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3 years ago

Solve each by elimination 4x - y = 105 x + 7y = -10

Mathematics

1 answer:

Svet_ta [14]3 years ago

4 0

Answer:

point form:

(25, -5)

Equation form:

x= 25, y= -5

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If h(x) = x - 7 and g(x) = x^2 , which expression is equivalent to (gOh)(5)?

Ann [662]

(5 - 7)^2 is your answer

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3 years ago

What are scenarios for the ratios 2:10, 10:2, & 12:1?

frozen [14]

Answer:

2:10 2/10 2 to 10 10:2 10/2 10 to 2 12:1 12/1 12 to 1

Step-by-step explanation:

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3 years ago

What is the radical form of each of the given expressions?

IceJOKER [234]

1: square root of 2
2: cube root of 2, squared
3: square root of 3, squared
4: cube root of 3

hopefully this helps you :)

6 0

3 years ago

Find the length of the hypotenuse. The measure of the hypotenuse?

Eduardwww [97]

Answer:

Since it's a right angled triangle

Hypotenuse = h

h² = 7²+24²

h= √49 + 576

h = √625

h= 25

Therefore hypotenuse is 25

Hope this helps.

8 0

3 years ago

Read 2 more answers

Consider the initial value problem yâ€²+2y=4t,y(0)=8.

Xelga [282]

Answer:

Please read the complete procedure below:

Step-by-step explanation:

You have the following initial value problem:

$y'+2y=4t\\\\y(0)=8$

a) The algebraic equation obtain by using the Laplace transform is:

$L[y']+2L[y]=4L[t]\\\\L[y']=sY(s)-y(0)\ \ \ \ (1)\\\\L[t]=\frac{1}{s^2}\ \ \ \ \ (2)\\\\$

next, you replace (1) and (2):

$sY(s)-y(0)+2Y(s)=\frac{4}{s^2}\\\\sY(s)+2Y(s)-8=\frac{4}{s^2}$ (this is the algebraic equation)

$sY(s)+2Y(s)-8=\frac{4}{s^2}\\\\Y(s)[s+2]=\frac{4}{s^2}+8\\\\Y(s)=\frac{4+8s^2}{s^2(s+2)}$ (this is the solution for Y(s))

$y(t)=L^{-1}Y(s)=L^{-1}[\frac{4}{s^2(s+2)}+\frac{8}{s+2}]\\\\=L^{-1}[\frac{4}{s^2(s+2)}]+L^{-1}[\frac{8}{s+2}]\\\\=L^{-1}[\frac{4}{s^2(s+2)}]+8e^{-2t}$

To find the inverse Laplace transform of the first term you use partial fractions:

$\frac{4}{s^2(s+2)}=\frac{-s+2}{s^2}+\frac{1}{s+2}\\\\=(\frac{-1}{s}+\frac{2}{s^2})+\frac{1}{s+2}$

Thus, you have:

$y(t)=L^{-1}[\frac{4}{s^2(s+2)}]+8e^{-2t}\\\\y(t)=L^{-1}[\frac{-1}{s}+\frac{2}{s^2}]+L^{-1}[\frac{1}{s+2}]+8e^{-2t}\\\\y(t)=-1+2t+e^{-2t}+8e^{-2t}=-1+2t+9e^{-2t}$

(this is the solution to the differential equation)

5 0

3 years ago