Simply plug in the value of x.
f(x) = -x² + 4x + 12
f(3) = -(3²) + 4(3) + 12 = -9 + 12 + 12 = -9 + 24 = 15
f(4) = -(4²) + 4(4) + 12 = -16 + 16 + 12 = 0 + 12 = 12
f(5) = -(5²) + 4(5) + 12 = -25 + 20 + 12 = -25 + 32 = 7
f(6) = -(6²) + 4(6) + 12 = -36 + 24 + 12 = -36 + 36 = 0
g(x) = x + 8
g(3) = 3 + 8 = 11
g(4) = 4 + 8 = 12
g(5) = 5 + 8 = 13
g(6) = 6 + 8 = 14
f(x) = g(x) when x = 4.
f(4) = g(4)
12 = 12
Answer:
There is only 1 solution for x.
Step-by-step explanation:
Hi there!
This is a linear-quadratic system. If the line is tangent to the parabola, it means that it would only have 1 solution.
Set y equal:
Move everything to the left side:
Divide both sides by 3:
Factor:
Solve for <em>x</em>:
Therefore, the only solution for x when y is set equal for both functions is 1. There is only 1 solution for x, so is tangent to the curve .
I hope this helps!
Answer:
5 meters
Step-by-step explanation:
We should derive an equation to solve this problem.
Let's assign x to width and y to length.
and
so
Width = 5 meters