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3 years ago

Factor the expression. 9y^2– 36

Mathematics

1 answer:

Nata [24]3 years ago

5 0

Answer:

Answer: 9 (y - 2) (y + 2)

Step-by-step explanation:

Factor the following:

9 y^2 - 36

Factor 9 out of 9 y^2 - 36:

9 (y^2 - 4)

y^2 - 4 = y^2 - 2^2:

9 (y^2 - 2^2)

Factor the difference of two squares. y^2 - 2^2 = (y - 2) (y + 2):

Answer: 9 (y - 2) (y + 2)

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What is the area of a square if the length is 4x-3

frez [133]

Answer:

The area of square in terms of x = 16x² -24x + 9

Step-by-step explanation:

It is stated in the question that the length of a square = 4x - 3

Formula to find the area of the square is

Area = length²

Area = ( 4x - 3 )²

by using ( a - b )² = a² + b² - 2ab

here a = 4x and b = -3

So,

(4x)² + (-3)² - 2(4x)(3)

16x² + 9 - 2(12x)

16x² + 9 - 24x

16x² -24x + 9

The area of square in terms of x = 16x² -24x + 9

3 0

3 years ago

Read 2 more answers

1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves

erastova [34]

(a) The differential equation is separable, so we separate the variables and integrate:

$(x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx$

$\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx$

$\ln|y| = x - \ln|x+1| + C$

When x = 0, we have y = 2, so we solve for the constant C :

$\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)$

Then the particular solution to the DE is

$\ln|y| = x - \ln|x+1| + \ln(2)$

We can go on to solve explicitly for y in terms of x :

$e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}$

(b) The curves y = x² and y = 2x - x² intersect for

$x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1$

and the bounded region is the set

$\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}$

The area of this region is

$\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}$

7 0

2 years ago

Owen receives $10 and puts it into his savings account. He adds $0.50 to the account each day for a number of days, d, after tha

makkiz [27]

Answer:

it is the sum of the initial amount and the additional amount after d days

Step-by-step explanation:

yw!!.

7 0

3 years ago

Which shows a rational number plotted correctly on a number line?

irinina [24]

Answer:

Top option

Step-by-step explanation:

$-19\frac{1}{2} = -\frac{39}{2}$

According to this, this is definitely in the right place.

I am joyous to assist you anytime.

7 0

3 years ago

Read 2 more answers

Help me thank u alot <333

Arisa [49]

Answer:

N~U

P~V

Q~S

R~T

(im confused on the second picture, give me time to figure it out)

Step-by-step explanation:

4 0

2 years ago