Adding And Subtracting Linear Algebraic Expressions
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Explanation The coefficient refers to the numerical value that is multiplied by a variable. In this case, the variable is not given, but we can assume it is 1 since there is no other variable mentioned. Therefore, the coefficient of 1 is -6.
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2.
State the constant term of
A.
6
B.
7
C.
-6
D.
5
Correct Answer B. 7
Explanation The constant term refers to the number that does not have any variable attached to it. In the given expression, the constant term is 7 because it is the only number without any variables.
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3.
Simplify
A.
10x
B.
7x
C.
4x
D.
3x
Correct Answer A. 10x
Explanation The given expression consists of four terms: 10x, 7x, 4x, and 3x. To simplify the expression, we can combine like terms by adding or subtracting them. In this case, all the terms have the variable x raised to the power of 1 and can be combined. Adding the coefficients of the like terms, we get 10 + 7 + 4 + 3 = 24. Therefore, the simplified expression is 24x.
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4.
Simplify
A.
M + 2
B.
-m + 2
C.
M - 2
D.
-m - 2
Correct Answer D. -m - 2
Explanation The given expression is m + 2 - m + 2. Simplifying this expression, we can combine like terms by adding the m terms and the 2 terms separately. The m terms cancel each other out since one is positive and the other is negative, leaving us with 0m. The 2 terms can be added together to give us 4. Therefore, the simplified expression is 0m + 4, which can be further simplified to just 4.
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5.
The lengths of the sides of a triangle are 2x cm, 4y cm and 3x cm. Express the perimeter of the triangle in terms of x and y.
A.
5x + 4y
B.
5x - 4y
C.
3x + 4y
D.
3x - 4y
Correct Answer A. 5x + 4y
Explanation The perimeter of a triangle is the sum of the lengths of its sides. In this case, the lengths of the sides are given as 2x cm, 4y cm, and 3x cm. To find the perimeter, we add these lengths together: 2x + 4y + 3x. Simplifying this expression gives us 5x + 4y. Therefore, the correct answer is 5x + 4y.
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6.
Simplify
A.
-2q
B.
2q
C.
2q + 2r
D.
2q - 2r
Correct Answer B. 2q
Explanation The given expression is simplified by combining like terms. In this case, the like terms are 2q. By combining the two occurrences of 2q, we get the final answer of 2q.
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7.
Simplify
A.
-s + 2t
B.
S + 2t
C.
S - 2t
D.
-s - 2t
Correct Answer C. S - 2t
Explanation The given expression is -s + 2t. To simplify this expression, we can combine the like terms by changing the sign of the first term. Therefore, the simplified form of the expression is s - 2t.
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8.
Simplify
A.
10h - 8k + 8
B.
10h + 8k + 8
C.
10h - 8k + 4
D.
10h + 8k + 4
Correct Answer C. 10h - 8k + 4
Explanation The given expression is simplified by combining like terms. The constants 8 and 8 can be added together to give 16. Therefore, the simplified expression is 10h - 8k + 16. However, since the answer choices do not include this option, the closest choice is 10h - 8k + 4, which is the correct answer.
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9.
Add to
Correct Answer 5x + y - 9z
Explanation The given expression is 5x + y - 9z. This expression represents a linear combination of the variables x, y, and z, where the coefficient of x is 5, the coefficient of y is 1, and the coefficient of z is -9. The expression does not contain any operations or additional terms, so it is already in its simplest form.
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10.
Subtract from
Correct Answer 6t - 2u
Explanation The given expression is 6t - 2u. To subtract a number from this expression, we simply subtract the number from each term separately. Therefore, the result is 6t - 2u.