Question 1

Solve.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve.
-
A) 
B) 
C) 
D) ...

Question 2

Solve the problem. If necessary, round to the nearest tenth.
-A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 15 feet and the height from the ground to the front doors is 5 feet, how long is the ramp?
A) 14.1 ft
B) 15.8 ft
C) 4.5 ft
D) 7.1 ft

Accepted Answer

The ramp, the height, and the distance from the building form a right triangle. Using the Pythagorean theorem: a² + b² = c², where a = 15 ft, b = 5 ft, and c is the hypotenuse (the ramp length). Solving gives c = √(15² + 5²) = √(225 + 25) = √250 ≈ 15.8 ft.

Question 3

Solve the problem. If necessary, round to the nearest tenth.
-On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 40 m long and the shadow is 32 m, how tall is the flag pole?
A) 64 m
B) 72 m
C) 24 m
D) 51 m

Accepted Answer

Using the Pythagorean theorem, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse, $a$ is the height of the flagpole, and $b$ is the length of the shadow. Given $c = 40$ m and $b = 32$ m, we solve for $a$: $a^2 = 40^2 - 32^2 = 1600 - 1024 = 576$. Taking the square root of 576 gives $a = 24$ m.

Question 4

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.
-a = 11, c = 16
A) b = 11.18
B) b = 245
C) b = 11.619
D) b = 19.416

Accepted Answer

Using the Pythagorean theorem, $a^2 + b^2 = c^2$. Given $a = 11$ and $c = 16$, we solve for $b$: $11^2 + b^2 = 16^2$, which simplifies to $b^2 = 256 - 121 = 135$. Taking the square root of 135 gives $b \approx 11.619$.

Question 5

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.
-a = 15, b = 20
A) c = 24
B) c = 13
C) c = 18
D) c = 25

Accepted Answer

The length of the missing side, c, can be found using the Pythagorean theorem: $c = \sqrt{a^2 + b^2}$. Substituting $a = 15$ and $b = 20$, we get $c = \sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25$.

Question 6

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.
-a = 20, b = 48
A) c = 36
B) c = 44
C) c = 49
D) c = 52

Accepted Answer

To find the length of the missing side (hypotenuse) in a right triangle, use the Pythagorean theorem: $c = \sqrt{a^2 + b^2}$. Here, $a = 20$ and $b = 48$, so $c = \sqrt{20^2 + 48^2} = \sqrt{400 + 2304} = \sqrt{2704} = 52$.

Question 7

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.
-a = 4, b = 5
A) c = 6.903
B) c = 4.5
C) c = 3
D) c = 6.403

Accepted Answer

To find the length of the missing side (hypotenuse) in a right triangle, you can use the Pythagorean theorem, which is $a^2 + b^2 = c^2$. Given $a = 4$ and $b = 5$, you get $4^2 + 5^2 = 16 + 25 = 41$. Taking the square root of 41 gives $c ≈ 6.403$.

Question 8

Solve the problem.
-A manufacturer's cost is given by  , where C is the cost and n is the number of parts produced. How many parts are produced when the cost is $6200?
A) 225
B) 3375
C) 6000
D) 27,000

Accepted Answer

The answer of Solve the problem.
-A manufacturer's cost is given...

Question 9

Solve the problem.
-The distance d in miles that can be seen on the surface of the ocean is given by  where h is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 12.5
Miles?
A) 92 ft
B) 96 ft
C) 203 ft
D) 156 ft

Accepted Answer

The answer of Solve the problem.
-The distance d in miles...

Question 10

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.
-b = 1, c = 
A) a = 4.742
B) a = 14.967
C) a = 3.742
D) a = 4

Accepted Answer

The answer of Find the length of the missing side...

Question 11

Solve the problem. If necessary, round to the nearest tenth.
-One airport has a ramp sloping down from the passenger waiting area to the plane. If the distance from the waiting area to the plane is 42 feet and the height from the ground to the waiting area is 7 feet, how long is the
Ramp?
A) 7.0 ft
B) 41.4 ft
C) 42.6 ft
D) 9.9 ft

Accepted Answer

Using the Pythagorean theorem, the ramp length is the hypotenuse: sqrt(42^2 + 7^2) = 42.6 ft.

Question 12

Solve the problem. If necessary, round to the nearest tenth.
-A car dealer advertised a big sale by stretching a string of banners from the top of the building to the edge of the driveway. If the building is 17 m high and the driveway is 49 m from the building, how long is the string of
Banners?
A) 24.0 m
B) 46.0 m
C) 51.9 m
D) 8.1 m

Accepted Answer

The length of the string of banners can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the building's height (17 m) and the distance from the building to the driveway (49 m) are the two shorter sides of the triangle. Thus, the length of the string (hypotenuse) is the square root of (17^2 + 49^2) = sqrt(289 + 2401) = sqrt(2690) ≈ 51.9 m.

Question 13

Solve.
-
A) 
B) 0
C) 1
D) No solution

Accepted Answer

The answer of Solve.
-
A) 
B) 0
C) 1
D) No solution...

Question 14

Solve the problem. If necessary, round to the nearest tenth.
-On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 40 m long and the tree is 32 m tall, how long is the shadow?
A) 51 m
B) 64 m
C) 24 m
D) 72 m

Accepted Answer

To find the length of the shadow, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). If we let the length of the shadow be $b$ and the height of the tree be $a$, then we have $a^2 + b^2 = c^2$. Plugging in the given values, $32^2 + b^2 = 40^2$. Solving for $b$, we find $b = \sqrt{40^2 - 32^2} = \sqrt{1600 - 1024} = \sqrt{576} = 24$. Therefore, the length of the shadow is 24 m.

Question 15

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.
-a = 3, b = 4
A) c = 5
B) c = 7
C) c = 12
D) c = 3.742

Accepted Answer

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Therefore, $c = \sqrt{a^2 + b^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.

Question 16

Solve the problem.
-A manufacturer's cost is given by  , where C is the cost and n is the number of parts produced. Find the cost when 125 parts are produced.
A) $80
B) $4672
C) $1200
D) $2200

Accepted Answer

The answer of Solve the problem.
-A manufacturer's cost is given...

Question 17

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.
-a = 15, c = 25
A) b = 18
B) b = 24
C) b = 20
D) b = 25

Accepted Answer

Using the Pythagorean theorem, $a^2 + b^2 = c^2$, with $a = 15$ and $c = 25$, we solve for $b$: $15^2 + b^2 = 25^2$. This simplifies to $225 + b^2 = 625$, and further to $b^2 = 400$. Taking the square root of both sides gives $b = 20$.

Question 18

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary.
-a = 10, c = 26
A) b = 24
B) b = 25
C) b = 28
D) b = 18

Accepted Answer

In a right triangle, the Pythagorean theorem states that a² + b² = c². Here, a = 10 and c = 26. So, 10² + b² = 26². Solving for b, we get b² = 676 - 100 = 576, thus b = √576 = 24.

Question 19

Solve.
-
A) 2, -2
B) 0
C) 
D) -2

Accepted Answer

The answer of Solve.
-
A) 2, -2
B) 0
C) 
D) -2...

Question 20

Solve the problem. If necessary, round to the nearest tenth.
-On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 33 m long and the shadow is 23 m, how tall is the building?
A) 40.2 m
B) 23.7 m
C) 10.0 m
D) 22.3 m

Accepted Answer

Using the Pythagorean theorem, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse (33 m), and $b$ is the shadow (23 m). Solving for $a$ (the height of the building), $a = \sqrt{c^2 - b^2} = \sqrt{33^2 - 23^2} = \sqrt{1089 - 529} = \sqrt{560}$, which is approximately 23.7 m.

Quiz 11: Radical Expressions, Equations, and Functions

Solve. -

Solve the problem. If necessary, round to the nearest tenth. -A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 15 feet and the height from the ground to the front doors is 5 feet, how long is the ramp?

Solve the problem. If necessary, round to the nearest tenth. -On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 40 m long and the shadow is 32 m, how tall is the flag pole?

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. -a = 11, c = 16

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. -a = 15, b = 20

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. -a = 20, b = 48

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. -a = 4, b = 5

Solve the problem. -A manufacturer's cost is given by , where C is the cost and n is the number of parts produced. How many parts are produced when the cost is $6200?

Solve the problem. -The distance d in miles that can be seen on the surface of the ocean is given by where h is the height in feet above the surface. How high (to the nearest foot) would a platform have to be to see a distance of 12.5 Miles?

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. -b = 1, c =

Solve the problem. If necessary, round to the nearest tenth. -One airport has a ramp sloping down from the passenger waiting area to the plane. If the distance from the waiting area to the plane is 42 feet and the height from the ground to the waiting area is 7 feet, how long is the Ramp?

Solve the problem. If necessary, round to the nearest tenth. -A car dealer advertised a big sale by stretching a string of banners from the top of the building to the edge of the driveway. If the building is 17 m high and the driveway is 49 m from the building, how long is the string of Banners?

Solve. -

Solve the problem. If necessary, round to the nearest tenth. -On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 40 m long and the tree is 32 m tall, how long is the shadow?

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. -a = 3, b = 4

Solve the problem. -A manufacturer's cost is given by , where C is the cost and n is the number of parts produced. Find the cost when 125 parts are produced.

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. -a = 15, c = 25

Find the length of the missing side of the right triangle. Round to three decimal places, if necessary. -a = 10, c = 26

Solve. -

Solve the problem. If necessary, round to the nearest tenth. -On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 33 m long and the shadow is 23 m, how tall is the building?