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2 years ago

Reduce to lowest term. 2x^2- 18/x^2+4x-21

Mathematics

1 answer:

Dovator [93]2 years ago

6 0

Answer:

$\frac{2(x+3)}{x+7}$

Step-by-step explanation:

Given

$\frac{2x^2-18}{x^2+4x-21}$ ← factorise numerator and denominator

2x² - 18 ( factor out 2 from each term )

= 2(x² - 9) ← difference of 2 squares

= 2(x - 3)(x + 3)

and

x² + 4x - 21 = (x + 7)(x - 3) , then

= $\frac{2(x-3)(x+3)}{(x+7)(x-3)}$ ← cancel common factor (x - 3) on numerator/ denominator

= $\frac{2(x+3)}{x+7}$

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Which of the following will generate a graph that is 3 units to the left of y = x3?

Mamont248 [21]

Answer:

(3) y=(x+3)

Step-by-step explanation:

I'm not sure what is the parent function, but in most graphs if you will shift it to the left or right (negative sign or positive sign, respectively), it will be inside a parenthesis and the opposite sign is the real movement.

For a cubic function these will be the movements:

f(x)=(x+/-h)^3+/-k

Only the opposite sign of h will be the real movement, while k's sign will automatically indicate the correct movement.

h= x-axis movement (horizontal, inside of the parenthesis in the equation)

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Hope it helps

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3 years ago

Find the area of the shaded figure. Give answer in decimal to the hundredth place.

Firdavs [7]

Answer:

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Step-by-step explanation:

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3 years ago

This is a picture of a square pyramid and the net for the square pyramid. What is the surface area of the square pyramid? 108 ft

Bad White [126]

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3 years ago

Read 2 more answers

Approximate the change in the volume of a sphere when its radius changes from r= 5ft to r= 5.1ft (v(r)= 3/4 pi r^3)?

leva [86]

Answer:

18.03 cubic feet

Step-by-step explanation:

Hello,

Step 1

find the volume of the sphere when radius= 5 ft

$v(r)= \frac{3}{4} \pi r^3\\v(5)= \frac{3}{4}\pi (5\ ft)^3\\v(5)= \frac{3}{4}\pi *125\ ft^{3} \\v(5)=294.52\ cubic\ feet\\$

Step 2

find the volume of the sphere when radius= 5.1 ft

$v(r)= \frac{3}{4}\pi r^3\\v(5.1)= \frac{3}{4} \pi (5.1\ ft)^3\\v(5.1)= \frac{3}{4}\pi *132.651\ ft^{3} \\v(5.1)=312.551\ cubic\ feet\\\\$

Step 3

Compare the Volumes to find the change

$\frac{v(r_{2})}{v(r_{1})} =\frac{312.551}{294.52} =1.06$

the volumen of the sphere with radius = 5.1 is 1.06 times bigger than the first one(r=5)

Now, find the change

$change= {v(r_{2})-{v(r_{1})}} \\change=312.551\ cubic\ feet\ -294.52 cubic feet \\ change=18.031\ cubic\ feet$

change=18.03 cubic feet

Have a great day.

4 0

3 years ago

Erin caught 8 more fish than Juan caught

Gennadij [26K]

Answer:

Second option: Equation, because 8 plus the fish that Juan caught equals the fish that Erin caught

Step-by-step explanation:

You can for sure make an equation, all you need is to have variables and that's allowed in this case.

E=J+8

E=Erin J=Juan

7 0

3 years ago

Reduce to lowest term. 2x^2- 18/x^2+4x-21​

Reduce to lowest term. 2x^2- 18/x^2+4x-21