Pre-algebra Chapter 9 Test Munden
(69).webp "Pre-algebra Chapter 9 Test Munden - Quiz")
Right Triangles, square roots, and real numbers
Questions and Answers
- 1.
Find all the solutions to the equation
- A.
X = 8, x = -8
- B.
X = 7.35, x = -7.35
- C.
X = 11.22, x = -11.22
- D.
Not given
Correct Answer
A. X = 8, x = -8Explanation
The given answer states that the solutions to the equation are x = 8 and x = -8. This means that when the equation is solved, the value of x can be either 8 or -8.Rate this question:
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- 2.
True or False? 3.14 is a rational number.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
A rational number is defined as a number that can be expressed as the quotient or fraction of two integers. In the case of 3.14, it can be expressed as 314/100, which is the quotient of the integers 314 and 100. Therefore, 3.14 is a rational number.Rate this question:
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- 3.
True or False? is an integer.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The statement "True or False? is an integer" is false. "True" and "False" are not integers, but rather boolean values. Integers are whole numbers that can be positive, negative, or zero, while boolean values are used to represent true or false conditions.Rate this question:
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- 4.
True or False? All rational numbers are also irrational numbers.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The statement "All rational numbers are also irrational numbers" is false. Rational numbers can be expressed as a fraction of two integers, whereas irrational numbers cannot be expressed as a fraction and have non-repeating, non-terminating decimal representations. Therefore, rational and irrational numbers are mutually exclusive categories.Rate this question:
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- 5.
True or False? All rational numbers are integers.
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The statement "All rational numbers are integers" is false. Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Integers are whole numbers, including both positive and negative numbers, but they do not include fractions or decimals. Therefore, not all rational numbers are integers as they can include fractions and decimals.Rate this question:
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- 6.
True or False? All integers are also rational numbers.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
All integers can be expressed as a fraction where the denominator is 1. Since rational numbers are defined as the ratio of two integers, it follows that all integers are also rational numbers. Therefore, the statement "All integers are also rational numbers" is true.Rate this question:
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- 7.
True or False? All rational numbers, irrational numbers, and integers, are real numbers.
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
All rational numbers, irrational numbers, and integers are real numbers because the set of real numbers includes all numbers that can be expressed as a fraction, numbers that cannot be expressed as a fraction, and whole numbers. Therefore, it is true that all rational numbers, irrational numbers, and integers are real numbers.Rate this question:
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- 8.
The A-frame below measures 16 feet high. The house measures 36 feet from one side to the other. What is the diagonal length of the roof?
- A.
About 24 feet
- B.
About 39.4 feet
- C.
About 34 feet
- D.
Not given
Correct Answer
A. About 24 feetExplanation
The diagonal length of the roof can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides. In this case, the height of the A-frame is one side (16 feet) and half of the house's width is the other side (18 feet). Using the theorem, we can calculate the diagonal length as √(16^2 + 18^2) = √(256 + 324) = √580 ≈ 24 feet.Rate this question:
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- 9.
The toy crane shown in the photo has a boom length (the length of the crane's arm) of 26 inches. If the tip of the boom is 20 inches above the ground, then how far out will the crane reach?
- A.
About 16.6 inches
- B.
About 276 inches
- C.
About 32.8 inches
- D.
Not given
Correct Answer
A. About 16.6 inchesExplanation
The crane's boom length is given as 26 inches, and the tip of the boom is 20 inches above the ground. To find how far out the crane will reach, we can use the Pythagorean theorem. The horizontal distance can be represented by the base of a right triangle, while the vertical distance can be represented by the height. By using the theorem, we can calculate the horizontal distance as the square root of (26^2 - 20^2), which is approximately 16.6 inches. Therefore, the crane will reach about 16.6 inches out.Rate this question:
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- 10.
What is the hypotenuse in the right triangle below?
- A.
50 feet
- B.
70 feet
- C.
2500 inches
- D.
Not given
Correct Answer
D. Not givenExplanation
The question does not provide any information or measurements about the sides of the right triangle. Therefore, it is not possible to determine the length of the hypotenuse.Rate this question:
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- 11.
You are part of a design team creating a new park for the city. In your design, you use a coordinate plane to represent the park. On your map, the locations of the bathroom is at (3,1). The location of a pavilion on the other side of the park is (8,6). Each unit on your map is 100 feet. How far apart are the bathrooms? Use the distance formula given.
- A.
About 7.1 feet
- B.
About 707 feet
- C.
About 283 feet
- D.
Not given
Correct Answer
B. About 707 feetExplanation
The distance between the bathroom and the pavilion can be calculated using the distance formula, which is derived from the Pythagorean theorem. The formula is: distance = √((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the bathroom are (3,1) and the coordinates of the pavilion are (8,6). Plugging these values into the formula, we get: distance = √((8-3)^2 + (6-1)^2) = √(5^2 + 5^2) = √(50 + 25) = √75. Simplifying further, we get: distance ≈ 8.66. Since each unit on the map represents 100 feet, we multiply the distance by 100 to get the final answer of about 707 feet.Rate this question:
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- 12.
You are part of a design team creating a new park for the city. In your design you use a coordinate plane to represent the park. On your map the locations of the bathroom is at (31). The location of a pavilion on the other side of the park is (86). What is the halfway (midpoint) between these two locations? Use the midpoint formula given.
- A.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- B.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- C.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- D.
Not given
Correct Answer
A. -
- 13.
Using the 45-45-90 triangle shown, what is the length of the hypotenuse?
- A.
5 cm
- B.
10 cm
- C.
8.66 cm
- D.
7.07 cm
Correct Answer
D. 7.07 cmExplanation
The length of the hypotenuse in a 45-45-90 triangle is equal to the length of either of the other two sides multiplied by the square root of 2. In this case, the length of one of the other sides is 5 cm, so the length of the hypotenuse is 5 cm multiplied by the square root of 2, which is approximately 7.07 cm.Rate this question:
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- 14.
Using the 30-60-90 triangle shown, what is the length of the hypotenuse?
- A.
8 inches
- B.
11.31 inches
- C.
13.9 inches
- D.
6.9 inches
Correct Answer
D. 6.9 inchesExplanation
The length of the hypotenuse can be found using the properties of a 30-60-90 triangle. In a 30-60-90 triangle, the length of the hypotenuse is always twice the length of the shorter leg. Since the shorter leg is given as 6.9 inches, the length of the hypotenuse would be 2 times 6.9 inches, which is equal to 13.8 inches.Rate this question:
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- 15.
Using the 30-60-90 triangle shown what is the length of the bottom missing leg?
- A.
4 inches
- B.
8 inches
- C.
5.7 inches
- D.
6.9 inches
Correct Answer
D. 6.9 inchesExplanation
In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:√3:2. The given triangle is a 30-60-90 triangle, so the length of the bottom missing leg can be found by multiplying the length of the known leg (4 inches) by 2. Therefore, the length of the bottom missing leg is 4 inches * 2 = 8 inches.Rate this question:
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- 16.
Using the triangle shown below, which of the following ratio's is true? Use SOH - CAH - TOA
- A.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- B.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- C.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- D.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
Correct Answer
B. -
- 17.
Using the triangle shown below which of the following ratio's is true? Use SOH - CAH - TOA
- A.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- B.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- C.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- D.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
Correct Answer
A. -
- 18.
Using the triangle shown below which of the following ratio's is true? Use SOH - CAH - TOA
- A.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- B.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- C.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
- D.
![Pre-algebra Chapter 9 Test Munden - Quiz]()
Correct Answer
B. -
- 19.
You want to measure the height of the cell phone tower shown. You measure the base angle to be 72 degrees while standing 120 feet from the bottom of the tower. How tall is the tower?
- A.
About 369 feet
- B.
About 3.08 feet
- C.
About 37 feet
- D.
Not given
Correct Answer
A. About 369 feetExplanation
To find the height of the tower, we can use trigonometry. The base angle of 72 degrees and the distance of 120 feet form a right triangle with the height of the tower as the opposite side. We can use the tangent function to find the height. tan(72) = height/120. Rearranging the equation, we get height = 120 * tan(72). Calculating this, we find that the height is about 369 feet.Rate this question:
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- 20.
What is the area of the triangle shown below?
- A.
About 39 square inches
- B.
About 78 square inches
- C.
About 34.5 square inches
- D.
Not given
Correct Answer
A. About 39 square inches -
- 21.
What is the perimeter of the triangle shown below?
- A.
About 39 inches
- B.
About 78 inches
- C.
About 30 inches
- D.
Not given
Correct Answer
D. Not given -
- 22.
Find all the solutions to the equation
- A.
Y = 10
- B.
Y = 10, y = -10
- C.
Y = 17.23, y = -17.23
- D.
Not given
Correct Answer
B. Y = 10, y = -10Explanation
The given equation y = 10 has two solutions: y = 10 and y = -10. This means that when y is equal to 10, the equation is satisfied, and when y is equal to -10, the equation is also satisfied. Therefore, both y = 10 and y = -10 are valid solutions to the equation.Rate this question:
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- 23.
Find all the solutions to the equation
- A.
A=4.58, a = -4.58
- B.
A=5.39, a = -5.39
- C.
No Solution
- D.
Not given
Correct Answer
C. No SolutionExplanation
The given equation is a=4.58, a=-4.58, a=5.39, a=-5.39. However, it is not possible for a single variable to have two different values simultaneously. Therefore, there are no solutions to the equation.Rate this question:
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- 24.
Find all solutions to the equation
- A.
N=3, n= -3
- B.
N = 5.1, n = - 5.1
- C.
N = 8.8, n = -8.8
- D.
Not given
Correct Answer
D. Not given -
.png "The A-frame below measures 16 feet high. The house measures 36 feet from one side to the other. What is the diagonal length of the roof?")
.jpg "The toy crane shown in the photo has a boom length (the length of the crane's arm) of 26 inches. If the tip of the boom is 20 inches above the ground, then how far out will the crane reach?")
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Mar 11, 2024Quiz Edited by
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Jan 11, 2012Quiz Created by
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