Answer:
Smallest number is 18. Largest number is 30.
Step-by-step explanation:
a:b:c = 4:5:3
∃x such that a = 4x, b = 5x, c = 3x
"sum of the numbers is 72"
a+b+c = 4x+5x+3x = 72
x = 6
a = 4x = 24
b = 5x = 30
c = 3x = 18
We already got
f(x)= a(x-2)(x-3)(x-5)
We got ![a=\frac{1}{6}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B1%7D%7B6%7D)
first we multiply the parenthesis in f(x)
f(x)= a(x-2)(x-3)(x-5)
![f(x)= a(x^2-5x+6)(x-5)](https://tex.z-dn.net/?f=f%28x%29%3D%20a%28x%5E2-5x%2B6%29%28x-5%29)
![f(x) = a(x^3 - 10 x^2 + 31 x - 30)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20a%28x%5E3%20-%2010%20x%5E2%20%2B%2031%20x%20-%2030%29)
Replace the value of 'a'
![f(x) = \frac{1}{6}(x^3 - 10 x^2 + 31 x - 30)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B6%7D%28x%5E3%20-%2010%20x%5E2%20%2B%2031%20x%20-%2030%29)
Multiply 1/16 inside the parenthesis
![f(x) = \frac{1}{6}x^3 - \frac{5}{3} x^2 + \frac{31}{6} x - 5](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B1%7D%7B6%7Dx%5E3%20-%20%5Cfrac%7B5%7D%7B3%7D%20x%5E2%20%2B%20%5Cfrac%7B31%7D%7B6%7D%20x%20-%205)
Answer:
Step-by-step explanation:
(x + 4)^2 =
(x + 4)(x + 4) =
x^2 + 4x + 4x + 16 =
x^2 + 8x + 16
Answer:
-4 ≤ y ≤ 2 or [-4 , 2]
Step-by-step explanation:
The maximum of the function is +2 while the minimum is -4, the range is
-4 ≤ y ≤ 2 or [-4 , 2]
Answer:
D. 9
Step-by-step explanation:
We know that cos theta = adjacent / hypotenuse
cos 60 = x /18
Multiply each side by 18
18 cos 60 = x/18 * 18
18 cos 60 =x
9 =x