Answer:
Subtract c from each side, using the subtraction property of equality
Step-by-step explanation:
0 = ax^2 + bx + c
Subtract c from each side, using the subtraction property of equality
-c = ax^2 + bx + c-c
-c = ax^2 + bx
Answer:
1. 72
2. 60
3. 35
4. 32
Step-by-step explanation:
1. 6 x 4 x 3= 72
2. 5 x 3 x 4= 60
3. 5 x 2 x 2= 20
5 x 3 x 1= 15
20 + 15= 35
4. 5 x 3= 15
2 x 2=4
4 x 8= 32
Answer: f(x) = -0.016x² + 1.6x
Step-by-step explanation:
If the lenght of the road over the arch is 100m, we can consider a coordinate plane and say that the road starts at point (0,0) and finishes at (100,0). The vertice of the parabola is at point (50,40), because the maximum height is 40 and it is always in the middle point of the roots.
So, we have
(0,0) (50,40) (100,0)
A quadratic function is always on the form: f(x) = ax² + bx + c
0 = a0² + b0 + c
40 = a50² + b50 + c
0 = a100² + b100 + c
0 = a0² + b0 + c → c = 0 ∴
40 = a50² + b50
0 = a100² + b100
_________________________
2500a + 50b = 40 (*2)
10000a + 100b = 0
_________________________
5000a + 100b = 80
10000a + 100b = 0 (-)
__________________________
-5000a = 80
-a=80/5000
a=-0.016
∴
2500a + 50b = 40
2500.(-0.016) + 50b = 40
-40 + 50b = 40
50b = 80
b = 80/50
b = 1.6
This way f(x) = -0.016x² + 1.6x
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that alpha and beta be conjugate complex numbers
such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}.
Let
since they are conjugates
Imaginary part of the above =0
i.e. 
So the value of alpha =
