Question 1

Solve for y.
-Levi borrowed $5007 at 6% simple interest for 5 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 5 months? Round answers to
The nearest cent if necessary.

Accepted Answer

The simple interest is calculated as Principal x Rate x Time. Here, $5007 x 0.06 x (5/12) = $125.18. The total amount to pay back is the principal plus interest: $5007 + $125.18 = $5132.18.

Question 2

Solve the problem.
-Find the length of a rectangular lot with a perimeter of 148 m if the length is 6 m more than the width.

Accepted Answer

The perimeter of a rectangle is given by the formula 2(length + width). Let the width be x meters. Then, the length is x + 6 meters. The perimeter is 2(x + x + 6) = 148 meters. Simplifying, we get 4x + 12 = 148, so 4x = 136, and x = 34 meters for the width. The length is x + 6 = 40 meters.

Question 3

Solve for y.
-$$5 x + 8 = 6 y - 9$$

Accepted Answer

To solve for y, add 9 to both sides to get $5x + 17 = 6y$. Then divide both sides by 6 to isolate y: $y = \frac{5x + 17}{6}$.

Question 4

Solve for y.
-Hannah borrowed $52,084 at 5% simple interest for 18 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 18 months? Round answers
To the nearest cent if necessary.

Accepted Answer

The simple interest is calculated using the formula I = PRT, where P is the principal ($52,084), R is the rate (5% or 0.05), and T is the time in years (18 months = 1.5 years). The interest is $3,906.30, and the total amount to be paid back is $52,084 + $3,906.30 = $55,990.30.

Question 5

Solve the problem.
-In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 25° 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 - 25. The equation is x + 3x + (x - 25) = 180. Solving gives x = 41°, so angle C = 41°, angle A = 123°, and angle B = 16°.

Question 6

Solve for y.
-Sophia borrowed $11,790 at 6% simple interest for 4 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 4 months? Round answers
To the nearest cent if necessary.

Accepted Answer

The interest is calculated using the formula I = PRT, where P = $11,790, R = 6% per annum (0.06), and T = 4/12 years. The interest is $235.80, and the total amount is $12,025.80.

Question 7

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.
-$$F = 5 ^ { \circ }$$

Accepted Answer

To convert $F = 5 ^ { \circ }$ to Celsius, use the formula $C = \frac { 5 } { 9 } ( F - 32 )$. Substituting $F = 5$, we get $C = \frac { 5 } { 9 } ( 5 - 32 ) = \frac { 5 } { 9 } ( -27 ) = -15 ^ { \circ }$.

Question 8

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.
-$$C = 87 ^ { \circ }$$

Accepted Answer

To convert $C = 87 ^ { \circ }$ to Fahrenheit, use the formula $F = \frac { 9 } { 5 } C + 32$. Substituting $C = 87$, we get $F = \frac { 9 } { 5 } \times 87 + 32 = 156.6 + 32 = 188.6 ^ { \circ }$.

Question 9

Solve the problem.
-Find the corresponding Celsius temperature for a temperature of 290°F. Round to the nearest tenth, if necessary.

Accepted Answer

The answer of Solve the problem.
-Find the corresponding Celsius temperature...

Question 10

Solve the problem.
-A rectangular Persian carpet has a perimeter of 208 inches. The length of the carpet is 18 in. more than the width. What are the dimensions of the carpet?

Accepted Answer

The perimeter of a rectangle is given by the formula $P = 2l + 2w$, where $l$ is the length and $w$ is the width. Given that the length is 18 inches more than the width ($l = w + 18$), and the perimeter is 208 inches, we can set up the equation $208 = 2(w + 18) + 2w$. Simplifying, we get $208 = 4w + 36$, and solving for $w$ gives $w = 43$ inches. Therefore, the length is $43 + 18 = 61$ inches.

Question 11

Solve the problem.
-Find the height of a moving box if its length is 31 in., its width is 29 in., and its surface area is 3358 in2. Assume that the surface area includes the top of the moving box.

Accepted Answer

The surface area (SA) of a box is given by the formula SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Given l = 31 in., w = 29 in., and SA = 3358 in², we can set up the equation 2(31)(29) + 2(31)h + 2(29)h = 3358. Simplifying, we get 1798 + 62h + 58h = 3358, leading to 120h = 1560, and thus h = 13 in.

Question 12

Solve the problem.
-In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 28° greater than that of angle A. Find the measure of the angles.

Accepted Answer

Let angle A = x degrees. Then, angle C = 6x degrees, and angle B = x + 28 degrees. The sum of angles in a triangle is 180 degrees, so x + 6x + (x + 28) = 180. Solving this equation gives x = 19 degrees, making angle A = 19°, angle B = 47°, and angle C = 114°.

Question 13

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.
-$$C = 1 ^ { \circ }$$

Accepted Answer

Using the formula $F = \frac { 9 } { 5 } C + 32$, substituting $C = 1$, we get $F = \frac { 9 } { 5 } (1) + 32 = 1.8 + 32 = 33.8$.

Question 14

Solve the problem.
-A cylindrical container has a volume of $$1088 \pi \mathrm { m } ^ { 3 }$$ and a radius of 8 m. Find the height of the container.

Accepted Answer

The volume of a cylinder is given by $V = \pi r^2 h$, where $V$ is the volume, $r$ is the radius, and $h$ is the height. Given $V = 1088\pi$ and $r = 8$, we can solve for $h$ as follows: $1088\pi = \pi(8)^2h$, simplifying to $1088 = 64h$, and solving for $h$ gives $h = 17$ meters.

Question 15

Solve the problem.
-A circular hole is filled with concrete to make a footing for a load-bearing pier. The hole measures 18 inches across and requires 2.1 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 answer of Solve the problem.
-A circular hole is filled...

Question 16

Solve the problem.
-A bookcase is to be constructed as shown in the figure below. The height of the bookcase is 2 feet longer than the length of a shelf. If 22 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 17

Solve the problem.
-A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 30. Find the length of a side.

Accepted Answer

The perimeter of a square is 4 times the length of a side. Let x be the length of a side. The equation is 4x = 9x - 30. Solving for x gives x = 6.

Question 18

Solve the problem.
-A triangular shaped lake-front lot has a perimeter of 1200 ft. One side is 100 ft longer than the shortest side, while the third side is 200 ft longer than the shortest side. Find the lengths of all three
Sides.

Accepted Answer

Let the shortest side be x. Then, the other sides are x + 100 and x + 200. The perimeter is the sum of all sides: x + (x + 100) + (x + 200) = 1200. Solving this equation, 3x + 300 = 1200, 3x = 900, x = 300. Therefore, the sides are 300 ft, 400 ft, and 500 ft.

Question 19

Solve the problem.
-Find the corresponding Fahrenheit temperature for a temperature of 90°C. Round to the nearest tenth, if necessary.

Accepted Answer

To convert Celsius to Fahrenheit, use the formula F = (C × 9/5) + 32. For 90°C, F = (90 × 9/5) + 32 = 194°F.

Question 20

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.
-$$F = 350 ^ { \circ }$$

Accepted Answer

To convert $F = 350 ^ { \circ }$ to Celsius, use the formula $C = \frac { 5 } { 9 } ( F - 32 )$. Substituting $F = 350$, we get $C = \frac { 5 } { 9 } ( 350 - 32 ) = \frac { 5 } { 9 } \times 318 = 176.7 ^ { \circ }$.

Quiz 2: Equations and Inequalities

Solve for y. -Levi borrowed $5007 at 6% simple interest for 5 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 5 months? Round answers to The nearest cent if necessary.

Solve the problem. -Find the length of a rectangular lot with a perimeter of 148 m if the length is 6 m more than the width.

Solve for y. - $5 x + 8 = 6 y - 9$

Solve for y. -Hannah borrowed $52,084 at 5% simple interest for 18 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 18 months? Round answers To the nearest cent if necessary.

Solve the problem. -In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 25° less than that of angle C. Find the measure of the angles.

Solve for y. -Sophia borrowed $11,790 at 6% simple interest for 4 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 4 months? Round answers To the nearest cent if necessary.

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. - $F = 5 ^ { \circ }$

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. - $C = 87 ^ { \circ }$

Solve the problem. -Find the corresponding Celsius temperature for a temperature of 290°F. Round to the nearest tenth, if necessary.

Solve the problem. -A rectangular Persian carpet has a perimeter of 208 inches. The length of the carpet is 18 in. more than the width. What are the dimensions of the carpet?

Solve the problem. -Find the height of a moving box if its length is 31 in., its width is 29 in., and its surface area is 3358 in2. Assume that the surface area includes the top of the moving box.

Solve the problem. -In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 28° greater than that of angle A. Find the measure of the angles.

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. - $C = 1 ^ { \circ }$

Solve the problem. -A cylindrical container has a volume of $1088 \pi \mathrm { m } ^ { 3 }$ and a radius of 8 m. Find the height of the container.

Solve the problem. -A square plywood platform has a perimeter which is 9 times the length of a side, decreased by 30. Find the length of a side.

Solve the problem. -A triangular shaped lake-front lot has a perimeter of 1200 ft. One side is 100 ft longer than the shortest side, while the third side is 200 ft longer than the shortest side. Find the lengths of all three Sides.

Solve the problem. -Find the corresponding Fahrenheit temperature for a temperature of 90°C. Round to the nearest tenth, if necessary.

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. - $F = 350 ^ { \circ }$