Which of the following is equivalent to the product of (2)/(3)z-(1)/(2) and 6z+12 ? Choose 1 answer: (A) (20)/(3)z+(23)/(3) (B) 9z-6 (c) 4z^(2)-6 (D) 4z^(2)+5z-6

Multiply Expressions: We need to multiply the two given expressions: (2/3)z - (1/2) and 6z + 12. We will use the distributive property to do this, which states that a(b + c) = ab + ac. So we will multiply each term in the first expression by each term in the second expression.Multiply (2/3)z by 6z: First, multiply (2/3)z by 6z: (2/3)z * 6z = (2*6/3)z^2 = 4z^2.Multiply (2/3)z by 12: Next, multiply (2/3)z by 12: (2/3)z * 12 = (2*12/3)z = 8z.Multiply (-1/2) by 6z: Now, multiply (-1/2) by 6z: (-1/2) * 6z = (-1*6/2)z = -3z.Multiply (-1/2) by 12: Finally, multiply (-1/2) by 12: (-1/2) * 12 = (-1*12/2) = -6.Add Products: Add all the products together to get the final expression: 4z^2 + 8z - 3z - 6.Combine Like Terms: Combine like terms: 4z^2 + (8z - 3z) - 6 = 4z^2 + 5z - 6.

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Which of the following is equivalent to the product of
(2)/(3)z-(1)/(2) and
6z+12 ?
Choose 1 answer:
(A)
(20)/(3)z+(23)/(3)
(B)
9z-6
(c)
4z^(2)-6
(D)
4z^(2)+5z-6

Which of the following is equivalent to the product of $\frac{2}{3} z-\frac{1}{2}$ and $6 z+12$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{20}{3} z+\frac{23}{3}$ $\newline$ (B) $9 z-6$ $\newline$ (C) $4 z^{2}-6$ $\newline$ (D) $4 z^{2}+5 z-6$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which of the following is equivalent to the product of

\frac{2}{3} z-\frac{1}{2}

and

6 z+12

\newline

Choose

1

answer:

\newline

(A)

\frac{20}{3} z+\frac{23}{3}

\newline

(B)

9 z-6

\newline

(C)

4 z^{2}-6

\newline

(D)

4 z^{2}+5 z-6

Multiply Expressions: We need to multiply the two given expressions: $(\frac{2}{3})z - (\frac{1}{2})$ and $6z + 12$ . We will use the distributive property to do this, which states that $a(b + c) = ab + ac$ . So we will multiply each term in the first expression by each term in the second expression.
Multiply $(\frac{2}{3})z$ by $6z$ : First, multiply $(\frac{2}{3})z$ by $6z$ : $(\frac{2}{3})z \times 6z = (\frac{2\times6}{3})z^2 = 4z^2$ .
Multiply $(\frac{2}{3})z$ by $12$ : Next, multiply $(\frac{2}{3})z$ by $12$ : $(\frac{2}{3})z \times 12 = (\frac{2\times12}{3})z = 8z$ .
Multiply $(-\frac{1}{2})$ by $6z$ : Now, multiply $(-\frac{1}{2})$ by $6z$ : $(-\frac{1}{2}) \times 6z = (-1\times6/2)z = -3z$ .
Multiply $(-\frac{1}{2})$ by $12$ : Finally, multiply $(-\frac{1}{2})$ by $12$ : (-\frac{$1$}{$2$}) \times \(12 = ( $-1$ \times $12$ / $2$ ) = $-6$ .
Add Products: Add all the products together to get the final expression: $4z^2 + 8z - 3z - 6$ .
Combine Like Terms: Combine like terms: $4z^2 + (8z - 3z) - 6 = 4z^2 + 5z - 6$ .