Answer:
The zeros of f(x) are: (x - 1), (x - 3) and (x - 8)
<em></em>
Step-by-step explanation:
Given
![f(x)=x^3-12x^2+35x-24](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3-12x%5E2%2B35x-24)
![f(8) = 0](https://tex.z-dn.net/?f=f%288%29%20%3D%200)
Required
Find all zeros of the f(x)
If
then:
![x = 8](https://tex.z-dn.net/?f=x%20%3D%208)
And
is a factor
Divide f(x) by x - 8
![\frac{f(x)}{x - 8} = \frac{x^3-12x^2+35x-24}{x - 8}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%29%7D%7Bx%20-%208%7D%20%3D%20%5Cfrac%7Bx%5E3-12x%5E2%2B35x-24%7D%7Bx%20-%208%7D)
Expand the numerator
![\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 -8x^2 + 3x + 32x - 24}{x - 8}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%29%7D%7Bx%20-%208%7D%20%3D%20%5Cfrac%7Bx%5E3%20-%204x%5E2%20-8x%5E2%20%2B%203x%20%2B%2032x%20-%2024%7D%7Bx%20-%208%7D)
Rewrite as:
![\frac{f(x)}{x - 8} = \frac{x^3 - 4x^2 + 3x - 8x^2 +32x - 24}{x - 8}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%29%7D%7Bx%20-%208%7D%20%3D%20%5Cfrac%7Bx%5E3%20-%204x%5E2%20%2B%203x%20-%208x%5E2%20%2B32x%20-%2024%7D%7Bx%20-%208%7D)
Factorize
![\frac{f(x)}{x - 8} = \frac{(x^2 - 4x + 3)(x - 8)}{x - 8}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%29%7D%7Bx%20-%208%7D%20%3D%20%5Cfrac%7B%28x%5E2%20-%204x%20%2B%203%29%28x%20-%208%29%7D%7Bx%20-%208%7D)
Expand
![\frac{f(x)}{x - 8} = \frac{(x^2 -x - 3x + 3)(x - 8)}{x - 8}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%29%7D%7Bx%20-%208%7D%20%3D%20%5Cfrac%7B%28x%5E2%20-x%20-%203x%20%2B%203%29%28x%20-%208%29%7D%7Bx%20-%208%7D)
Factorize
![\frac{f(x)}{x - 8} = \frac{(x - 1)(x - 3)(x - 8)}{x - 8}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%29%7D%7Bx%20-%208%7D%20%3D%20%5Cfrac%7B%28x%20-%201%29%28x%20-%203%29%28x%20-%208%29%7D%7Bx%20-%208%7D)
![\frac{f(x)}{x - 8} = (x - 1)(x - 3)](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%29%7D%7Bx%20-%208%7D%20%3D%20%28x%20-%201%29%28x%20-%203%29)
Multiply both sides by x - 8
![f(x) = (x - 1)(x - 3)(x - 8)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%20-%201%29%28x%20-%203%29%28x%20-%208%29)
<em>Hence, the zeros of f(x) are: (x - 1), (x - 3) and (x - 8)</em>
Answer:
8.0
Step-by-step explanation:
Angle in a semi circle is 90°
<a = 180-90-<b = 90-28 = 62°
opposite angles of a cyclic quadrilateral sums up to 180°
<b + <a = 180
<b = 180-62
<b = 118°
So,
The secret to solving problems with ratios is to find the value of one unit.
5:7 = 12 units total
To find one unit, divide the total number of students by the total number of units.
600/12 = a
Simplify
50/1 = a
50 = a
The value of each unit is 50.
Now, multiply the units by the numbers in the ratio.
50(5) = b
250 = boys
50(7) = x
350 = x
There are 350 girls.
first, distribute -6 to (2b + 1), giving you -12b - 6, and then on the another side of the equation, distribute -2 to (5 + 4b) giving you, -10 - 8b. now we need to put our coefficients on one side so we will add 8b to each side of the equation, giving us -6 = -10 - 8b + 12b, then we will add 10 to both sides of the equation giving us, 10 -6 = -8b +12b, this gives u 4 = 4b. then, you would solve for b, which equals 1.