Pre-algebra Chapter 9 Test Munden

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.

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.

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.

not-available-via-ai

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.

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.

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.

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.

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.

not-available-via-ai

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.

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.

not-available-via-ai

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.

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.

not-available-via-ai

not-available-via-ai

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.

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.

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.

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.

not-available-via-ai

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.

not-available-via-ai