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3 years ago

Write an equation for the translation of y = |x|. 13 units down

1 answer:

7 0

The idea for transitions for an equation like this is
$y = m|x - h| + k$
where m = slope
h = how much left or right (note the negative)
k = how much up or down

moving 13 down would mean
k = -13

so
$y = |x| - 13$
D. would be your answer

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Divide f(x) by d(x), and write a summary statement in the form indicated.

Mandarinka [93]

Answer:

The correct option is B) $f(x) =(x^2+1)(x^2+4x+5)$

Step-by-step explanation:

Consider the provided function.

$f(x) = x^4 + 4x^3 + 6x^2 + 4x + 5$ and $d(x) = x^2+1$

We need to divide f(x) by d(x)

As we know: Dividend = Divisor × Quotient + Remainder

In the above function f(x) is dividend and divisor is d(x)

Divide the leading term of the dividend by the leading term of the divisor: $\frac{x^4}{x^2}=x^2$

Write the calculated result in upper part of the table.

Multiply it by the divisor: $x^2(x^2+1)=x^4+x^2$

Now Subtract the dividend from the obtained result:

$(x^4 + 4x^3 + 6x^2 + 4x + 5)-(x^4-x^2)=4x^3+5x^2+4x+5$

Again divide the leading term of the obtained remainder by the leading term of the divisor: $\frac{4x^3}{x^2}=4x$

Write the calculated result in upper part of the table.

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$(4x^3+5x^2+4x+5)-(4x^3+4x)=5x^2+5$

Divide the leading term of the obtained remainder by the leading term of the divisor: $\frac{5x^2}{x^2}=5$

Multiply it by the divisor: $5(x^2+1)=5x^2+5$

Subtract the dividend:

$(5x^2+5)-(5x^2+5)=0$

Therefore,

Dividend = $x^4 + 4x^3 + 6x^2 + 4x + 5$

Divisor = $x^2+1$

Quotient = $x^2+4x+5$

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Dividend = Divisor × Quotient + Remainder

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Hence, the correct option is B) $f(x) =(x^2+1)(x^2+4x+5)$

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Answer:

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