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3 years ago

Use the graph to find the factorization of x2 - 6x + 8.

Mathematics

1 answer:

WARRIOR [948]3 years ago

4 0

Answer:

D. (x-2)(x-4)

Step-by-step explanation:

The graph cross the x-axis in points with x-coordinates of 2 and 4

then 2 and 4 are roots of x² - 6x + 8.

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Solve:<br><br> a.x3+x2-8x - 12x+2<br> b. x3-4x2-3x + 18x-3<br> c. x2 + 4x + 4<br> d. x2 - 6x + 9

NeTakaya

<h2>Steps:</h2>

So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\div \frac{x-3}{x+2}$

Next, remember that <u>dividing by a number is the same as multiplying by its reciprocal.</u> To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:

$(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\times \frac{x+2}{x-3}$

Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:

$(\frac{f}{g})(x)=\frac{x^2+2x-3x-6}{1}\times \frac{x+2}{x-3}$

Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

$(\frac{f}{g})(x)=\frac{x(x+2)-3(x+2)}{1}\times \frac{x+2}{x-3}$

Now you can rewrite it as:

$(\frac{f}{g})(x)=\frac{(x-3)(x+2)}{1}\times \frac{x+2}{x-3}$

Next, multiply:

$(\frac{f}{g})(x)=\frac{(x-3)(x+2)^2}{x-3}$

Next, divide:

$(\frac{f}{g})(x)=(x+2)^2$

And lastly, simplify:

A good tip: $(x+y)^2=x^2+2xy+y^2$

$(\frac{f}{g})(x)=x^2+4x+4$

<h2>Answer:</h2>

<u>The correct option is C. x² + 4x + 4.</u>

7 0

4 years ago

Show work and answer #9

Kisachek [45]

(4/5)-(3/8)=17/40 or 0.425 mile

6 0

3 years ago

Identify the cross section of the solid shown in the diagram

Ivahew [28]

Given:

Image of the pyramid

To identify:

The cross section of the solid.

Solution:

The given image is a pyramid.

The base of the pyramid have 5 edges.

So, it is a pentagonal pyramid.

In the cross section also have 5 edges.

Therefore the cross section of the solid shown in the diagram is pentagon.

6 0

3 years ago

What are the solutions of x^2+10x+21=0?

Luden [163]

(x+7)(x+3) so therefore you set each equation = 0...
x + 7 = 0
x + 3= 0
and solve
x = -3
x = -7

6 0

3 years ago

Read 2 more answers

A meter is 3.37 inches more than a yard swimmer a swims 100 meters and swimmer b swims 100 yeards how many more feet did swimmer

olga_2 [115]

Swimmer a swims 100 meters, which is 100 1-meters, which is 100
(1 yards +3.37 inches) = 100 yards + 337 inches.

1 yard is 3 feet, so 100 yards are 300 feet.

100 in is 8.33 feet so
337 in is (337*8.33)/100=28.07 feet

Swimmer b swims 100 yards, which is 300 feet

Swimmer a swam 28.07 feet.

4 0

3 years ago