Answer:
Step-by-step explanation:
1. x+6=14
14-6=8
x=8
2. 15/x=3
15/3=x
x=5
3. 7*x=56
56/7=8
x=8
4. x^2-4=12
x=4, x=-4
5. 1/4x=10
x/4 = 10
x = 40
6. 3x-9=18
x=9
7. 1/2x-10=14
x/2-10=14
x=48
8.x/8=9
8*9=72
x=72
9.2x+3=24
2x=21
x=21/2
10.20*x=140
140/20=7
x=7
<h2>Steps:</h2>
So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:
![(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\div \frac{x-3}{x+2}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%3D%5Cfrac%7Bx%5E2-x-6%7D%7B1%7D%5Cdiv%20%5Cfrac%7Bx-3%7D%7Bx%2B2%7D)
Next, remember that <u>dividing by a number is the same as multiplying by its reciprocal.</u> To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:
![(\frac{f}{g})(x)=\frac{x^2-x-6}{1}\times \frac{x+2}{x-3}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%3D%5Cfrac%7Bx%5E2-x-6%7D%7B1%7D%5Ctimes%20%5Cfrac%7Bx%2B2%7D%7Bx-3%7D)
Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:
![(\frac{f}{g})(x)=\frac{x^2+2x-3x-6}{1}\times \frac{x+2}{x-3}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%3D%5Cfrac%7Bx%5E2%2B2x-3x-6%7D%7B1%7D%5Ctimes%20%5Cfrac%7Bx%2B2%7D%7Bx-3%7D)
Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:
![(\frac{f}{g})(x)=\frac{x(x+2)-3(x+2)}{1}\times \frac{x+2}{x-3}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%3D%5Cfrac%7Bx%28x%2B2%29-3%28x%2B2%29%7D%7B1%7D%5Ctimes%20%5Cfrac%7Bx%2B2%7D%7Bx-3%7D)
Now you can rewrite it as:
![(\frac{f}{g})(x)=\frac{(x-3)(x+2)}{1}\times \frac{x+2}{x-3}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%3D%5Cfrac%7B%28x-3%29%28x%2B2%29%7D%7B1%7D%5Ctimes%20%5Cfrac%7Bx%2B2%7D%7Bx-3%7D)
Next, multiply:
![(\frac{f}{g})(x)=\frac{(x-3)(x+2)^2}{x-3}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%3D%5Cfrac%7B%28x-3%29%28x%2B2%29%5E2%7D%7Bx-3%7D)
Next, divide:
![(\frac{f}{g})(x)=(x+2)^2](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%3D%28x%2B2%29%5E2)
And lastly, simplify:
- A good tip:
![(x+y)^2=x^2+2xy+y^2](https://tex.z-dn.net/?f=%28x%2By%29%5E2%3Dx%5E2%2B2xy%2By%5E2)
![(\frac{f}{g})(x)=x^2+4x+4](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%3Dx%5E2%2B4x%2B4)
<h2>Answer:</h2>
<u>The correct option is C. x² + 4x + 4.</u>
Answer:
<h2>
w = -8</h2>
Step-by-step explanation:
Given the equation solved by Ernesto expressed as
, the extraneous solution obtained by Ernesto is shown below;
![\sqrt{\dfrac{1}{2}w+8}=-2\\\\square\ both \ sides \ of \ the \ equation\\(\sqrt{\dfrac{1}{2}w+8})^2=(-2)^2\\\\\dfrac{1}{2}w+8 = 4\\\\Subtract \ 8 \ from \ both \ sides\\\\\dfrac{1}{2}w+8 - 8= 4- 8\\\\\dfrac{1}{2}w= -4\\\\multiply \ both \ sides \ by \ 2\\\\\dfrac{1}{2}w*2= -4*2\\\\w = -8](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cdfrac%7B1%7D%7B2%7Dw%2B8%7D%3D-2%5C%5C%5C%5Csquare%5C%20both%20%5C%20sides%20%5C%20of%20%5C%20the%20%5C%20equation%5C%5C%28%5Csqrt%7B%5Cdfrac%7B1%7D%7B2%7Dw%2B8%7D%29%5E2%3D%28-2%29%5E2%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B2%7Dw%2B8%20%3D%204%5C%5C%5C%5CSubtract%20%5C%208%20%5C%20from%20%5C%20both%20%5C%20sides%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B2%7Dw%2B8%20-%208%3D%204-%208%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B2%7Dw%3D%20-4%5C%5C%5C%5Cmultiply%20%5C%20both%20%5C%20sides%20%5C%20by%20%5C%202%5C%5C%5C%5C%5Cdfrac%7B1%7D%7B2%7Dw%2A2%3D%20-4%2A2%5C%5C%5C%5Cw%20%3D%20-8)
Hence, the extraneous solution that Ernesto obtained is w = -8
Answer:
2 fluid ounce/hour
Step-by-step explanation:
2 hours to 5 hours ; 3 hours apart
leaks: 48 -42 = 6 fluid ounce
rate of leak = 6/3 = 2 fluid ounce/hour
Answer:
12
Step-by-step explanation:
4u - 8u = -63 + 15 ( collecting like terms)
-4u = -48
u = 12