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3 years ago

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

Mathematics

1 answer:

Vladimir79 [104]3 years 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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the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width

-BARSIC- [3]

Length and width of rectangle is 15 inches and 6 inches respectively

<h3><u>Solution:</u></h3>

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

<em><u>The formula for area of rectangle is given as:</u></em>

$\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}$

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

$\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}$

On solving the above expression for x we get

$\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}$

$\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}$

Hence length and width of rectangle is 15 inches and 6 inches.

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4 years ago

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3 years ago

Sylvia plans to place 617 stamps in an album. Each page of the album holds 5 stamps. She uses division to find out how many full

bija089 [108]

Answer:

123 full pages

Step-by-step explanation:

Given

$Total\ Stamps = 617\ stamps$

$Each\ Page = 5\ stamps$

Required

Determine the number of full page

To do this, we simply divide the total stamps by stamps in each page;

$Pages = \frac{Total\ Stamps}{Each\ Page}$

$Pages = \frac{617}{5}$

$Pages = 123.4$

Then we record only the quotient

The quotient is the digits before the decimal

$Pages = 123$

<em>Hence, she has 123 full pages</em>

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3 years ago

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Vesnalui [34]

Answer:

228.4

Step-by-step explanation:

9.2 + 9.2 + 60 + 75 +75 which is 228.4. Remember to divide the triangles by two after you do base times height.

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3 years ago

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Ugo [173]

Answer:

$y=-3.2\\\\y=-2.2\\\\y=-1.8$

Step-by-step explanation:

Insert the given x values for the given equation to find the corresponding y coordinate:

$y=0.2x-2$

$x:-6,-1,1$

Insert -6:

$y=0.2(-6)-2$

Simplify multiplication (when multiplying a negative and a positive, the result will always be negative):

$y=-1.2-2$

Simplify (when subtracting from a negative number, add the values, but keep the negative symbol):

$y=-3.2$

Insert -1:

$y=0.2(-1)-2\\\\y=-0.2-2\\\\y=-2.2$

Insert 1:

$y=0.2(1)-2\\\\y=0.2-2\\\\y=-1.8$

:Done

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3 years ago