new cube be?
216
1/(2^-5) =
2^5
If log 2 =a and log 3 =b, the expression log9- log20 is equivalent to
2b-a-1
Expressed in simplest form,3y/(2y−6) + 9/(6−2y) is equivalent to
3/2
LCM of 5 and 6
30
If the campers at Camp Grilled Meat prefer hot dogs to hamburgers by a ratio of 4:3, and they need 500 hot dogs, how many hamburgers will they need?
375
Irrational Numbers
Any real number which cant be expressed as a fraction of two integers
Using a known formula to calculate a solution to an algebra equation is an example of which type of reasoning?
Deductive
If you run around a field for a total of 1300 meters and end up back where you started, what was your distance, and what was your displacement?
Distance: 1300 m Displacement: 0m
Celsius to Fahrenheit
F= 1.8 (C) +32
Multiplicative Inverse of a Matrix
If A and B are square matrices and AB = BA = I, then B is the multiplicative inverse of A, written A^-1.
Inverse
If not p, then not q
Contrapositive
If not q, then not p
Converse
If q, then p
Matrix A * I = _________________ A*A^-1 =________________
Matrix A I
Which of the following is the inverse of this matrix? (it is one square matrix) [2 4 4 1]
One square matrix: [(-1/14) (2/7) (2/7) (-1/7)] Multiplying the two matrices together, we get the identity matrix. The upper left number is -2/14 + 8/7 = 1. The upper right is 4/7 - 4/7 = 0. The lower left is -4/14 + 2/7 = 0. The lower right is 8/7 - 1/7 = 1.
Prime Number
Only divisible by itself and one.
Nathan just bought some jelly filled doughnuts for $1 a piece and some creme filled doughnuts for $2 a piece. All together, he got 18 doughnuts, and he spent $25, and we want to know how many of each doughnut he bought. In using the guess, check, and revise method, our first guess is that he got 9 jelly filled doughnuts and 9 creme filled doughnuts. When we check, we see that 9*1 + 9*2 = 27, so we know this guess is a little high since he only spent $25. Which of the following is the best second guess? 9jel and 6cr 8cr and 8jel 8 cr and 10 jel
Since our initial guess resulted in the amount spent being a little too high, it would make sense to reduce the more expensive option (creme filled) and increase the cheaper option (jelly filled). We also have to keep in mind that the total number of doughnuts is 18. Of all the guesses given, 8 creme filled doughnuts and 10 jelly filled doughnuts is the only one that meets this criteria. Therefore, this is the best second guess.
Which matrix will you get when you multiply a matrix with its inverse?
The identity matrix
greatest common factor (GCF)
The largest factor that two or more numbers have in common.
Commutative Property
The property that says that two or more numbers can be added or multiplied in any order without changing the result. a+b = b+a
square matrix
a matrix with the same number of rows and columns
multiplying matrices
columns in matrix A has to be the same as the rows in matrix B. The resulting matrix has dimensions that are equivalent to the rows of A and the columns of B.
Change in volume is the scale factor __________.
cubed
deductive reasoning
general to specific
miles to kilometers
km= mi/0.6
km to miles
mi = km * 0.6
How do you subtract vectors?
place the heads of the two vectors together, the line drawn from the tails of the vectors is your subtracted vector
How do you add vectors?
the head of one arrow meets the tail of the second, the line drawn from the tail of the first and the head of the second is your added vector
scalar multiplication
the process of multiplying each element of a matrix by a real number or scalar
When shapes are similar that means they are...
the same shape but not the same size.
resultant vector
the vector sum of two or more vectors
If the inverse of matrix A is this, what is the solution when the constants are 10 and 13? [(-1/14) (2/7) (2/7) (-1/7)]
x = 3 y = 1 Multiplying the inverse with the constants of 10 and 13, we get for the top row, -10/14 + 26/7 = 21/7 = 3 and for the bottom row we get 20/7 - 13/7 = 7/7 = 1. So our answers are x = 3 and y = 1.
The quantities p and q vary inversely. If p= 20 when q=−2, and p=x when q=−2x+ 2,then x equals
x= -4, 5
(x^a)(x^b) =
x^a+b
(x^a) / (x^b) =
x^a-b
(x/y)^a =
x^a/y^a