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3 years ago

Factor the polynomial by its greatest common monomial factor

Mathematics

1 answer:

givi [52]3 years ago

5 0

Answer:

$\large\boxed{9b^8+24b^3=(3b^3)(3b^5+8)}$

Step-by-step explanation:

$9b^8=3\cdot3\cdot b^{3+5}=\bold{3}\cdot3\cdot\bold{b^3}\cdot b^5=\bold{(3b^3)}(3b^5)\\\\24b^3=\bold3\cdot8\cdot\bold{b^3}=\bold{(3b^3)}(8)\\\\9b^8+24b^3=\bold{(3b^3)}(3b^5)+\bold{(3b^3)}(8)=\bold{(3b^3)}(3b^5+8)\\\\\text{Used}\\\\a^n\cdot a^m=a^{n+m}\\\\\text{distributive property:}\ a(b+c)=ab+ac$

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Which of the following systems of nonlinear inequalities is graphed below?

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3 years ago

Jayson buys a car and pays by installments. Each installment is $ 567 per month. After 48 months, Jayson owes $ 1250. What was t

LuckyWell [14K]

The total price of the vehicle is $28466.

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3 years ago

Solve for n: 2n < 6 Math pls answer this

True [87]

Answer:

n can be a number less than 3

Step-by-step explanation:

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3 years ago

Read 2 more answers

Determine the standard form of the equation of the line that passes through (6, -9) and (-8, 6)

horrorfan [7]

9514 1404 393

Answer:

A. 15x +14y = -36

Step-by-step explanation:

Since we are given two points, we can start with the 2-point form of the equation for a line.

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

y = (6 -(-9))/(-8 -6)(x -6) +(-9)

y = 15/-14(x -6) -9

Multiplying by -14, we have ...

-14y = 15x -90 +126

Adding 14y-36 to both sides gives ...

-36 = 15x +14y . . . . matches choice A

The standard-form equation is ...

15x +14y = -36

_____

Additional comments

It can be easier to start with the form ...

(Δy)x -(Δx)y = (Δy)x1 -(Δx)y1 . . . . . where Δx = x2-x1 and Δy = y2-y1

This gives ...

(6+9)x -(-8-6)y = 15(6) +14(-9)

15x +14y = -36 . . . simplified

You can also start with the slope-intercept form or the point-slope form, if you're more familiar with those. The result will be the same. I find it handy to be familiar with a number of different forms of the equation for a line.

4 0

3 years ago

In supply (and demand) problems, y is the number of items the supplier will produce (or the public will buy) if the price of the

SSSSS [86.1K]

Answer:

A) (17 ; 550)

B) $17/item

C) 550

Step-by-step explanation:

First we must calculate the intersection point of the two lines. Since in that point y has the same value in both equations, we can obtain x by equalling the two equations and then using that value for obtaining y:

$5x+465=-6x+652\\5x+6x=652-465\\11x=187\\x=\frac{187}{11}\\x=17$

So the value of x in the intersection point is 17. We now use this value with either one of the equations to obtain y. Let's use the supply equation:

$y=5*17+465\\y=550$

So the intersection point is (17 ; 550)

Supply and demand are in equilibrium when the amount of items on supply are the same as the ones on demand. That is the point were the two lines intersect, which means the selling price is the x coordinate and the amount of items is the y coordinate, so that is a selling price of $17/item with a number of items of 550.

3 0

3 years ago