We are asked to solve for the angle of BDC in the figure which is rectangle ACBD.
Since it is a rectangle, each corner has a 90°. Initially, it was given that angle BDA is equal to 50°. Then we can solve for BDC, such as the solution is shown below:
90° = ∠ BDC + ∠ BDA
90° = ∠BDC + 50°
∠BDC = 90° - 50°
∠ BDC = 40°
The answer is 40°.
(3,2)
(-2,4)
that makes both equations
16=16
2=2
I hope this is what you were looking for
Answer:
Vertex = (12,64)
The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.
X-intercepts: 4 and 20
The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.
Step-by-step explanation:
To find the vertex we can use the formula for the x-coordinate of the vertex:
x_v = -b/2a
Where a and b are coefficients of the quadratic equation (in this case, a = -1 and b = 24)
So we have that:
x_v = -24 / (-2) = 12
The vertex is 12 cups of coffee. Now we apply this value to find the y-coordinate of the vertex:
f(x) = -12^2 + 24*12 - 80 = 64
So the vertex is (12,64). The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.
To find the x-intercepts, we need to make f(x) = 0 and find the values of x:
-x2 + 24x - 80 = 0
Delta = 24^2 - 80*4 = 256
sqrt(Delta) = 16
x1 = (-24 + 16)/(-2) = 4
x2 = (-24 - 16)/(-2) = 20
The x-intercepts are 4 and 20. The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.
12(x^2+7)2−8(x^2+7)(2x−1)−15(2x−1)^2
Distribute:
=12x^4+168x^2+588+−16x^3+8x^2+−112x+56+−60x^2+60x+−15
Combine Like Terms:
=12x^4+168x^2+588+−16x^3+8x^2+−112x+56+−60x^2+60x+−15
=(12x^4)+(−16x^3)+(168x^2+8x^2+−60x^2)+(−112x+60x)+(588+56+−15)
=12x^4+−16x^3+116x^2+−52x+629
