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3 years ago

5

Factor by grouping 20p³+15p²+24p+18

1 answer:

ivolga24 [154]3 years ago

7 0

(4p +3)(5p2 + 6) is your answer

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Rewrite the function by completing the square.<br> f(x) = x2 – 10x + 44<br> +<br> f(x) = (x+

iVinArrow [24]

Answer:

$f(x)=(x-5)^{2}+19$

Step-by-step explanation:

we have

$f(x)=x^{2}-10x+44$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-44=x^{2}-10x$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)-44+25=x^{2}-10x+25$

$f(x)-19=x^{2}-10x+25$

Rewrite as perfect squares

$f(x)-19=(x-5)^{2}$

$f(x)=(x-5)^{2}+19$

8 0

3 years ago

When using substitution to solve this system of equations, what is the result of the first step?

Allushta [10]

Answer:

The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

Step-by-step explanation:

Hope this helps you

3 0

2 years ago

Read 2 more answers

Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

1 year ago

7. In a quiz bee, Marlon scored 132 points during the first round. This score was thrice as much as his score during the second

podryga [215]

Answer:

II + III = 176

II = 44

III = 132

Step-by-step explanation:

Third round: 132

Second round: 3x=132

x=44 (second round)

2rounds: 132+44=176

4 0

2 years ago

Select the choice that translates the following verbal phrase correctly to algebra: y less than 21

8_murik_8 [283]

Y less than 21 = 21 - y

Remember, "less than" indicates a subtraction with the terms in inverted order.

Hope I helped!

4 0

3 years ago

Read 2 more answers