1.
Evaluate for x = 11
x + 4
Correct Answer
C. 15
Explanation
The correct answer is 15. To evaluate an expression for a given value of a variable, we need to substitute the value in place of the variable and simplify the expression. For example, if x = 11, then x + 4 becomes 11 + 4, which is equal to 15. We can write this using LaTeX as follows:
x+4=11+4=15
2.
Evaluate for n = 0: 2 (4 + n) - 5
Correct Answer
D. 3
Explanation
When evaluating the expression for n = 0, we substitute 0 for n in the expression. Therefore, the expression becomes 2(4 + 0) - 5. Simplifying further, we have 2(4) - 5, which is equal to 8 - 5. Finally, subtracting 5 from 8 gives us the answer 3.
3.
Evaluate for x = 8 and y = 10: 3x + 2y
Correct Answer
C. 44
Explanation
The expression 3x + 2y can be evaluated by substituting x = 8 and y = 10. Plugging in these values, we get 3(8) + 2(10) which simplifies to 24 + 20. Adding these two numbers gives us the final result of 44.
4.
Write an algebraic expression for 77 more than the product of 2 and u
Correct Answer
C. 77 + 2u.
Explanation
The question asks for an algebraic expression for "77 more than the product of 2 and u". This means we need to multiply 2 and u, and then add 77 to the result. The expression that represents this is 77 + 2u.
5.
Determine the result of the expression: | -10 - (|4| + 1) |
Correct Answer
A. 15.
Explanation
Let's break down the expression step by step:
Absolute Value of 4: The absolute value of 4 is simply 4 because the absolute value of a positive number is the number itself.
Absolute Value of -10: The absolute value of -10 is 10 because it's the positive distance from zero to -10 on the number line.
Now, we have the expression: | -10 - (|4| + 1) |
Inside the innermost parentheses, we calculate |4| + 1, which is 4 + 1 = 5.
Then, we have -10 - 5 inside the outer parentheses, which is -15.
Finally, we take the absolute value of -15, which is 15.
So, the absolute value of -10 minus the absolute value of 4 plus 1 is indeed 15.
6.
Which is bigger? -14 _____ 0
Correct Answer
A. -14 < 0
Explanation
In the given question, we are comparing -14 with 0. 0 is bigger than any negative number. Thus, -14 is less than 0 and the correct answer is A.
7.
What is: 6 + (-4)
Correct Answer
A. 2.
Explanation
The sum of 6 and -4 is equal to 2. When adding a positive number with a negative number, we subtract the absolute value of the smaller number from the absolute value of the larger number, and then assign the sign of the larger number to the result. In this case, the absolute value of 6 is larger than the absolute value of -4, so we subtract 4 from 6, resulting in 2.
8.
Evaluate for m = -5: m + 7
Correct Answer
C. 2.
Explanation
When evaluating the expression for m = -5, we substitute -5 into the expression m + 7. So, -5 + 7 equals 2. Therefore, the correct answer is 2.
9.
What is: 8 - (-4)
Correct Answer
D. 12.
Explanation
The expression 8 - (-4) can be simplified by changing the subtraction of a negative number to addition. So, it becomes 8 + 4, which equals 12.
10.
Evaluate for m = -8: 9 - m
Correct Answer
B. 17.
Explanation
When evaluating for m = -8, we substitute -8 into the expression 9 - m. This gives us 9 - (-8), which simplifies to 9 + 8. Adding 9 and 8 gives us 17. Therefore, the answer is 17.
11.
What is: -7 (-4) (3)
Correct Answer
D. 84.
Explanation
The given expression is -7 (-4) (3). To simplify this expression, we first multiply -4 and 3, which gives us -12. Then, we multiply -7 and -12, which gives us 84. Therefore, the correct answer is 84.
12.
What is: [-3 (4) (2)]/-8
Correct Answer
C. 3.
Explanation
The given expression can be simplified by performing the division first. Dividing -3 by -8 gives a positive value of 3/8. The expression (4) and (2) are in parentheses, which indicate multiplication. Multiplying 3/8 by 4 gives 3/2, and multiplying 3/2 by 2 gives 3. Therefore, the value of the expression is 3.
13.
Is x equal to 10, 12, or 25?: x + 6 = 18
Correct Answer
B. 12.
Explanation
The equation x + 6 = 18 can be solved by subtracting 6 from both sides of the equation to isolate x. This gives us x = 12. Therefore, the correct answer is 12.
14.
Solve. 1785 = t - (-836)
Correct Answer
B. 949
Explanation
The equation given is 1785 = t - (-836). To solve for t, we need to simplify the equation. The negative sign before -836 means that it is subtracted from t. To simplify, we can remove the parentheses and change the subtraction to addition by changing the sign of -836. This gives us 1785 = t + 836. To isolate t, we subtract 836 from both sides of the equation. This gives us t = 1785 - 836 = 949. Therefore, the correct answer is 949.
15.
Solve. -7x = 105
Correct Answer
D. None of the above.
Explanation
The given equation is -7x = 105. To solve for x, we need to isolate the variable by dividing both sides of the equation by -7. This gives us x = -105/7, which simplifies to x = -15. None of the answer choices -12, -13, -14, are equal to -15, so the correct answer is None of the above.
16.
Translate: The quotient of a number t and 7, plus 2, is -4.
Correct Answer
C. T/7 + 2 = -4.
Explanation
The correct answer is "t/7 + 2 = -4" because the given information states that the quotient of a number t and 7, plus 2, is -4. This can be translated into an equation as t/7 + 2 = -4.
17.
Write as a decimal: 1/4
Correct Answer
C. 0.25.
Explanation
The decimal representation of 1/4 is 0.25. To convert a fraction to a decimal, divide the numerator (1) by the denominator (4). In this case, 1 divided by 4 equals 0.25. Therefore, the correct answer is 0.25.
18.
Write as a fraction. Simplify!: 0.4
Correct Answer
B. 2/5.
Explanation
The correct answer is 2/5 because when we simplify the fraction 4/10, we divide both the numerator and denominator by their greatest common factor, which is 2. 4 divided by 2 is 2, and 10 divided by 2 is 5, so the simplified fraction is 2/5.
19.
Write as a fraction. Simplify!: 0.55555...
Correct Answer
A. 5/9
Explanation
To express the repeating decimal 0.55555... as a fraction and simplify it, we can set up the following equation:
x = 0.55555...
Now, we'll subtract this repeating decimal from 10x, which should eliminate the repeating part:
10x - x = 5.55555... - 0.55555...
9x = 5
Now, divide both sides by 9 to solve for x:
x = 5/9
So, the repeating decimal 0.55555... is equal to the fraction 5/9.
20.
Which is greater?: -3/7 _____ -0.375
Correct Answer
A. -3/7 < -0.375
Explanation
The answer is -3/7 < -0.375. This is because -3/7 is a fraction that is less than -0.375, which is a decimal. When comparing fractions and decimals, we can convert the fraction to a decimal to easily compare them. In this case, -3/7 as a decimal is approximately -0.429, which is greater than -0.375. Therefore, -3/7 is less than -0.375.