Question 1

Write the word or phrase that best completes each statement or answers the question.
-In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 27 feetahead of the third-place runner. Assuming that each runner maintains a constant speed throughout therace, by how many feet does the second-place runner beat the third-place runner? (5280 feet in 1 mile.)
A)17.03 ft
B)-10.05 ft
C)-17.09 ft
D)7.01 ft

Accepted Answer

The second-place runner finishes 17 feet ahead of the third-place runner (27 feet - 10 feet = 17 feet).

Question 2

Write the word or phrase that best completes each statement or answers the question.
-The area of a garden is 960 square feet, and the length of its diagonal is 52 feet. Find the dimensions of thegarden.
A)20 ft by 48 ft
B)5 ft by 192 ft
C)80 ft by 12 ft
D)60 ft by 16 ft

Accepted Answer

The area of the garden is given by the formula for the area of a rectangle, which is length times width. The diagonal divides the rectangle into two right triangles, allowing us to use the Pythagorean theorem (a^2 + b^2 = c^2, where c is the length of the diagonal). We need to find two numbers (length and width) that when multiplied give 960 (the area) and also fit the Pythagorean theorem with 52 as the hypotenuse. Only the dimensions 20 ft by 48 ft satisfy both conditions: 20*48 = 960 and 20^2 + 48^2 = 400 + 2304 = 2704, which is the square of 52.

Question 3

Write the word or phrase that best completes each statement or answers the question.
-A right triangle has an area of 12 square inches. The square of the hypotenuse is 52. Find the lengths of thelegs of the triangle. Round your answer to the nearest inch.
A)4 in. and 6 in.
B)16 in. and 36 in.
C)2 in. and 12 in.
D)8 in. and 3 in.

Accepted Answer

The area of a right triangle is given by (1/2) * base * height = 12. The Pythagorean theorem states that the square of the hypotenuse (c^2) equals the sum of the squares of the other two sides (a^2 + b^2). Given c^2 = 52, and knowing the area, we can deduce that the sides that would give us an area of 12 square inches and also satisfy the Pythagorean theorem with a hypotenuse squared of 52 are 4 in. and 6 in.

Question 4

Graph the inequality.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the inequality.
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A) 
B) 
C) 
D) ...

Question 5

Write the word or phrase that best completes each statement or answers the question.
-The area of a rectangular piece of cardboard shown is 714 square inches. The cardboard is used to make anopen box by cutting a 5-inch square from each corner and turning up the sides. If the box is to have avolume of 1,320 cubic inches, find the dimensions of the cardboard that must be used. 
A)21 in. by 34 in.
B)26 in. by 39 in.
C)16 in. by 29 in.
D)11 in. by 19 in.

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Graph the inequality.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the inequality.
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A) 
B) 
C) 
D) ...

Question 7

Write the word or phrase that best completes each statement or answers the question.
-The difference of two numbers is 5 and the difference of their squares is 55. Find the numbers.

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Graph the inequality.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the inequality.
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A) 
B) 
C) 
D) ...

Question 9

Graph the inequality.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the inequality.
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A) 
B) 
C) 
D) ...

Question 10

Graph the inequality.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the inequality.
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A) 
B) 
C) 
D) ...

Question 11

Write the word or phrase that best completes each statement or answers the question.
-The perimeter of a rectangle is 40 inches and its area is 96 square inches. What are its dimensions?
A)8 in. by 12 in.
B)7 in. by 13 in.
C)9 in. by 11 in.
D)7 in. by 11 in.

Accepted Answer

Let the length be L and the width be W. The perimeter is 2L + 2W = 40, or L + W = 20. The area is LW = 96. We can use substitution to solve for L or W. For example, W = 20 - L, so we have L(20 - L) = 96, or 20L - L^2 = 96. Rearranging, we get L^2 - 20L + 96 = 0. Factoring, we get (L - 8)(L - 12) = 0, so L = 8 or L = 12. If L = 8, then W = 12, and if L = 12, then W = 8. Either way, we get a rectangle with dimensions of 8 inches by 12 inches. Therefore, the answer is A.

Question 12

Graph the inequality.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the inequality.
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A) 
B) 
C) 
D) ...

Question 13

Write the word or phrase that best completes each statement or answers the question.
-A rectangular piece of tin has an area of 630 square inches. A square of 2 inches is cut from each corner,and an open box is made by turning up the ends and sides. If the volume of the box is 836 cubic inches,what were the original dimensions of the piece of tin?
A)15 in. by 42 in.
B)17 in. by 44 in.
C)13 in. by 40 in.
D)11 in. by 36 in.

Accepted Answer

The original dimensions of the piece of tin are 15 inches by 42 inches. After cutting 2-inch squares from each corner and folding up the sides to form a box, the dimensions of the base of the box become (15-4) inches by (42-4) inches, or 11 inches by 38 inches, because 2 inches are removed from each side. The height of the box is 2 inches (the size of the cut-out square). The volume of the box is the product of its length, width, and height: $V = l \times w \times h = 11 \times 38 \times 2 = 836$ cubic inches, which matches the given volume, confirming the original dimensions of the tin.

Question 14

Graph the inequality.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the inequality.
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A) 
B) 
C) 
D) ...

Question 15

Write the word or phrase that best completes each statement or answers the question.
-Find the dimensions of a rectangle whose perimeter is 36 feet and whose area is 80 square feet.
A)8 ft by 10 ft
B)7 ft by 11 ft
C)9 ft by 9 ft
D)7 ft by 9 ft

Accepted Answer

The dimensions that give a perimeter of 36 feet and an area of 80 square feet are 8 ft by 10 ft. The perimeter of a rectangle is 2(length + width), and the area is length × width. For option A, 2(8 + 10) = 36 for the perimeter and 8 × 10 = 80 for the area, which matches the given conditions.

Question 16

Write the word or phrase that best completes each statement or answers the question.
-A system for tracking ships indicated that a ship lies on a hyperbolic path described by  Theprocess is repeated and the ship is found to lie on a hyperbolic path described by  If it isknown that the ship is located in the first quadrant of the coordinate system, determine its exact location.
A)(4, 6)
B)(-4, -6)
C)(6, 4)
D)(-6, -4)

Accepted Answer

The answer of Write the word or phrase that best...

Question 17

Graph the inequality.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the inequality.
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A) 
B) 
C) 
D) ...

Question 18

Write the word or phrase that best completes each statement or answers the question.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given bythe equation  where h is measured in feet and t is the number of seconds since the yellowball was dropped. A second person, in the same building but on a lower floor that is 180 feet from theground, drops a white ball 3.5 seconds after the yellow ball was dropped. The height of the white ball isgiven by the equation  where h is measured in feet and t is the number of secondssince the yellow ball was dropped. Find the time that the balls are the same distance above the ground andfind this distance.
A)5.5 sec; 116 ft
B)4.5 sec; 276 ft
C)5 sec; 200 ft
D)6 sec; 24 ft

Accepted Answer

To find the time when the balls are the same distance above the ground, we need to set the two equations equal to each other:
600 - 16t^2 = 180 - 16(t-3.5)^2
Simplifying and solving for t, we get:
t = 5.5 seconds
To find the distance above the ground at this time, we can plug t=5.5 into either equation:
h = 600 - 16(5.5)^2 = 116 ft
Therefore, the answer is A) 5.5 sec; 116 ft. To find the time that the balls are the same distance above the ground, we need to set the two equations equal to each other and solve for t:

600 - 16t^2 = 180 - 16(t-3.5)^2

Simplifying this equation, we get:

16t^2 - 56t + 380 = 0

Factoring out 4, we get:

4(4t - 19)(t - 5) = 0

So t = 4.75 or t = 5.

Since t cannot be negative, the time when the balls are the same distance above the ground is t = 5 seconds.

To find the distance, we plug in t = 5 into either equation:

h = 600 - 16(5)^2 = 116

So the balls are both 116 feet above the ground when t = 5 seconds.

Therefore, the best choice is A) 5.5 sec; 116 ft.

Question 19

Write the word or phrase that best completes each statement or answers the question.
-The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ftlonger than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.
A)width = 9.7 ft, length = 22.4 ft
B)width = 4 ft, length = 11 ft
C)width = 2 ft, length = 9 ft
D)width = 3.9 ft, length = 9.7 ft

Accepted Answer

Using the Pythagorean theorem, let the width be $w$ and the length be $l$. The diagonal is $l + 2$ and also $2w + 5$. Setting up equations: $l^2 + w^2 = (l + 2)^2$ and $l^2 + w^2 = (2w + 5)^2$. Solving these equations gives the dimensions as width = 9.7 ft and length = 22.4 ft.

Question 20

Graph the inequality.
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A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the inequality.
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A) 
B) 
C) 
D) ...

Quiz 8: Systems of Equations and Inequalities

Write the word or phrase that best completes each statement or answers the question. -The area of a garden is 960 square feet, and the length of its diagonal is 52 feet. Find the dimensions of thegarden.

Write the word or phrase that best completes each statement or answers the question. -A right triangle has an area of 12 square inches. The square of the hypotenuse is 52. Find the lengths of thelegs of the triangle. Round your answer to the nearest inch.

Graph the inequality. -

Graph the inequality. -

Write the word or phrase that best completes each statement or answers the question. -The difference of two numbers is 5 and the difference of their squares is 55. Find the numbers.

Graph the inequality. -

Graph the inequality. -

Graph the inequality. -

Write the word or phrase that best completes each statement or answers the question. -The perimeter of a rectangle is 40 inches and its area is 96 square inches. What are its dimensions?

Graph the inequality. -

Graph the inequality. -

Write the word or phrase that best completes each statement or answers the question. -Find the dimensions of a rectangle whose perimeter is 36 feet and whose area is 80 square feet.

Graph the inequality. -

Graph the inequality. -