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(y-10)/(14z^(2))*(3z)/(10-y)
Which expression is equivalent to the product for all
y < 0 and
z < 0 ?
Choose 1 answer:
(A)
(3)/(14 z)
(B)
-(3)/(14 z)
(C)
(42z^(3))/(y^(2)-100)
(D)
(42z^(3))/(y^(2)-20 y+100)

$\frac{y-10}{14 z^{2}} \cdot \frac{3 z}{10-y}$ $\newline$ Which expression is equivalent to the product for all y<0 and z<0 ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{3}{14 z}$ $\newline$ (B) $-\frac{3}{14 z}$ $\newline$ (C) $\frac{42 z^{3}}{y^{2}-100}$ $\newline$ (D) $\frac{42 z^{3}}{y^{2}-20 y+100}$

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Compare linear and exponential growth

Full solution

Q.

\frac{y-10}{14 z^{2}} \cdot \frac{3 z}{10-y}

\newline

Which expression is equivalent to the product for all

y<0

and

z<0

?

\newline

Choose

1

answer:

\newline

(A)

\frac{3}{14 z}

\newline

(B)

-\frac{3}{14 z}

\newline

(C)

\frac{42 z^{3}}{y^{2}-100}

\newline

(D)

\frac{42 z^{3}}{y^{2}-20 y+100}

Given Expression: We are given the expression $(y-10)/(14z^{2}) \times (3z)/(10-y)$ and we need to simplify it. $\newline$ First, notice that $(y-10)$ and $(10-y)$ are negatives of each other. We can rewrite $(10-y)$ as $- (y-10)$ .
Rewrite with Negatives: Now, let's rewrite the expression with $(10-y)$ replaced by $-(y-10)$ : $\left(\frac{(y-10)}{14z^{2}}\right) \cdot \left(\frac{3z}{-(y-10)}\right)$
Cancel Common Factor: Next, we can simplify the expression by canceling out the common factor $(y-10)$ in the numerator and denominator: $\newline$ $\frac{1}{14z^{2}}$ * $\frac{3z}{-1}$
Multiply Numerators and Denominators: Now, multiply the numerators and the denominators separately: $(1 \times 3z) / (14z^{2} \times -1)$
Simplify Multiplication: Simplify the multiplication: $\frac{3z}{(-14z^{2})}$
Cancel Out $z$ : We can simplify the expression further by canceling out a $z$ from the numerator and denominator: $\frac{3}{-14z}$
Finalize with Negative Sign: Since $z$ is negative and we have a negative sign in the denominator, the overall expression is negative: $-\left(\frac{3}{14z}\right)$
Simplified Expression: We have simplified the expression to $-(\frac{3}{14z})$ , which corresponds to answer choice $(B)$ .

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