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Maslowich
2 years ago
12

Write an equation in slope-intercept form for the line with slope 4/3 and -3 intercept .

Mathematics
1 answer:
mojhsa [17]2 years ago
4 0

Answer:

The equation would be y = 4/3x - 3

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What is the weight of the cow?
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3 years ago
Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator
SpyIntel [72]
\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}
\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)

When x=3, you're left with

147=49a_1\implies a_1=\dfrac{147}{49}=3

When x=\sqrt2 or x=-\sqrt2, you're left with

\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}

Adding the two equations together gives -10=2a_5, or a_5=-5. Subtracting them gives 2\sqrt2=2\sqrt2a_4, a_4=1.

Now, you have

5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)
5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)
2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that a_2x^4=2x^4 and a_3(-3)(-2)=6a_3=-6. These alone tell you that you must have a_2=2 and a_3=-1.

So the partial fraction decomposition is

\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}
7 0
3 years ago
I am having trouble<br> 2(10-13x)=-34x+60
morpeh [17]
<span>Simplifying 2(10 + -13x) = -34x + 60
(10 * 2 + -13x * 2) = -34x + 60
(20 + -26x) = -34x + 60
 Reorder the terms: 20 + -26x = 60 + -34x
 Solving 20 + -26x = 60 + -34x
 Solving for variable 'x'.
 Move all terms containing x to the left, all other terms to the right.
 Add '34x' to each side of the equation. 20 + -26x + 34x = 60 + -34x + 34x
 Combine like terms: -26x + 34x = 8x 20 + 8x = 60 + -34x + 34x
 Combine like terms: -34x + 34x = 0 20 + 8x = 60 + 0 20 + 8x = 60
Add '-20' to each side of the equation. 20 + -20 + 8x = 60 + -20
 Combine like terms: 20 + -20 = 0 0 + 8x = 60 + -20 8x = 60 + -20
 Combine like terms: 60 + -20 = 40 8x = 40
 Divide each side by '8'. x = 5
 Simplifying x = 5</span>
7 0
3 years ago
Write a function describing the relationship of the given variables.
PtichkaEL [24]

Answer:

a

Step-by-step explanation:

uh

6 0
3 years ago
Simplify completely quantity x squared plus 4 x minus 45 all over x squared plus 10 x plus 9 and find the restrictions on the va
dem82 [27]
(x² + 4x - 45)/(x² + 10x + 9) 
<span>
Numerator = N = x² + 4x - 45 </span>
= x² + 9x - 5x - 45 
= (x² + 9x) - (5x + 45) 
= x(x + 9) - 5(x + 9) 
= (x + 9)(x - 5) 
<span>
Denominator = D = x² + 10x + 9 </span>
= x² + x + 9x + 9 
= (x² + x) + (9x + 9) 
= x(x + 1) + 9(x + 1) 
= (x + 1)(x + 9) 
<span>
Hence, the given expr. = N/D </span>
= {(x + 9)(x - 5)}/{(x + 1)(x + 9) 
= (x - 5)/(x + 1) 
<span>
Restrictions : x ≠ - 1, x = 5 </span>


I hope my answer has come to your help. Thank you for posting your question here in Brainly.
7 0
3 years ago
Read 2 more answers
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