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Terms in this set (54)
What is the reciprocal of
3π/ r²?
r²/3π
What is the reciprocal of zx
y/zx
√25 + 3√27 =?
5+ 3 = 8
What expression is equivalent to
x⁵x⁴ ?
x⁵⁺⁴
x⁹
The perimeter, P, of a square may be found using the formula P=4√A, where A is the area of the square. What is the perimeter of a square with an area of 81 square inches?
4 x 9=
36 inches
If x= -10,
then -x= ?
-(-10)
10
What is the Transitive Property of Equality?
If one quantity equals a second quantity and the second quantity equals a third quantity, then the first quantity equals the third quantity
(if a=b, and b=c, then a=c)
What is the Reflexive Property of Equality?
Any quantity is equal to itself.
(For any number a, a=a)
What is the multiplicative inverse property?
For every number a/b, where a, b ≠zero, there is exactly one number b/a such that the product of a/b and b/a is 1.
(⅔ •³⁄₂ = 6/6= 1)
Which number disproves the statement below:
n² + 1 is a prime number for all numbers n.
When n= 3,
n² + 1
3² + 1
9 + 1
10
If x is an integer, what is the solution set to 4ΙxΙ = 16?
x = { -4, 4}
Use the distributive property to simplify the following equation
3(3-2x) = 5-4(2-3x)
9-6x= 5- 8+12x
9- 6x= -3 + 12x
+3 +3
12 - 6x = 12x
+6x +6x
12 = 18x
Simplify
8- 2x > 5(x-4)
8- 2x > 5x-20
+20 +20
28 -2x > 5x
+2x +2x
28 > 7x
⎯ ⎯
7 7
4 > x (or x<4)
Solve the following
4 = 2
⎯ ⎯
x x-1
Cross multiply
4(x-1) = 2x
4x - 4 = 2x
-4x -4x
-4= -2x
2 = x
Simplify the following
2-x > 2(x-3)
2-x > 2(x-3)
2-x > 2x -6
+6 +6
8 - x > 2x
+x +x
8 > 3x
8/3 >x (or x< 8/3)
The cost, c, in dollars of renting the pool for a pool party for h hours is
c= 50 + 10h.
IF the total cost was $100, for how many hours was the pool rented?
c= 50 + 10h
100= 50 + 10h
-50 -50
50 = 10h
⎯ ⎯
10 10
5 = hours
A 10-foot-long board is cut into two pieces. The first piece is 2 feet longer than the second piece. What is the length of the longer piece of board?
x + x + 2 = 10
2x + 2= 10
2x = 8
x= 4
x+2= 6
What is the
y-intercept of the graph of
3x + 2y = 6?
Make x= 0
2y = 6
y= 3
(o,3) is the answer
What is the x-intercept of the graph of x + 4y = -8?
Make y = 0
x = -8
(-8, 0) is the answer
What is the
y-intercept?
The y-intercept is where the graph of the equation crosses the y-axis. (Where x= 0)
What is the
x-intercept?
The x-intercept is where the graph of the equation crosses the x-axis. (Where y = 0)
What is the equation of the line that has a slope of 3 and passes through the point
(2, -4) ?
y - (-4) = 3(x-2)
y+4= 3x-6
y= 3x-10
What is the point-slope form?
y - y1 = m(x- x1)
where (x1 , y1) is a point on the line &
m= slope
What is the slope-intercept form?
y = mx + b
Where m = slope &
b= y-intercept
What is the slope of a line?
The slope of a line is the ratio of the change in the y-coordinates (rise) to the change in the x-coordinates (run) as you move in the positive direction
Slope = rise= y2-y1
⎯⎯ ⎯⎯⎯
run = x2-x1
What is the standard form of a line?
The standard form of a linear equation is
Ax + By = C
Where A ≥0, A & B are not both zero, & A, B, C are integers with a GCF of 1.
Which point lies on the line defined by
2x + 5y = 15?
(2,0) (2, 5)
(5,0) (5, 1)
(5, 1)
What is the slope of a line parallel to the line y= -2/3 x + 5?
-2/3
(parallel lines have the same slope).
Parallel lines have the _______ slope.
SAME
The slopes of perpendicular lines are ____ ___.
Opposite reciprocals
(or negative inverse)
ex. ⅖ and -5/2
When you have a system of two linear equations with two variables, what are the three ways you can solve them?
By elimination, substitution, or by graphing (which requires you to create a table).
Solve the following:
2x⁴
⎯⎯ =
6x⁸
2x⁴ 1 1
⎯⎯ = ⎯⎯⎯ = ⎯⎯
6x⁸ 3x⁸ˉ⁴ 3x⁴
(6x²+3x+2)-(2x²-4x+1)=
6x²+3x+2
-2x²+4x-1
⎯⎯⎯⎯⎯⎯⎯
4x2 +7x +1
The length of a rectangle is 4 units longer than the width. Which expression could be used to represent the area of the rectangle?
Area= length x width
A= w(w+4)= w² +4w
What is the factored form of
2x²- 2xy-12y²?
Pull out the common factor first...
2x²- 2xy-12y²=
2(x²- xy-6y²)=
2(x +2y)(x- 3y)
What does it mean to "complete the square"?
Complete the square means to rewrite the equation so that the left side is a perfect square.
What is a quadratic equation?
A quadratic equation is an equation of the form ax² + bx + c = 0, where a 0.
AND
_________
x = -b ±√b²-4ac
⎯⎯⎯⎯⎯⎯⎯⎯⎯
2a
Justin can mow a lawn in 2 hours. David can mow a lawn in 3 hours. How long will it take them to mow one lawn together?
Since they are working together, it will take less time than either of them alone.
½t + ⅓t= 1
3/6t + 2/6t =1
⅚t= 1
t= 6/5 hours
What is the formula for rate problems?
d= rt,
"d" is distance, "r" is rate, and "t" is time.
What defines a function?
In a function, each x-value must be mapped to only one y-value.
What is a variable?
Any letter used to represent a number or set of numbers
What is the domain?
The first numbers of the ordered pairs in a set; all the x-values in a line
What is the range?
The second numbers of the ordered pair in a set; all the y-values in a line.
In a graph, what is the vertical axis called?
The y-axis
In a graph, what is the horizontal axis called?
The x-axis
What is the independent variable?
The variable in a function with a value that is subject to choice; usually graphed on x-axis.
What is the dependent variable?
The variable in a relation with a value that depends on the value of the independent variable; usually graphed on the y-axis.
What is the range of the function shown below?
{(2,3), (-1,5), (3,1), (1,0)}
The range is the set of y-values:
{0,1,3, 5}
What is the domain of the function shown below?
{(2,3), (-1,5), (3,1), (1,0)}
The domain is the set of x-values:
{-1, 1, 2, 3}
When looking at a graph, how do you determine whether a relation is a function?
Use the vertical line test.
If a vertical line can be drawn so that it crosses the graph in more than one point, then the graph is NOT a function.
What are the steps to "completing the square"?
Step 1: find ½ of "b", the coefficient of "x."
Step 2: Square the result of Step 1.
Step 3: Add the result of Step 2 to x²+bx, the original expression.
In the Quadratic Formula, what is the "discriminant"?
The discriminant is the expression under the radical sign,
b2 - 4ac
What is the hypothesis of the following statement?
If it is raining, then the pool is closed.
The hypothesis follows the word "if":
It is raining.
What is the conclusion of the following statement?
If it is raining, then the pool is closed.
The conclusion follows the word "then":
The pool is closed.
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