1.
Find all the solutions to the equation
Correct Answer
A. X = 8, x = -8
Explanation
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.
2.
True or False? 3.14 is a rational number.
Correct Answer
A. True
Explanation
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.
3.
True or False? is an integer.
Correct Answer
B. False
Explanation
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.
4.
True or False? All rational numbers are also irrational numbers.
Correct Answer
B. False
Explanation
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.
5.
True or False? All rational numbers are integers.
Correct Answer
B. False
Explanation
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.
6.
True or False? All integers are also rational numbers.
Correct Answer
A. True
Explanation
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.
7.
True or False? All rational numbers, irrational numbers, and integers, are real numbers.
Correct Answer
A. True
Explanation
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.
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?
Correct Answer
A. About 24 feet
Explanation
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 âˆš(16^2 + 18^2) = âˆš(256 + 324) = âˆš580 â‰ˆ 24 feet.
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?
Correct Answer
A. About 16.6 inches
Explanation
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.
10.
What is the hypotenuse in the right triangle below?
Correct Answer
D. Not given
Explanation
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.
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.
Correct Answer
B. About 707 feet
Explanation
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 = âˆš((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 = âˆš((8-3)^2 + (6-1)^2) = âˆš(5^2 + 5^2) = âˆš(50 + 25) = âˆš75. Simplifying further, we get: distance â‰ˆ 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.
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.
Correct Answer
A.
13.
Using the 45-45-90 triangle shown, what is the length of the hypotenuse?
Correct Answer
D. 7.07 cm
Explanation
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.
14.
Using the 30-60-90 triangle shown, what is the length of the hypotenuse?
Correct Answer
D. 6.9 inches
Explanation
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.
15.
Using the 30-60-90 triangle shown what is the length of the bottom missing leg?
Correct Answer
D. 6.9 inches
Explanation
In a 30-60-90 triangle, the ratio of the lengths of the sides is 1:âˆš3:2. 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.
16.
Using the triangle shown below, which of the following ratio's is true? Use SOH - CAH - TOA
Correct Answer
B.
17.
Using the triangle shown below which of the following ratio's is true? Use SOH - CAH - TOA
Correct Answer
A.
18.
Using the triangle shown below which of the following ratio's is true? Use SOH - CAH - TOA
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?
Correct Answer
A. About 369 feet
Explanation
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.
20.
What is the area of the triangle shown below?
Correct Answer
A. About 39 square inches
21.
What is the perimeter of the triangle shown below?
Correct Answer
D. Not given
22.
Find all the solutions to the equation
Correct Answer
B. Y = 10, y = -10
Explanation
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.
23.
Find all the solutions to the equation
Correct Answer
C. No Solution
Explanation
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.
24.
Find all solutions to the equation
Correct Answer
D. Not given