Answer:
k = 9.
Step-by-step explanation:
2x + 3y -8=0
3y = -2x + 8
y = -2/3 x + 8/3
So the slope of this line is -2/3.
Therefore the slope of a line perpendicular to the above is -1 /-2/3
= 3/2.
kx - 6y = 9
6y = kx - 9
y = k/6x - 3/2
But the slope is 3/2,
So k/6 = 3/2
2k = 18
k = 9.
Factorizing the denominator gives
![\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{x^4}{x(x^2+1)(x^2-x+7)} = \dfrac{x^3}{(x^2+1)(x^2-x+7)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E4%7D%7B%28x%5E3%2Bx%29%28x%5E2-x%2B7%29%7D%20%3D%20%5Cdfrac%7Bx%5E4%7D%7Bx%28x%5E2%2B1%29%28x%5E2-x%2B7%29%7D%20%3D%20%5Cdfrac%7Bx%5E3%7D%7B%28x%5E2%2B1%29%28x%5E2-x%2B7%29%7D)
Then the partial fraction decomposition would take the form
![\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{a_0x + b_0}{x^2+1} + \dfrac{a_1x + b_1}{x^2-x+7}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E4%7D%7B%28x%5E3%2Bx%29%28x%5E2-x%2B7%29%7D%20%3D%20%5Cdfrac%7Ba_0x%20%2B%20b_0%7D%7Bx%5E2%2B1%7D%20%2B%20%5Cdfrac%7Ba_1x%20%2B%20b_1%7D%7Bx%5E2-x%2B7%7D)
She can buy a basket and three more pounds of vegetables with 50 cents left
Answer:
3
![3 {y}^{0}](https://tex.z-dn.net/?f=3%20%7By%7D%5E%7B0%7D%20)
![= 3 \times 1](https://tex.z-dn.net/?f=%20%3D%203%20%5Ctimes%201)
![= 3](https://tex.z-dn.net/?f=%20%3D%203)
If any numbers or constant power is zero then it will be 1