Vertex form formula: y = a(x-h)^2 +k, with vertex (h,k)
There are multiple ways to find the vertex. One way is to find the roots and then find the x value exactly in between them, because this parabola is symmetrical.
0 = (x - 3)(x + 2), so x = 3 and -2. The point directly in the middle is x = 1/2 = h
To find the y value of the vertex, plug in 1/2 to the equation.
(1/2)^2 - 2(1/2) + 5 = 4.25 = k
y = (x - 0.5)^2 + 4.25
Answer:
The length of the pencils is 4.1 inches and for the crayons 1.5 inches
Step-by-step explanation:
We can solve by means of a 2x2 system of equations, we have to:
let "x" be the length of the pencils
let "y" be the length of the crayons
4 * x + 3 * y = 20.9
5 * x + 4 * y = 26.5 => x = (26.5 - 4 * y) / 5
Replacing:
4 * (26.5 - 4 * y) / 5 + 3 * y = 20.9
21.2 - 3.2 * y + 3 * y = 20.9
-0.2 * y = 20.9 - 21.2
y = -0.3 / -0.2
y = 1.5
now for x:
x = (26.5 - 4 * 1.5) / 5
x = 4.1
This means that the length of the pencils is 4.1 inches and for the crayons 1.5 inches
Answer:
$14,277.80
Step-by-step explanation:
The standard formula for compound interest is given as;
A = P(1+r/n)^(nt) .....1
Where;
A = final amount/value
P = initial amount/value (principal)
r = rate yearly
n = number of times compounded yearly.
t = time of investment in years
For this case;
P = $7,400
t = 8 years
n = 4 (quarterly)
r = 9.5% = 0.095
Using equation 1.
A = $7,400(1+0.095/4)^(4×7)
A = $7,400(1.02375)^(28)
A = $7,400(1.929432606035)
A = $14,277.80
final amount/value after 8 years A =$14,277.80
Answer:
He had been in a hospital with friends since his birth
