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1 year ago

Factor –7x3 + 21x2 + 3x – 9 by grouping. What is the resulting expression?

Mathematics

1 answer:

Vladimir79 [104]1 year ago

3 0

Answer:

$(-7x^2+3)(x-3)$

Step-by-step explanation:

To factor by grouping, take the first two numbers and last two numbers. First, look at the first two numbers.

$-7x^3+21x^2$

Each number can be divided by 7 and x^2, so pull it out as a GCF.

$-7x^3+21x^2 = -7x^2(x-3)$

Next, look at the last two numbers.

$3x-9$

Each number can be divided by 3, so we will pull it out as a GCF.

$3x-9=3(x-3)$

Add the two results together.

$-7x^2(x-3)+3(x-3)$

When factoring by grouping, the two expressions in the parenthesis should always be the same. In this case, it is x-3.

Combine the numbers outside and inside parenthesis.

$(-7x^2+3)(x-3)$

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Solve 5/3x + 1/3x = 13 1/3 + 8/3x then identify x.

belka [17]

After solving $\frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x$ we get value of x = -20

Step-by-step explanation:

We need to solve the fractions and find value of x.

The given fraction is:

$\frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x$

Solving:

$\frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x\\\frac{5}{3}x+\frac{1}{3}x=\frac{40}{3}+\frac{8}{3}x\\ Subtract\,\,\frac{8}{3}x\,\,on\,\,both\,\,sides:\\ \frac{5}{3}x+\frac{1}{3}x-\frac{8}{3}x=\frac{40}{3}+\frac{8}{3}x-\frac{8}{3}x\\Simplifying:\\ \frac{5x+1x-8x}{3}=\frac{40}{3}\\ \frac{-2x}{3}=\frac{40}{3}\\Multiply\,\,both\,\,sides\,\,by\,\,3\\-2x=40\\x=\frac{40}{-2}\\x=-20$

So, After solving $\frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x$ we get value of x = -20

Keywords: Solving fractions

Learn more about Solving fractions at:

#learnwithBrainly

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2 years ago

On January 1, year 1, Klondike issued 10-year bonds with a stated rate of 10% and a face amount of $100,000. The bonds pay inter

Nataliya [291]

Answer:

91,000

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

The value of the x- intercept for the graph of 4x-5y=40 is

andrew-mc [135]

4x - 5y = 40

4x = 40 + 5y
x = 10 + 5/4y

The x intercept is 10.

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1 year ago

Which will result in a difference of squares? (negative 7 x + 4)(negative 7 x + 4) (negative 7 x + 4)(4 minus 7 x) (negative 7 x

nevsk [136]

Answer:

(negative 7 x + 4)(negative 7 x minus 4)

Step-by-step explanation:

Consider two real numbers a and b. A difference of squares involving a and b is usually given as;

$a^{2}-b^{2}$

The difference of the two squares above can be factored to yield;

$(a-b)(a+b)$

This implies that in order to have the difference of squares we must have a product involving the difference and the sum of the numbers.

The expression;

(negative 7 x + 4)(negative 7 x minus 4) can also be written as ( 4 - 7x) ( -4 - 7x)

( 4 - 7x) ( -4 - 7x) = ( 4 - 7x) (-1( 4 + 7x)) = -1 *( 4 - 7x) ( 4 + 7x)

Expanding the last expression yields;

-1 (16 + 28x -28x - 49x^2) = -1 (16 - 49x^2) = 49x^2 - 16 which is in deed a difference of squares

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2 years ago

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Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the

xenn [34]

Answer:

As per the given statement:

The region bounded by the given curves about the y-axis, $y = 13e^{-x^2}$ , y=0, x = 0 and x = 1

Using cylindrical shell method:

The volume of solid(V) is obtained by rotating about y-axis and the region under the curve y = f(x) from a to b is;

$V = \int_{a}^{b} 2\pi x f(x) dx$ where $0\leq a$

where x is the radius of the cylinder

f(x) is the height of the cylinder.

From the given figure:

radius = x

height(h) =f(x) =y= $13e^{-x^2}$

a = 0 and b = 1

So, the volume V generated by rotating the given region:

$V =2 \pi \int_{0}^{1} x ( 13e^{-x^2}) dx\\\\V=2\pi\left [ -\frac{13}{2}e^{-x^2} \right ]_{0}^{1}\\\\V=2\pi\left (-\frac{13}{2e}-\left(-\frac{13}{2}\right) \right )\\\\V=-\frac{13\pi }{e}+13\pi$

therefore, the volume of V generated by rotating the given region is $V=-\frac{13\pi }{e}+13\pi$

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1 year ago