Vertex form of a parabola
<span>y = a (x - h)^2 + k </span>
<span>where (h, k) is the vertex </span>
Substituting the values of h and k.
we get,
<span>y = a(x + 4)^2 + 2 </span>
<span>substituting in the point (0, -30) for x and y
</span><span>-30 = a (0 + 4)^2 + 2
</span>solve for a,
<span>-30 = 16 a + 2 </span>
<span>-32 = 16 a </span>
<span>-2 = a </span>
<span>y = -2(x + 4)^2 + 2 </span>
<span>Put y = 0 </span>
<span>-2 x^2 - 16 x - 30 = 0 </span>
<span>-2(x^2 + 8 x + 15) = 0 </span>
<span>x^2 + 8 x + 15 = 0 </span>
<span>(x + 3)(x + 5) = 0 </span>
<span>x = -3
x = -5</span>
Answer:
What do you need help on?
Step-by-step explanation:
Answer:
15000(1.003425)^12t ;
4.11%
4.188%
Step-by-step explanation:
Given that:
Loan amount = principal = $15000
Interest rate, r = 4.11% = 0.0411
n = number of times compounded per period, monthly = 12 (number of months in a year)
Total amount, F owed, after t years in college ;
F(t) = P(1 + r/n)^nt
F(t) = 15000(1 + 0.0411/12)^12t
F(t) = 15000(1.003425)^12t
2.) The annual percentage rate is the interest rate without compounding = 4.11%
3.)
The APY
APY = (1 + APR/n)^n - 1
APY = (1 + 0.0411/12)^12 - 1
APY = (1.003425)^12 - 1
APY = 1.04188 - 1
APY = 0.04188
APY = 0.04188 * 100% = 4.188%
Answer:
6 < x ≤ 20
Step-by-step explanation:
First, let's use the points (0, 50) and (20, 0) to find the equation of the line.
m = Δy / Δx
m = (0 − 50) / (20 − 0)
m = -2.5
y = -2.5x + 50
Now find the time when y = 35.
35 = -2.5x + 50
-15 = -2.5x
x = 6
So there is less than 35 gallons in the barrel when 6 < x ≤ 20.
Answer:
-2
Step-by-step explanation:
8-10 = -2
20-19 = 1
-2/1 = -2
