Question 1

Solve the problem.
-A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 4 feet longer than the length of a shelf. If 20 feet of lumber is available for the entire unit (including the
Shelves, but NOT the back of the bookcase), find the length and height of the unit.

Accepted Answer

The answer of Solve the problem.
-A bookcase is to be...

Question 2

Use these equations to convert between the two systems. $$C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$$ Round answer to the nearest tenth of a degree if necessary.
-$$\mathrm { C } = 12 ^ { \circ }$$

Accepted Answer

To convert $12^\circ C$ to Fahrenheit, use the formula $F = \frac{9}{5}C + 32$. Substituting $C = 12$, we get $F = \frac{9}{5} \times 12 + 32 = 53.6^\circ F$.

Question 3

Solve the problem.
-In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 35° less than that of angle C. Find the measure of the angles.

Accepted Answer

The sum of angles in a triangle is 180°. Let angle C = x°, then angle A = 3x°, and angle B = x° - 35°. The equation is x + 3x + (x - 35) = 180, solving gives x = 43°, so angle C = 43°, angle A = 129°, and angle B = 8°.

Question 4

Solve the problem.
-Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 93 miles in the same time that Dana travels 84 miles. If Chuckʹs rate of travel is 3 mph more than Danaʹs, and they
Travel the same length of time, at what speed does Chuck travel?

Accepted Answer

Chuck's speed is 31 mph, derived from the relationship between distance, speed, and time, where Chuck's distance is 93 miles and Dana's is 84 miles, with Chuck traveling 3 mph faster than Dana.

Question 5

Solve the problem.
-Find the length of a rectangular lot with a perimeter of $132 \mathrm {~m}$ if the length is $8 \mathrm {~m}$ more than the width.

Accepted Answer

The answer of Solve the problem.
-Find the length of a...

Question 6

Solve the problem.
-Find the height of a moving box if its length is 32 in., its width is 26 in., and its surface area is 2940 in $^ { 2 }$. Assume that the surface area includes the top of the moving box.

Accepted Answer

The surface area of a box is given by $2lw + 2lh + 2wh$, where $l$ is the length, $w$ is the width, and $h$ is the height. Plugging in the given values, we get $2(32)(26) + 2(32)h + 2(26)h = 2940$. Simplifying, $1664 + 64h + 52h = 2940$, which simplifies to $116h = 1276$, giving $h = 11$ inches.

Question 7

Solve the problem.
-From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 14 miles per hour. In how many hours will they be 69 miles apart?

Accepted Answer

The relative speed of the two boats is 9 + 14 = 23 miles per hour. To be 69 miles apart, it will take 69 / 23 = 3 hours.

Question 8

Solve the problem.
-In the morning, May drove to an appointment at $50 \mathrm { mph }$. Her average speed on the return trip in the afternoon was $40 \mathrm { mph }$. The return trip took $\frac { 1 } { 5 }$ hour longer. How far did she travel to the appointment?

Accepted Answer

The answer of Solve the problem.
-In the morning, May drove...

Question 9

Use these equations to convert between the two systems. $$C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$$ Round answer to the nearest tenth of a degree if necessary.
-$$\mathrm { F } = 10 ^ { \circ }$$

Accepted Answer

Using the formula $C = \frac{5}{9}(F - 32)$, substitute $F = 10$: $C = \frac{5}{9}(10 - 32) = \frac{5}{9}(-22) = -12.2$.

Question 10

Solve the problem.
-A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 15 . Find the length of a side.

Accepted Answer

The answer of Solve the problem.
-A square plywood platform has...

Question 11

Solve the problem.
-A triangular shaped lake-front lot has a perimeter of 1300 ft. One side is 100 ft longer than the shortest side, while the third side is 300 ft longer than the shortest side. Find the lengths of all three
Sides.

Accepted Answer

The answer of Solve the problem.
-A triangular shaped lake-front lot...

Question 12

Solve the problem.
-Noah and Ben are running in the Walker Street Fun Run. Noah runs at 7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are 16 mile apart?

Accepted Answer

The answer of Solve the problem.
-Noah and Ben are running...

Question 13

Solve the problem.
-A cylindrical container has a volume of $1936 \pi \mathrm { m } ^ { 3 }$ and a radius of $11 \mathrm {~m}$. Find the height of the container.

Accepted Answer

The volume of a cylinder is given by the formula $ V = \pi r^2 h $. Given $ V = 1936 \pi $, $ r = 11 $, we can solve for $ h $:  $ 1936 \pi = \pi (11)^2 h $  $ 1936 = 121h $  $ h = \frac{1936}{121} = 16 \mathrm{~m} $.

Question 14

Solve the problem.
-A circular hole is filled with concrete to make a footing for a load-bearing pier. The hole measures 15 inches across and requires 1.9 bags of concrete in order to fill it to ground level. What is the
Depth of the hole? Round your answer to the nearest inch. (One bag of concrete, when mixed with
The appropriate amount of water, makes 1800 in.3 of material.)

Accepted Answer

The volume of concrete required is 1.9 bags × 1800 in³/bag = 3420 in³. The volume of a cylinder (the hole) is given by V = πr²h, where r is the radius and h is the depth. The radius is half the diameter, so r = 15 in / 2 = 7.5 in. Rearranging the formula for volume to solve for h gives h = V / (πr²). Substituting the given values, h = 3420 in³ / (π * (7.5 in)²) ≈ 19.3 in, which rounds to 19 inches.

Question 15

Solve the problem.
-A rectangular Persian carpet has a perimeter of 216 inches. The length of the carpet is 26 in. more than the width. What are the dimensions of the carpet?

Accepted Answer

The perimeter of a rectangle is given by the formula $2l + 2w = P$, where $l$ is the length, $w$ is the width, and $P$ is the perimeter. Given that the length is 26 inches more than the width ($l = w + 26$) and the perimeter is 216 inches, we can set up the equation $2(w + 26) + 2w = 216$. Simplifying gives $4w + 52 = 216$, and further simplification gives $w = 41$ inches. Substituting $w = 41$ into $l = w + 26$ gives $l = 67$ inches.

Question 16

Solve the problem.
-In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 44° greater than that of angle A. Find the measure of the angles.

Accepted Answer

The answer of Solve the problem.
-In triangle ABC, the angle...

Question 17

Solve the problem.
-Find the corresponding Fahrenheit temperature for a temperature of $73 ^ { \circ } \mathrm { C }$. Round to the nearest tenth, if necessary.

Accepted Answer

To convert Celsius to Fahrenheit, use the formula $ F = \frac{9}{5}C + 32 $. For $73 ^{\circ} \mathrm{C}$, $ F = \frac{9}{5} \times 73 + 32 = 163.4 ^{\circ} \mathrm{F} $.

Question 18

Solve the problem.
-Jill is 10 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2 kilometers per hour. They meet in 2 hours. How fast is Joe walking?

Accepted Answer

Since they meet in 2 hours and Jill walks at 2 kilometers per hour, she covers 4 kilometers in that time. The total distance is 10 kilometers, so Joe covers the remaining 6 kilometers in 2 hours, which means he walks at 3 kilometers per hour.

Question 19

Solve the problem.
-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 7 miles per hour, and Delvis is traveling at a speed of 15 miles per hour. In 5 hours what is the distance
Between them (assuming that they began at the same point and time)?

Accepted Answer

In 5 hours, Candy travels 35 miles (7 mph * 5 hours) and Delvis travels 75 miles (15 mph * 5 hours). The distance between them is 75 - 35 = 40 miles.

Question 20

Solve the problem.
-Find the corresponding Celsius temperature for a temperature of $143 ^ { \circ } \mathrm { F }$. Round to the nearest tenth, if necessary.

Accepted Answer

To convert Fahrenheit to Celsius, use the formula $ C = \frac{5}{9}(F - 32) $. For $143 ^{\circ} \mathrm{F}$, $ C = \frac{5}{9}(143 - 32) = 61.7 ^{\circ} \mathrm{C} $.

Quiz 1: Equations and Inequalities

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $\mathrm { C } = 12 ^ { \circ }$

Solve the problem. -In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 35° less than that of angle C. Find the measure of the angles.

Solve the problem. -Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 93 miles in the same time that Dana travels 84 miles. If Chuckʹs rate of travel is 3 mph more than Danaʹs, and they Travel the same length of time, at what speed does Chuck travel?

Solve the problem. -Find the length of a rectangular lot with a perimeter of $132 \mathrm {~m}$ if the length is $8 \mathrm {~m}$ more than the width.

Solve the problem. -Find the height of a moving box if its length is 32 in., its width is 26 in., and its surface area is 2940 in $^ { 2 }$ . Assume that the surface area includes the top of the moving box.

Solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 14 miles per hour. In how many hours will they be 69 miles apart?

Solve the problem. -In the morning, May drove to an appointment at $50 \mathrm { mph }$ . Her average speed on the return trip in the afternoon was $40 \mathrm { mph }$ . The return trip took $\frac { 1 } { 5 }$ hour longer. How far did she travel to the appointment?

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $\mathrm { F } = 10 ^ { \circ }$

Solve the problem. -A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 15 . Find the length of a side.

Solve the problem. -A triangular shaped lake-front lot has a perimeter of 1300 ft. One side is 100 ft longer than the shortest side, while the third side is 300 ft longer than the shortest side. Find the lengths of all three Sides.

Solve the problem. -Noah and Ben are running in the Walker Street Fun Run. Noah runs at 7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are 16 mile apart?

Solve the problem. -A cylindrical container has a volume of $1936 \pi \mathrm { m } ^ { 3 }$ and a radius of $11 \mathrm {~m}$ . Find the height of the container.

Solve the problem. -A rectangular Persian carpet has a perimeter of 216 inches. The length of the carpet is 26 in. more than the width. What are the dimensions of the carpet?

Solve the problem. -In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 44° greater than that of angle A. Find the measure of the angles.

Solve the problem. -Find the corresponding Fahrenheit temperature for a temperature of $73 ^ { \circ } \mathrm { C }$ . Round to the nearest tenth, if necessary.

Solve the problem. -Jill is 10 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2 kilometers per hour. They meet in 2 hours. How fast is Joe walking?

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 7 miles per hour, and Delvis is traveling at a speed of 15 miles per hour. In 5 hours what is the distance Between them (assuming that they began at the same point and time) ?

Solve the problem. -Find the corresponding Celsius temperature for a temperature of $143 ^ { \circ } \mathrm { F }$ . Round to the nearest tenth, if necessary.