Semester 2 Math Final Study Guide

Jenna is solving the equation 2x - 4 = -1/2(-4x + 8).
How many solutions to this equation?

• One Solution

• No Solution

• Infinitely Many Solutions

Solve the following equation for x.
2(x - 4) + 3x = 7

The grid below shows a system of linear equations. What is the solution?

Solve for x. Keep answer as a fraction.
3(x - 4) = 13

A donut shop offers a discount on purchases of donuts and coffee that total more than 10 items. Cynthia orders 8 donuts and 4 cups of coffee for a total of $16. Write an equation for this situation, let d represent the discounted cost of a donut and c represent the discounted cost of a cup of coffee.

CD connects the point C(-4, 8) to the point D(-4, -5). The segment is translated 4 units down, then reflected across the x-axis to form C'D'. What is the length in units of C'D'?

On the coordinate plane below, figure 1 was transformed twice to form figure 2. What could have been the two transformations? Choose all that apply.

• 1- Rotation 180 degrees

  2- Translation down

• 1- Reflection over the y-axis

  2- Reflection over the x-axis

• 1- Reflection over the x-axis

  2- Translation right

• 1- Rotation 270 degrees

  2- Translation right

The coordinate plane below shows the location of triangle D'E'F'. Triangle D'E'F' was formed after triangle DEF was translated 2 units to the right and 4 units up. Before the translation, what was the location of vertex E? Think backwards

Triangle XYZ is shown below. Which statement is TRUE?

• The measure of ∠X = 180° minus the measure of ∠Y because adjacent angles in a triangle are supplementary.

• The measure of ∠X = 60° because each angle is equal to a third of the triangle's total angle measure of 180°.

• The measure of ∠Y = 85° because the three angles represent proportional parts of the triangle's total angle measure of 180°.

• The measure of ∠Z = 42.5° because the sum of the measures of the triangle's three angles total 180°.

The figure shows the rectangular foundation for a new house. What is w, the width of the foundation? (number only)