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If
(20 y+5)(4y-30)=80y^(2)+by-150 for all values of
y where
b is a constant, then which of the following is the value of
b ?
Choose 1 answer:
(A) -580
(B) -40
(C) 0
(D) 620
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If $(20 y+5)(4y-30)=80y^{2}+by-150$ for all values of $y$ where $b$ is a constant, then which of the following is the value of $b$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-580$ $\newline$ (B) $-40$ $\newline$ (C) $0$ $\newline$ (D) $620$ $\newline$

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Experimental probability

Full solution

Q. If

(20 y+5)(4y-30)=80y^{2}+by-150

for all values of

y

where

b

is a constant, then which of the following is the value of

b

?

\newline

Choose

1

answer:

\newline

(A)

-580

\newline

(B)

-40

\newline

(C)

0

\newline

(D)

620

\newline

Expand Left Side: First, we need to expand the left side of the equation using the distributive property (also known as the FOIL method for binomials). $\newline$ $(20y+5)(4y-30) = 20y \times 4y + 20y \times (-30) + 5 \times 4y + 5 \times (-30)$
Perform Multiplication: Now, let's perform the multiplication for each term. $\newline$ $20y \times 4y = 80y^2$ $\newline$ $20y \times (-30) = -600y$ $\newline$ $5 \times 4y = 20y$ $\newline$ $5 \times (-30) = -150$ $\newline$ So, the expanded form is $80y^2 - 600y + 20y - 150$ .
Combine Like Terms: Next, we combine like terms on the left side of the equation. $80y^2 - 600y + 20y - 150 = 80y^2 - 580y - 150$
Compare Coefficients: Now, we compare the coefficients of the $y$ terms from the expanded left side with the right side of the given equation. $\newline$ The coefficient of $y$ on the left side is $-580$ , and on the right side, it is represented by $b$ . $\newline$ Therefore, $b = -580$ .
Check Answer Choices: We can now check the answer choices to see which one matches our value for $b$ . $\text{(A)}$ $-580$ $\text{(B)}$ $-40$ $\text{(C)}$ $0$ $1$ $2$ The correct answer is $\text{(A)}$ $-580$ .

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