Let's first calculate the roots of f(x) = x³-18x²+101x-180
a) f(4) = 4³ - 18.(4²) +101.(4) -180 =0, then x=4 is a root.
b) to find the 2 other roots divide x³-18x²+101x-180 by (x-4) = x²-14x+45
c) this quadratic equation has the following roots: x=5 and x=9. Hence:
f(x) = x³-18x²+101x-180 = (x-4)(x-5)(x-9)
the x-intercepts are x₁ = 4, x₂ = 5, x₃ = 9.
To find the y intercept plug x= 0 in f(x) = x³-18x²+101x-180
f(x) = y = -180 (y intercept
The graph starts from - ∞ to + ∞ and passes through one maximum and one minimum
∠СXA = ∠BXA + ∠СXB = 30°20' + 40°35' = 70°55'
Answer: That would be A and C
- A. = 26/3
- B. = -20
- C. = 1
- D. = -3
Step-by-step explanation:
I hope it helps :)
A.
![\frac{ - 4 + ( - 5)( - 6)}{3} \\ \frac{ - 4 + 30}{3} \\ \frac{26}{3} = 8 \frac{2}{3} = 8.67](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%204%20%2B%20%28%20-%205%29%28%20-%206%29%7D%7B3%7D%20%20%5C%5C%20%20%5Cfrac%7B%20-%204%20%2B%2030%7D%7B3%7D%20%20%5C%5C%20%20%5Cfrac%7B26%7D%7B3%7D%20%20%3D%208%20%5Cfrac%7B2%7D%7B3%7D%20%20%3D%208.67)
B.
![8( \frac{10}{(2)( - 2)} ) \\ 8( \frac{10}{ - 4} ) \\ 8( - \frac{5}{ 2} ) = - 20 \\](https://tex.z-dn.net/?f=8%28%20%5Cfrac%7B10%7D%7B%282%29%28%20-%202%29%7D%20%29%20%5C%5C%208%28%20%5Cfrac%7B10%7D%7B%20-%204%7D%20%29%20%5C%5C%208%28%20%20-%20%5Cfrac%7B5%7D%7B%20%202%7D%20%29%20%3D%20-%20%2020%20%5C%5C%20)
C.
![3( \frac{ - 64}{8} ) + 25 \\ 3( - 8) + 25 \\ = - 24 + 25 \\ = 1](https://tex.z-dn.net/?f=3%28%20%5Cfrac%7B%20-%2064%7D%7B8%7D%20%29%20%2B%2025%20%5C%5C%203%28%20%20-%208%29%20%2B%2025%20%5C%5C%20%20%3D%20%20-%2024%20%2B%2025%20%20%5C%5C%20%3D%201)
D.
![\frac{ - 2( - 5)( - 3)}{10} \\ \frac{ - 30}{10} \\ = - 3](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%202%28%20-%205%29%28%20-%203%29%7D%7B10%7D%20%20%5C%5C%20%20%5Cfrac%7B%20-%2030%7D%7B10%7D%20%20%5C%5C%20%20%3D%20%20-%203)
it had to be 15 because if you add the total the 2 items together that $5 and subtract $5 from $73 I got 15 because she would have a dollar left
The answer is 221. And it’s solved with PEMDAS