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4 years ago

The polynomial x3 + 4x2 – 9x – 36 has 4 terms. Use factoring by grouping to find the correct factorization.

Mathematics

2 answers:

adell [148]4 years ago

6 0

lesya [120]4 years ago

5 0

<span>x^3 + 4x^2 – 9x – 36</span>
Factor out common terms in the first two terms and the last two terms
x^2 (x + 4) - 9 (x + 4)
factor out the common term (x + 4)
(x + 4) (x^2 - 9)
Rewrite
(x + 4) ( x^2 - 3^2)
Use the difference of squares
(x + 4) (x + 3) (x - 3)

Hope this helps :)

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What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 27 − x^2? show your

LUCKY_DIMON [66]

Answer:

Option B.

Step-by-step explanation:

The given curve is

$y=27-x^2$

We need to find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve $y=27-x^2$ .

Let the vertex in quadrant I be (x,y), then the vertex in quadrant II is (-x,y) .

Length of the rectangle = 2x

Width of the rectangle = y

Area of a rectangle is

$Area=Length\times width$

$Area=2x\times y$

Substitute the value of y from the given equation.

$Area=2x(27-x^2)$

$A=54x-2x^3$ .... (1)

Differentiate with respect to x.

$\frac{dA}{dx}=54-6x^2$

Equate $\frac{dA}{dx}=0$ , to find the critical points.

$0=54-6x^2$

$6x^2=54$

Divide both sides by 6.

$x^2=9$

$x=\pm 3$

The value of x can not be negative because side length can not be negative.

Substitute x=3 in equation (1).

$A=54(3)-2(3)^3$

$A=162-54$

$A=108$

The area of the largest rectangle is 108 square units.

Therefore, the correct option is B.

7 0

3 years ago

I really need help!! God bless you.

Nastasia [14]

Ok so 65 percent of 10,000 is 6500. This means that she has to get the other 3500 herself. Since she has a year to save divide 3500 by 12 for each month of the year which is equal to $291.67. Then simply round up to get your answer which is A. $292.

Hope this helped and good luck

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4 years ago

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Amiraneli [1.4K]

Answer:

252 in.

Step-by-step explanation:

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3 years ago

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Setler79 [48]

Answer:

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