Question

1. john runs at different speeds as part of his training program. the graph shows his target heart rate at different times during his workout. on which interval is the target heart rate strictly increasing then strictly decreasing? a) between 0 and 30 minutes b) between 40 and 60 minutes c) between 50 and 65 minutes d) between 70 and 90 minutes
2. if y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5? a) 6 b) 15 c) 20 d) 23
3. in the figure above, lines l and m are parallel and lines s and t are parallel. if the measure of ∠1 is 35°, what is the measure of ∠2? a) 35° b) 55° c) 70° d) 145°
4. if 16 + 4x is 10 more than 14, what is the value of 8x? a) 2 b) 6 c) 16 d) 80
5. which of the following graphs best shows a strong negative association between d and t? a) graph with scattered points b) graph with scattered points c) graph with scattered points d) graph with scattered points
6. 1 decagram = 10 grams, 1,000 milligrams = 1 gram. a hospital stores one type of medicine in 2 - decagram containers. based on the information given in the box above, how many 1 - milligram doses are there in one 2 - decagram container? a) 0.002 b) 200 c) 2,000 d) 20,000

Explanation:

1.

Step1: Analyze the graph

Check the intervals where the heart - rate graph is increasing then decreasing.

Step2: Evaluate each option

• Option A: Between 0 and 30 minutes, the heart rate is constant.
• Option B: Between 40 and 60 minutes, the heart rate first decreases then increases.
• Option C: Between 50 and 65 minutes, the heart rate first increases (from the value at 50 minutes to a higher value) and then decreases.
• Option D: Between 70 and 90 minutes, the heart rate is constant then decreases.

Step1: Find the value of k

Given \(y = kx\), when \(y = 24\) and \(x = 6\), we can find \(k\) using the formula \(k=\frac{y}{x}\). So \(k=\frac{24}{6}=4\).

Step2: Find y when x = 5

Substitute \(k = 4\) and \(x = 5\) into \(y=kx\). Then \(y=4\times5 = 20\).

Step1: Use the property of parallel lines

Since lines \(\ell\) and \(m\) are parallel and lines \(s\) and \(t\) are parallel, \(\angle1\) and \(\angle2\) are corresponding angles (or vertical - angle relationships with corresponding angles). Corresponding angles formed by parallel lines are equal.

Answer:

C

2.