Question 1

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

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

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.
-$$\mathrm { F } = 22 ^ { \circ }$$

Accepted Answer

To convert $22^\circ F$ to Celsius, use the formula $C = \frac{5}{9}(F - 32)$. Substituting $F = 22$, we get $C = \frac{5}{9}(22 - 32) = \frac{5}{9}(-10) = -5.6^\circ C$.

Question 3

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.
-$$\mathrm { F } = 229 ^ { \circ }$$

Accepted Answer

The answer of Use these equations to convert between the...

Question 4

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 5

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 6

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.
-Find the corresponding Celsius temperature for a temperature of 242°F. Round to the nearest tenth, if necessary.

Accepted Answer

To convert 242°F to Celsius, use the formula $C = \frac { 5 } { 9 } ( F - 32 )$. Plugging in 242 for F gives $C = \frac { 5 } { 9 } ( 242 - 32 ) = \frac { 5 } { 9 } \times 210 = 116.7 ^ { \circ } \mathrm { C }$.

Question 7

Solve for y.
-Levi borrowed $6944 at 4% simple interest for 6 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 6 months? Round answers to the nearest cent if
Necessary.

Accepted Answer

The interest can be calculated using the formula I = PRT, where P is the principal amount ($6944), R is the rate (4% or 0.04), and T is the time in years (6 months or 0.5 years). So, I = 6944 * 0.04 * 0.5 = $138.88. The total amount to be paid back is the principal plus interest, which is $6944 + $138.88 = $7082.88.

Question 8

Solve for y.
-Sophia borrowed $13,671 at 6% simple interest for 3 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 3 months? Round answers to the nearest cent if
Necessary.

Accepted Answer

The interest can be calculated using the formula I = PRT, where P is the principal amount ($13,671), R is the annual interest rate (6% or 0.06), and T is the time in years (3/12 or 0.25 years). Thus, I = $13,671 * 0.06 * 0.25 = $205.065, which rounds to $205.07. The total amount to be paid back is the principal plus interest, which is $13,671 + $205.07 = $13,876.07.

Question 9

Solve for y.
-Hannah borrowed $47,838 at 5% simple interest for 15 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 15 months? Round answers to the nearest cent if
Necessary.

Accepted Answer

The interest can be calculated using the formula I = PRT, where P is the principal amount ($47,838), R is the rate of interest per year (5% or 0.05), and T is the time in years (15 months or 1.25 years). Thus, I = $47,838 * 0.05 * 1.25 = $2,989.88. The total amount to be paid back is the principal plus interest, which is $47,838 + $2,989.88 = $50,827.88.

Question 10

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.
-Find the corresponding Fahrenheit temperature for a temperature of 84°C. Round to the nearest tenth, if necessary.

Accepted Answer

The answer of Use these equations to convert between the...

Question 11

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.
-Find the length of a rectangular lot with a perimeter of 92 m if the length is 6 m more than the width.

Accepted Answer

The perimeter of a rectangle is given by $P = 2l + 2w$, where $l$ is the length and $w$ is the width. Given that the length is 6 m more than the width, we can express the length as $l = w + 6$. Substituting this into the perimeter formula gives $92 = 2(w + 6) + 2w$. Simplifying, we get $92 = 4w + 12$, and solving for $w$ gives $w = 20$. Therefore, the length $l = 20 + 6 = 26$ m.

Question 12

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 1.5 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 the hole is (18/2)^2 * pi * h = 1800, where h is the depth of the hole. Solving for h gives h = 11.

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.
-$$C = 8 ^ { \circ }$$

Accepted Answer

Using the formula $ F = \frac{9}{5}C + 32 $, substituting $ C = 8 $, we get $ F = \frac{9}{5} \times 8 + 32 = 46.4^\circ $.

Question 14

Solve the problem.
-A triangular shaped lake-front lot has a perimeter of 1500 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) = 1500. Solving this equation, 3x + 300 = 1500, 3x = 1200, x = 400. Therefore, the sides are 400 ft, 500 ft, and 600 ft.

Question 15

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.
-$C = 76 ^ { \circ }$

Accepted Answer

The answer of Use these equations to convert between the...

Question 16

Solve the problem.
-A rectangular Persian carpet has a perimeter of 224 inches. The length of the carpet is 24 in. more than the width. What are the dimensions of the carpet?

Accepted Answer

The answer of Solve the problem.
-A rectangular Persian carpet has...

Question 17

Solve for y.
-$$9 x ^ { 2 } - y + 7 x = 0$$

Accepted Answer

To solve for $y$, we rearrange the equation to isolate $y$ on one side: $y = 9x^2 + 7x$. This is achieved by adding $y$ to both sides and then subtracting $0$ from both sides, resulting in the expression for $y$.

Question 18

Solve the problem.
-A cylindrical container has a volume of $$1936 \pi \mathrm { cm } ^ { 3 }$$ and a radius of 11 cm. 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 $V = 1936 \pi \mathrm { cm } ^ { 3 }$ and $r = 11 \mathrm { cm }$, we can solve for $h$ as follows: $1936 \pi = \pi (11)^2 h$. Simplifying, $1936 = 121h$, so $h = 16 \mathrm { cm }$.

Question 19

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.
-A square plywood platform has a perimeter which is 7 times the length of a side, decreased by 18. Find the length of a side.

Accepted Answer

Let the length of a side of the square be $x$. The perimeter of a square is $4x$. According to the problem, $4x = 7x - 18$. Solving for $x$, we get $3x = 18$, so $x = 6$.

Question 20

Solve for y.
-$$7 x + 9 = 5 y - 9$$

Accepted Answer

To solve for $y$, first add 9 to both sides to get $7x + 18 = 5y$. Then, divide both sides by 5 to isolate $y$, resulting in $y = \frac{7x + 18}{5}$.

Quiz 2: Equations and Inequalities

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.

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. - $\mathrm { F } = 22 ^ { \circ }$

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. - $\mathrm { F } = 229 ^ { \circ }$

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.

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. -Find the corresponding Celsius temperature for a temperature of 242°F. Round to the nearest tenth, if necessary.

Solve for y. -Levi borrowed $6944 at 4% simple interest for 6 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 6 months? Round answers to the nearest cent if Necessary.

Solve for y. -Sophia borrowed $13,671 at 6% simple interest for 3 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 3 months? Round answers to the nearest cent if Necessary.

Solve for y. -Hannah borrowed $47,838 at 5% simple interest for 15 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 15 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. -Find the length of a rectangular lot with a perimeter of 92 m if the length is 6 m more than the width.

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. - $C = 8 ^ { \circ }$

Solve the problem. -A triangular shaped lake-front lot has a perimeter of 1500 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.

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. - $C = 76 ^ { \circ }$

Solve the problem. -A rectangular Persian carpet has a perimeter of 224 inches. The length of the carpet is 24 in. more than the width. What are the dimensions of the carpet?

Solve for y. - $9 x ^ { 2 } - y + 7 x = 0$

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

Solve for y. - $7 x + 9 = 5 y - 9$

Quiz 2: Equations and Inequalities

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.

Use these equations to convert between the two systems. C=59(F−32) F=95C+32C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32C=95​(F−32) F=59​C+32 Round answer to the nearest tenth of a degree if necessary. - F=22∘\mathrm { F } = 22 ^ { \circ }F=22∘

Use these equations to convert between the two systems. C=59(F−32) F=95C+32C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32C=95​(F−32) F=59​C+32 Round answer to the nearest tenth of a degree if necessary. - F=229∘\mathrm { F } = 229 ^ { \circ }F=229∘

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 for y. -Levi borrowed $6944 at 4% simple interest for 6 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 6 months? Round answers to the nearest cent if Necessary.

Solve for y. -Sophia borrowed $13,671 at 6% simple interest for 3 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 3 months? Round answers to the nearest cent if Necessary.

Solve for y. -Hannah borrowed $47,838 at 5% simple interest for 15 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 15 months? Round answers to the nearest cent if Necessary.

Use these equations to convert between the two systems. C=59(F−32) F=95C+32C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32C=95​(F−32) F=59​C+32 Round answer to the nearest tenth of a degree if necessary. - C=8∘C = 8 ^ { \circ }C=8∘

Solve the problem. -A triangular shaped lake-front lot has a perimeter of 1500 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.

Use these equations to convert between the two systems. C=59(F−32) F=95C+32C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32C=95​(F−32) F=59​C+32 Round answer to the nearest tenth of a degree if necessary. - C=76∘C = 76 ^ { \circ }C=76∘

Solve the problem. -A rectangular Persian carpet has a perimeter of 224 inches. The length of the carpet is 24 in. more than the width. What are the dimensions of the carpet?

Solve for y. - 9x2−y+7x=09 x ^ { 2 } - y + 7 x = 09x2−y+7x=0

Solve the problem. -A cylindrical container has a volume of 1936πcm31936 \pi \mathrm { cm } ^ { 3 }1936πcm3 and a radius of 11 cm. Find the height of the container.

Solve for y. - 7x+9=5y−97 x + 9 = 5 y - 97x+9=5y−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. - $\mathrm { F } = 22 ^ { \circ }$

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. - $\mathrm { F } = 229 ^ { \circ }$

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. - $C = 8 ^ { \circ }$

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. - $C = 76 ^ { \circ }$

Solve for y. - $9 x ^ { 2 } - y + 7 x = 0$

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

Solve for y. - $7 x + 9 = 5 y - 9$