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
Answer:
Just remember that straight lines are always 180° (a + b = f)
Step-by-step explanation:
Assuming the triangle is equiangular and equilateral, a b and c are the same, so they are interchangeable.
f + c = 180 becuase it is a straight line. you can switch out c with a because they are the same. So:
f+a=180
(switch out with b)
f+b=180
GUESSING this is equiangular, a and b must add up to 120 because they are are both 60.
If a line is 180 degrees and c is 60 (same as a and b) then f will be 180-60 which is 120. 120 is the same as the sum of a and b, so you could write:
a + b = f
Answer:
x = 4, x = 8
Step-by-step explanation:
Given
(x - 7)(x - 5) = 3 ← expand factors using FOIL
x² - 12x + 35 = 3 ( subtract 3 from both sides )
x² - 12x + 32 = 0 ← in standard form
(x - 4)(x - 8) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 8 = 0 ⇒ x = 8
I think you do 550 x .16(16%)=88 and each CD sells for 44 so 88/44
Answer= He needs to sell 2 CD's
Answer: 1,045 passengers
Step-by-step explanation:
This question involves multiple steps. Let's first try to figure the number of children on the cruise.
The ratio of girls to the total number of children was 2:5. There are 198 boys.
This information tells me that for every 5 children, there's 2 girls and 3 boys.
Based off of this information, we can divide the total number of boys by 3 in order to find the number of children.
198÷3=66
Let's multiply 66 by 5 since that's the number of groupings based off the ratio.
66×5=330
Let's check the number of children. Since the ratio of girls to total children is 2:5 and we already confirmed there's 198 boys, there should be 132 girls. We can turn this ratio into a fraction where 2/5 of the children are girls. we can confirm this by multiply 330 by 2/5 (0.4) and getting 132.
There are 330 children on the cruise.
The ratio of the number of adults to the number of children was 13:6.
For every 6 children, there were 13 adults. Let's divide the number of children by 6 in order to find the number of groupings.
330÷6=55
Let's now multiply the groupings by 13 to find the number of adults.
55×13=715
So there should be 715 adults and 330 children on the cruise.
715+330=1,045