Answer:
c
Step-by-step explanation:
The red graph is the black graph translated vertically by 1 unit
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Thus f(x) + 1
Note
y - 1 = f(x) ← add 1 to both sides
y = f(x) + 1 ← as required
The equation of the red graph is
y - 1 = f(x) → c
Answer: height = 6, radius = 8, Volume = 401.92
Explanation:
Height = 6 given
Find radius:
Use Pythagorean’s theorem to find the side of the right triangle:
a^2 + b^2 = c^2
b^2 = c^2 - a^2
b^2 = 10^2 - 6^2
b^2 = 100-36
b^2 = 64
b = 8
And since length b is also the radius of the circle then radius = 8
Find volume:
V = pi x r^2 x h/3
V = 3.14 x 8^2 x 6/3
V = 3.14 x 64 x 2
V = 401.92
Answer:
D
Step-by-step explanation:
For simplify the work we can start to factorise all the possibles expressions:
2x + 8.
8 is multiple of 2, so it can became
2(x+4)
x^2 - 16 this is a difference of two squares, so it can be rewritten as:
(x+4)(x-4)
x^2 + 8x + 16
we have to find two numbers whose sum is 8 and whose product is 16
the two number are 4 and 4
it becames:
(x+4)(x+4)
x+ 4 can‘t be simplified
if we look at the expression, we can find that x-4 appears at the numerator so
x^2 - 16 must be at numerator
but the second factor (x+4) doesn’t appear, so has been simplified. This situation can be possible only in the D option
in fact
(x+4)(x-4)/2(x+4) * (x+4)/(x+4)(x+4)
it became
(x+4)(x-4)/2 * 1/(x+4)(x+4)
(x-4)/2(x+4)
If this is a 30, 60, 90 triangle, which I think it is, it would b 4
