FreezeFrame, a social networking site, sent out a survey in which the users simply click a response to join the sample. One of t

Response:

∠PQL=∠TRN [Angles corresponding]

Thus, PQ║RS and PQ=RS

Detailed explanation:

The side PQ has been drawn.

A second side QR is traced, forming an acute angle with side PQ.

Now side QR is extended to the left.

Create an arc from point Q such that it intersects QP at M and extends RQ at L. Without altering the compass width (i.e., the distance between the nib and pencil), draw an arc from R to intersect RQ at N. Now measure the distance LM with a compass. Position the compass at N and mark an arc cut from point R. Designate this intersection as T. Draw a line from point R through T. Then measure the length of PQ with the compass. Position your compass at R and create an arc on the produced line RT at S. Thus, we ascertain that PQ║RS and PQ=RS.

This occurs because

∠MQL=∠NRT [corresponding angles, with QR acting as the transversal]

Out of the four students who illustrated their explanations

Student 2 presented a partially correct but valid explanation.

Answer:

40%

Detailed solution:

John Smith and Susan Jones have contributed $240,000 and $160,000 respectively toward Expo Company. We are tasked with determining the proportion of the business owned by Susan.

First, calculate the total investment by summing both contributions.

Next, find what percentage $160,000 is of the total $400,000.

Thus, Susan's share in the company is 40%.

Part A:

Please refer to the attached image to view the graph illustrating the inequalities.

There are two distinct lines shown, one with a steeper negative slope than the other. The shaded region in between indicates the solution set.

The green line corresponds to 2x+y≤8, while the blue line represents x+y≥4

Part B:

To determine if (8, 10) is included, substitute x = 8 and y = 10 into both inequalities. If it fails to satisfy either inequality, then it won't be part of the solution area.

2(8) + 10 ≤ 8

16 + 10 ≤ 8

26 ≤ 8... 26 is NOT less than or equal to 8

Hence, (8, 10) cannot be a solution because the inequality does not hold.

Part C:

I will select a random point from the graph, such as (2, 3). For your answer, any point within the shaded region where both x and y are positive would suffice.

The point (2, 3) indicates that Sarah can purchase 2 cupcakes and 3 pieces of fudge, ensuring that she acquires at least 4 pastries for her siblings while adhering to her 8 dollar budget.

Please let me know if you need any further clarification. Happy studying!