Answer: x+2 / x+ 9, x = -2, x=-9 ( A )
Solution:
Breakdown the problem into two sets
Step 1: simplify x^2 -10x - 24
Factorize the above equation,
Multiply the last term (24) with the first term coefficient i.e. 1
Step 2: Then, find the factors of 24 in a way that when you add or subtract it sums up to 10
x2 - 12x + 2x - 24 >>>> (x2-12x) + (2x-24) >>> take common
>>>> x(x-12) + 2( x-12)
Step 3: (x + 2) (x - 12)
Step 4: Step 1: simplify x^2 - 3x - 108 using the same steps
x2 - 12x + 9x - 108 >>>> take common x(x-12) + 9 ( x -12) >>>
(x + 9) (x - 12) final product
Now, Simplify the equation as a whole
(x + 2) (x - 12) / (x + 9) (x - 12) Note: (x - 12) cancels out
= (x + 2) / (x + 9) with x= -2 and x= -9
<u> Equation:</u>
x(x - 5) + 3(x + 5)
<u>Steps:</u>
x(x - 5) + 3(x + 5)
<u>Expand:</u>
x(x - 5 ): x^2 - 5x
x^2 - 5x + 3(x + 5)
<u>Expand:</u>
3(x + 5): 3x + 15
x^2 - 5x + 3x + 15
<u>Add Similar Elements: </u>
-5x + 3x
= -2x
Answer x^2 - 2x + 15 Doesn't Factor
Hope that helps!!! : )
F(x) represents how many pages in total Antonia has read, while x represents the number of days.
72-24=48
x% of 72=48
(/72)x/100 *72=48 (/72)
(*100 ) x/100=2/3 (*100)
x= 66.67%
100% -66.67%=33.33% discount
The value of x is
.
Solution:
Given expression is
.
Switch both sides.
![8-3 \sqrt[5]{x^{3}}=-7](https://tex.z-dn.net/?f=8-3%20%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%7D%3D-7)
Subtract 8 from both side of the equation.
![8-3 \sqrt[5]{x^{3}}-8=-7-8](https://tex.z-dn.net/?f=8-3%20%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%7D-8%3D-7-8)
![-3 \sqrt[5]{x^{3}}=-15](https://tex.z-dn.net/?f=-3%20%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%7D%3D-15)
Divide by –3 on both side of the equation.
![$\frac{-3 \sqrt[5]{x^{3}}}{-3} =\frac{-15}{-3}](https://tex.z-dn.net/?f=%24%5Cfrac%7B-3%20%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%7D%7D%7B-3%7D%20%3D%5Cfrac%7B-15%7D%7B-3%7D)
![\sqrt[5]{x^{3}}=-5](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%7D%3D-5)
To cancel the cube root, raise the power 5 on both sides.
![(\sqrt[5]{x^{3}})^5=(-5)^5](https://tex.z-dn.net/?f=%28%5Csqrt%5B5%5D%7Bx%5E%7B3%7D%7D%29%5E5%3D%28-5%29%5E5)

To find the value of x, take square root on both sides.
![\sqrt[3]{x^3}=\sqrt[3]{25}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E3%7D%3D%5Csqrt%5B3%5D%7B25%7D)
![x=5\sqrt[3]{25}](https://tex.z-dn.net/?f=x%3D5%5Csqrt%5B3%5D%7B25%7D)
Hence the value of x is
.