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3 years ago

Simplify the expression.

Mathematics

1 answer:

Xelga [282]3 years ago

5 0

Divide. Note that when dividing 2 numbers with negative signs, you're answer will be positive.

-42/-6 = 7

7 is your answer

hope this helps

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Which polynomial is prime?

faust18 [17]

X2+16 is the prime polynomial.
x2+16 is the only polynomial that couldn't be factored out anymore

x2-36 --> (x-6)(x+6)
x2-7x+12 --> (x-3)(x-4)
x2-x-20 --> (x+5)(x-4)

5 0

3 years ago

Read 2 more answers

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:

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

We have:

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

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

Un ganadero está reparando una mezcla de avena y harina de maíz para ganado. Cada onza de avena proporciona 4 gramos de proteína

Feliz [49]

Answer:i love you

Step-by-step explanation:

3 0

3 years ago

A triangle has two sides with lengths 7 m and 12 m. Which of the following lengths could represent the length of the third side?

KatRina [158]

Answer:

i think its 17

please rate and leave a like :-)

3 0

3 years ago

Plz help ty :)))))))))

Neporo4naja [7]

3x - 3y = -12 ------------- (1)
7x + 2y = -19 --------------(2)

(1) x 2 : 6x - 6y = - 24 ----------- (1a)
(2) x 3 : 21x + 6y = -57 ----------- (2a)

(1a) + (2a) : 27x = - 81
x = - 3

Sub x = -3 into (1) : 3(-3) - 3y = - 12
y = - 12 + 9
y = - 3

Answer( -3, -3)

3 0

2 years ago