Equations and Expressions
Simplify the expression:
8(x + 3) + 2(9x - 10)
8x + 24 + 18x - 20
26x + 4
Write an equation to represent the situation in the table.
y = 1.25x
Name a pair of alternate interior angles and a pair of vertical angles.
Alternate Interior: Angles 2 and 7 or Angles 3 and 8
Vertical Angles: Angles 1 and 2, Angles 3 and 4, Angles 5 and 8, or Angles 6 and 7.
Given the function:
{(0, 3), (-1, 5), (2, 7), (-8, 2)}
What is the output when the input is 2?
Output is 7.
Find the value of 7^-4. State if the answer is rational or irrational and justify.
1/2401. Rational - it can be written as a fraction.
Find the value of the expression below when x = 8.
8(x - 9) - 2(x + 1)
8(8-9) - 2(8+1)
8(-1) - 2(9)
-8 - 18
-26
Write an equation of the line graphed.
y = -3/2x + 4
Can the following angle measures be the angles of a triangle?
98 degrees, 15 degrees, and 77 degrees
No, they add up to 190 degrees.
Point A (-12, 6) and B (-21, 18) are being dilated by a scale factor of 1/3. What are the coordinates of A' and B'?
A' (-4, 2)
B' (-7, 6)
What is the cube root of 15? State if the answer is rational or irrational and justify.
2.466212...
Irrational because it is non-terminating and non-repeating.
Solve for x.
8x - 9 = 14x + 15
-9 = 6x + 15
-24 = 6x
-4 = x
Write an equation of a line that has a slope of 4 and passes through the point (2, 12).
y = mx + b
12 = 4(2) + b
12 = 8 + b
4 = b
y = 4x + 4
What type of angles are angle XPY and angle WPZ? If angle XPY = 7x - 16 and angle WPZ = 68, what is the value of x?
Vertical Angles.
7x - 16 = 68
7x = 84
x = 12
Ben starts with $300 in his savings account. He decides to save $40 per month. Write an equation to represent this function.
y = 40x + 300
Two babysitters have different rates. Babysitter A charges $40 for gas and $12 per hour of babysitting. Babysitter B charges $35 for gas and $15 per hour of babysitting. Write a system of equations to represent the total owed, y, after a number of hours, x.
y = 12x + 40
y = 15x + 35
Solve for x.
-2(x + 11) - 4x = -3(2x + 4)
-2x - 22 - 4x = -6x - 12
-6x - 22 = -6x - 12
-22 = -12
No Solution
Find the slope of the line that passes through the points (-2, 6) and (14, 18).
18 - 6 / 14 - (-2)
12/16
m = 3/4
Find the measures of angles R, S, and T.
Angle R = 65 degrees
Angle S = 85 degrees
Angles T = 30 degrees
Determine if each table is a linear function or not. If it is, state the constant rate of change.
Table A is not a linear function.
Table B is a linear function. The constant rate of change is 4.
Graph the system of equations below and find the solution.
y = 2x - 1
y = -3x + 4
(1, 1)
Solve for x.
8.52x - 8.98 = 12.3 + 7.40x
1.12x - 8.98 = 12.3
1.12x = 21.28
x = 19
Find the slope of the table from 4 hours to 9 hours.
450 - 210 / 9 - 4
240 / 5
48 miles per hour
Find the volume of the cylinder. Round to the nearest tenth.
Volume = pi(4^2)(9)
Volume = 452.4 cm^3
Triangle ABC is at points A(1, 3), B(2, 4), and C (3, 1). Reflect the triangle over the x-axis.
A'(1, -3)
B'(2, -4)
C'(3, -1)
Use the Pythagorean Theorem to find the missing side length. Round to the nearest hundredth.
48.54 cm