Question

this exam must be turned in by december 17th by 3pm. you may use your notes, study guides, or homework questions to answers these questions. correct answers without the work to support the answer will earn only 50%. you may use figures, graphs, or equations to support your answers. record your answer in the blank before the number. 1. show all work. distance on a straight highway, the distance from loretta’s house to a park is 43 miles. her friend jamal lives along this same highway between loretta’s house and the park. the distance from loretta’s house to jamal’s house is 31 miles. how many miles is it from jamal’s house to the park? (lesson 1-2) yz = 2. show all work. find the measure of \\(\overline{yz}\\) if y is the midpoint of \\(\overline{xz}\\). (lesson 1-4) image of a line segment with points x, y, z. x to y is labeled 12 - x, y to z is labeled 3x + 4

Explanation:

Question 1:

Step1: Define the total and partial distance

Let the distance from Loretta’s house to the park be \( L = 43 \) miles, and the distance from Loretta’s house to Jamal’s house be \( l = 31 \) miles. We need to find the distance from Jamal’s house to the park, let's call it \( d \).

Step2: Use subtraction for segment addition

Since Jamal lives between Loretta’s house and the park, the total distance \( L \) is the sum of the distance from Loretta’s to Jamal’s (\( l \)) and from Jamal’s to the park (\( d \)). So \( L=l + d \), which means \( d = L - l \).
Substitute \( L = 43 \) and \( l = 31 \) into the formula: \( d=43 - 31 = 12 \).

Step1: Use midpoint property

Since \( Y \) is the midpoint of \( \overline{XZ} \), then \( XY = YZ \). Given \( XY=12 - x \) and \( YZ = 3x + 4 \), so we set \( 12 - x=3x + 4 \).

Step2: Solve for \( x \)

Add \( x \) to both sides: \( 12=4x + 4 \).
Subtract 4 from both sides: \( 8 = 4x \).
Divide both sides by 4: \( x = 2 \).

Step3: Find \( YZ \)

Substitute \( x = 2 \) into \( YZ = 3x + 4 \): \( YZ=3(2)+4=6 + 4 = 10 \).

Answer:

12

Question 2: