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Write an equation perpendicular to the line y=3/2x-2 that goes through (-4,3)

Goryan [66]

Answer: y=-2/3x-2/3

Step-by-step explanation:

concept to know: two lines that are perpendicular has opposite reciprocal slopes.

y=-2/3x+b

in order to find b or the y-intercept, we need to plug in a point

3=-2/3(-4)+b

3=8/3+b

b=-2/3

y=-2/3x-2/3

Hope this helps!! :)

4 0

3 years ago

What is the equation of a line with a slope of 2 and a y-intercept of -5?

RSB [31]

Y=2x-5

Hope this helps ya :D

7 0

2 years ago

1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

german

Answer:

Step-by-step explanation:

1.

To write the form of the partial fraction decomposition of the rational expression:

We have:

$\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}$

2.

Using partial fraction decomposition to find the definite integral of:

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx$

By using the long division method; we have:

$x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }$

$- 2x^3 -16x^2-40x$

$x+ 20$

So;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}$

By using partial fraction decomposition:

$\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}$

$= \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}$

x + 20 = A(x + 2) + B(x - 10)

x + 20 = (A + B)x + (2A - 10B)

Now; we have to relate like terms on both sides; we have:

A + B = 1 ; 2A - 10 B = 20

By solvong the expressions above; we have:

$A = \dfrac{5}{2}$ $B = \dfrac{3}{2}$

Now;

$\dfrac{x+20}{(x-10)(x+2)} = \dfrac{5}{2(x-10)} + \dfrac{3}{2(x+2)}$

Thus;

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)}$

Now; the integral is:

$\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx$

$\mathbf{\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = x^2 + \dfrac{5}{2}In | x-10|\dfrac{3}{2} In |x+2|+C}$

3. Due to the fact that the maximum words this text box can contain are 5000 words, we decided to write the solution for question 3 and upload it in an image format.

Please check to the attached image below for the solution to question number 3.

4 0

3 years ago

What is 8(3+a)? Please answer

alisha [4.7K]

The Answer is

or, 8a + 24

To get the answer we have to distribute the 8, which means we have to multiply both terms in the parentheses by 8.

8 x 3 = 24

8 x a = 8a

So the answer is 24 + 8a

7 0

2 years ago

Read 2 more answers

PLZ HELP ASAP. (25 points)

Otrada [13]

Stretched vertically three times because you take the result of x^2+4x+4 aka (x+2)^2 and then multiply it by 3 for 3 times the output

7 0

3 years ago