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3 years ago

Factor out the greatest common factor. 10a3b−6a2b2

Mathematics

1 answer:

podryga [215]3 years ago

4 0

Answer:

2a^2b(5a-3b)

If not then the other way is

5a-3b

Step-by-step explanation:

The GCF of 10a^3b and -6a^2b^2 is 2a^2b

So divide by that you will get

2a^2b(5a-3b)

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A circle has the equation 2x²+12x+2y²−16y−150=0.

KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

$(x-h)^{2} +(y-k)^{2}=r^{2}$ (1)

Where $(h,k)$ are the coordinates of the center and $r$ is the radius.

Now, we are given the equation of this circle as follows:

$2x^{2}+12x+2y^{2}-16y-150=0$ (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

$2(x^{2}+6x+y^{2}-8y-75)=0$ (3)

Rearranging the equation:

$x^{2}+6x+y^{2}-8y=75$ (4)

$(x^{2}+6x)+(y^{2}-8y)=75$ (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :

For the first parenthesis:

$x^{2}+6x+b^{2}$

We can rewrite this as:

$x^{2}+2(3)x+b^{2}$

Hence in this case $b=3$ and $b^{2}=9$ :

$x^{2}+2(3)x+3^{2}=x^{2}+6x+9=(x+3)^{2}$

For the second parenthesis:

$y^{2}-8y+b^{2}$

We can rewrite this as:

$y^{2}-2(4)y+b^{2}$

Hence in this case $b=-3$ and $b^{2}=9$ :

$y^{2}-2(4)y+4^{2}=y^{2}-8y+16=(y-4)^{2}$

Then, equation (5) is rewritten as follows:

$(x^{2}+6x+9)+(y^{2}-8y+16)=75+9+16$ (6)

Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.

Rearranging:

$(x-3)^{2}+(y-4)^{2}=100$ (7)

At this point we have the circle equation in the center radius form $(x-h)^{2} +(y-k)^{2}=r^{2}$

Hence:

$h=-3$

$k=4$

$r=\sqrt{100}=10$

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3 years ago

Which statement about the scenario represented in the table is true? Assume time is the independent variable

Verizon [17]

Answer:B

Step-by-step explanation:

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Dominik [7]

Answer: Commutative Property of.

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Step-by-step explanation:

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A grocery store has three locations: Central, North, and South. The grocery store counted the number of cantaloupes sold at each

Nikolay [14]

A) the number of the cantaloupes sold at Central varied less than did the number sold at North.
Because in Central it is 45 and 4.1 in sales of MAD and It is 47 5.7 in North
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3 years ago

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Find the value of x. 3x -8° 2x + 1°

Naddik [55]

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2 years ago