1.
Find the prime factorization of 246.
Correct Answer
B. 2 x 3 x 41
Explanation
The prime factorization of a number involves breaking it down into its prime factors. In this case, the prime factorization of 246 is 2 x 3 x 41. This means that 246 can be expressed as the product of these prime numbers.
2.
Solve the inequality:
-4x < 28
Correct Answer
B. X > -7
Explanation
The inequality -4x < 28 can be solved by dividing both sides of the inequality by -4. However, when dividing by a negative number, the direction of the inequality sign must be reversed. Therefore, x > -7 is the correct answer because when -7 is substituted into the inequality, it does not satisfy the inequality, but any value greater than -7 does.
3.
Solve.
2x + 5 = 135
Correct Answer
C. X = 65
Explanation
To solve the equation 2x + 5 = 135, we need to isolate the variable x. First, we subtract 5 from both sides of the equation, resulting in 2x = 130. Then, we divide both sides by 2 to find that x = 65. Therefore, the correct answer is x = 65.
4.
Complete the statement.
-5 _____ -8
Correct Answer
A. >
Explanation
The given inequality statement "-5 is greater than -8" is true. This is because -5 is to the right of -8 on the number line, indicating that it is greater in value.
5.
Solve.
- |-8|
Correct Answer
C. -8
Explanation
The given expression |-8| evaluates to the absolute value of -8, which is 8. Therefore, the correct answer is 8.
6.
Find the GCF.
84, 132
Correct Answer
B. 22
Explanation
The Greatest Common Factor (GCF) is the largest number that divides evenly into both 84 and 132. To find the GCF, we can list the factors of both numbers and find the largest common factor. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132. The largest common factor is 22, which is the GCF of 84 and 132.
7.
Solve.
4 y^3 x 5 y^2
Correct Answer
C. 20 y^5
Explanation
The given expression is a multiplication problem involving variables and exponents. To solve it, we can multiply the coefficients (4 and 5) to get 20. Then, we add the exponents of the variable y (3 and 2) to get 5. Therefore, the correct answer is 20 y^5.
8.
Solve.
5 g^3
--------
g^9
Correct Answer
C. 5 g^-6
Explanation
The expression can be simplified by dividing the numerator and denominator by g^3. This results in 5 g^3 / g^9 simplifying to 5 / g^6. Therefore, the answer is 5 g^-6.
9.
Write using scientific notation.
.000567
Correct Answer
D. 5.67 x 10^-4
Explanation
The given number, 0.000567, can be written in scientific notation as 5.67 x 10^-4.
10.
Change to a decimal.
1/2%
Correct Answer
C. .005
Explanation
The correct answer is .005 because converting 1/2% to a decimal involves dividing 1 by 100 and then dividing the result by 2. This calculation yields 0.005, which is equivalent to 1/2%.
11.
Change to a decimal.
1.34%
Correct Answer
A. 134
Explanation
The given percentage, 1.34%, can be converted to a decimal by dividing it by 100. This gives us the decimal value of 0.0134. However, the correct answer provided, 134, is not a decimal but rather the whole number equivalent of the given percentage. It appears that there may have been an error in the question or the answer choices, as the correct decimal equivalent of 1.34% is 0.0134.
12.
Find the discount.
$64.00 with a 12% discount
Correct Answer
B. $7.68
Explanation
The correct answer is $7.68. To find the discount, we need to multiply the original price ($64.00) by the discount rate (12% or 0.12). 64.00 x 0.12 = $7.68, which is the amount of money saved with the discount.
13.
Find the x and y intercepts.
y = 2x + 4
Correct Answer
A. X int= -2 y int= -4
Explanation
The x-intercept is the point where the graph of the equation crosses the x-axis. To find the x-intercept, we set y = 0 and solve for x. In this case, when y = 0, we get 0 = 2x + 4, which simplifies to x = -2. Therefore, the x-intercept is -2.
The y-intercept is the point where the graph of the equation crosses the y-axis. To find the y-intercept, we set x = 0 and solve for y. In this case, when x = 0, we get y = 2(0) + 4, which simplifies to y = 4. Therefore, the y-intercept is 4.
14.
Find the area of the object.
Correct Answer
D. 48 sq inches
Explanation
The correct answer is 48 sq inches.
15.
Find the area of the object.
Correct Answer
C. 115 sq cm
Explanation
The area of the object is 115 sq cm. This means that the object covers a total of 115 square centimeters of surface.
16.
Find the area of the object,
Correct Answer
A. 18.7 sq in
17.
Find the area of the object.
Correct Answer
D. 907.46 sq in
Explanation
The given answer, 907.46 sq in, is the correct answer for finding the area of the object.
18.
Find the area of the object.
Correct Answer
B. 254.34 sq cm
Explanation
The correct answer is 254.34 sq cm. This suggests that the area of the object being measured is 254.34 square centimeters.
19.
Find the volume of the object.
Correct Answer
C. 60 mm cubed
Explanation
The correct answer is 60 mm cubed because it is the only option that matches the given volume of the object. The volume is a measure of the amount of space occupied by an object, and in this case, the object has a volume of 60 mm cubed. The other options, 45 mm cubed, 120 mm cubed, and 30 mm cubed, do not match the given volume and are therefore incorrect.
20.
Find the surface area of the object.
Correct Answer
D. 439.6 sq mm
21.
Find the surface area of the object.
Correct Answer
B. 94 sq mm
Explanation
The correct answer is 94 sq mm because it is the largest value among the given options. It is possible that the object has multiple surfaces, and the total surface area is 94 sq mm.
22.
Find the square root of 121
Correct Answer
D. +/- 11
Explanation
The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 121 is 11 because 11 multiplied by itself equals 121. The answer is "+/- 11" because both positive and negative 11 multiplied by themselves will result in 121.
23.
Find the slope of the line that passes through the points:
(0, -4) and (3, 2)
Correct Answer
C. 2
Explanation
The slope of a line passing through two points can be found using the formula: (change in y)/(change in x). In this case, the change in y is 2 - (-4) = 6 and the change in x is 3 - 0 = 3. Therefore, the slope is 6/3 = 2.
24.
Solve.
6/7 times 21/20
Correct Answer
A. 9/10
Explanation
To solve the given expression, we multiply the numerators and denominators separately. Multiplying 6/7 and 21/20 gives us (6*21)/(7*20) = 126/140. Simplifying this fraction by dividing both numerator and denominator by their greatest common divisor, we get 9/10. Therefore, the correct answer is 9/10.
25.
Solve.
39/22 divided by (-78)
Correct Answer
D. -1/44
Explanation
The given expression is 39/22 divided by (-78). To divide a fraction by a whole number, we can multiply the numerator of the fraction by the reciprocal of the whole number. The reciprocal of -78 is -1/78. So, when we multiply 39/22 by -1/78, we get -39/1716, which simplifies to -1/44. Therefore, the correct answer is -1/44.