Answer:
z = 8
Step-by-step explanation:
All angles inside a triangle add up to 180 so:
90 + 40 + 5z + 10 = 180
5z + 140 = 180
5z = 40
z = 8
Answer:
$0.90 per pound.
Step-by-step explanation:
4.50:5
5/5=1
4.50/5=0.90
Answer:
f(x) has three real roots and two imaginary roots.
Step-by-step explanation:
Given that three roots of a fifth degree polynomial function f(x) are -2,2 and (4+i).
Now we need to find about which of the given statements describes the number and nature of all roots for this function.
We know that imaginary roots always occur in conjugate pairs.
So if (4+i) is root then (4-i) must also be the root.
So now we have total 4 roots
-2, 2, (4+i) and (4-i).
Degree of the polynomial is 5 so that means 1 root is still remaining. It can't be imaginary as that must be in pairs
So that means 5th root is real.
Hence correct choice is :
f(x) has three real roots and two imaginary roots.
B because there is only one negative and -63 divided by 7 equals -9. If it were -7 divided by 63 that would give you an answer in decimal form.
Answer:
<h3>
(2, 124)</h3>
Step-by-step explanation:
f(x) = a(x - h)² + k - the vertex form of the equation of the parabola with vertex (h, k)
![f(x) = -16x^2+ 64x + 80\\\\f(x) = -16(x^2- 4x) + 80\\\\f(x) = -16(\underline {x^2-2\cdot2x\cdot2+2^2}-2^2) + 80\\\\f(x) = -16\big[(x-2)^2-4\big] + 80\\\\f(x) = -16(x-2)^2+64 + 80\\\\\bold{f(x)=-16(x-2)^2+124\quad\implies\quad h=2\,,\quad k=124}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-16x%5E2%2B%2064x%20%2B%2080%5C%5C%5C%5Cf%28x%29%20%3D%20-16%28x%5E2-%204x%29%20%2B%2080%5C%5C%5C%5Cf%28x%29%20%3D%20-16%28%5Cunderline%20%7Bx%5E2-2%5Ccdot2x%5Ccdot2%2B2%5E2%7D-2%5E2%29%20%2B%2080%5C%5C%5C%5Cf%28x%29%20%3D%20-16%5Cbig%5B%28x-2%29%5E2-4%5Cbig%5D%20%2B%2080%5C%5C%5C%5Cf%28x%29%20%3D%20-16%28x-2%29%5E2%2B64%20%2B%2080%5C%5C%5C%5C%5Cbold%7Bf%28x%29%3D-16%28x-2%29%5E2%2B124%5Cquad%5Cimplies%5Cquad%20h%3D2%5C%2C%2C%5Cquad%20k%3D124%7D)
<u>The vertex is </u><u>(2, 124)</u>
