Question 1

Does the point (2, 14) satisfy the inequality y $\le$ 2x - 2?

Accepted Answer

To determine if the point (2, 14) satisfies the inequality $y \leq 2x - 2$, substitute $x = 2$ and $y = 14$ into the inequality: $14 \leq 2(2) - 2$, which simplifies to $14 \leq 2$. Since 14 is not less than or equal to 2, the point (2, 14) does not satisfy the inequality.

Question 2

The time to drive from Gotham City to Farmville varies inversely with the average speed. If the drive takes 6.2 hours at 42 mph, then how long will it take at 63 mph? Round to the nearest tenth of an hour.

Accepted Answer

The time to drive varies inversely with speed, so $T = \frac{k}{v}$, where $T$ is time, $v$ is speed, and $k$ is a constant. Given $T = 6.2$ hours at $v = 42$ mph, we find $k = 6.2 \times 42$. To find the time at $63$ mph, solve $T = \frac{k}{63}$, substituting $k$ from the first part. This gives $T = \frac{6.2 \times 42}{63} = 4.13$, which rounds to $4.1$ hours.

Question 3

If s varies inversely as x and s = 4 when x = -4, then find s when x = 2.

Accepted Answer

Since s varies inversely as x, we have s = k/x for some constant k. Given s = 4 when x = -4, we find k = 4 * (-4) = -16. When x = 2, s = -16/2 = -8.

Question 4

Which graph below correctly indicates the solution set of the linear inequality  ?

Accepted Answer

The answer of Which graph below correctly indicates the solution...

Question 5

Tim works at a bakery and can prepare a birthday cake in 4 hours. It takes him 5 hours to prepare a wedding cake. If Tim works a 40-hour week, which graph below correctly illustrates the number of each type of cake Tim can bake per week?

Accepted Answer

The answer of Tim works at a bakery and can...

Question 6

Write a formula that expresses the relationship described below. P varies jointly as x and y and P = 4 when x = 7 and y = -7

Accepted Answer

If P varies jointly as x and y, then we can express this relationship using the formula:
P = kxy
where k is the constant of proportionality.

To find k, we can use the given information that P = 4 when x = 7 and y = -7:
4 = k(7)(-7)
Solving for k, we get:
k = -1/7

Substituting k into the original formula, we get:
P = (-1/7)xy

Therefore, the formula that expresses the relationship is:
P = (-1/7)xy

And the correct choice is B, which represents the formula in a standard format.

Quiz 3: Section 1: Linear Equations and Inequalities in Two Variables

Does the point (2, 14) satisfy the inequality y ≤\le≤ 2x - 2?

The time to drive from Gotham City to Farmville varies inversely with the average speed. If the drive takes 6.2 hours at 42 mph, then how long will it take at 63 mph? Round to the nearest tenth of an hour.

If s varies inversely as x and s = 4 when x = -4, then find s when x = 2.

Which graph below correctly indicates the solution set of the linear inequality ?

Tim works at a bakery and can prepare a birthday cake in 4 hours. It takes him 5 hours to prepare a wedding cake. If Tim works a 40-hour week, which graph below correctly illustrates the number of each type of cake Tim can bake per week?

Write a formula that expresses the relationship described below. P varies jointly as x and y and P = 4 when x = 7 and y = -7

Does the point (2, 14) satisfy the inequality y $\le$ 2x - 2?