Answer: Choice A
y = -3(x+2)^2 + 10
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Work Shown:
y = -3x^2-12x-2 is in the form y = ax^2+bx+c with
a = -3
b = -12
c = -2
The x coordinate of the vertex is
h = -b/(2a)
h = -(-12)/(2*(-3))
h = 12/(-6)
h = -2
We'll plug this into the original equation to find the corresponding y coordinate of the vertex.
y = -3x^2-12x-2
y = -3(-2)^2-12(-2)-2
y = 10
So k = 10 is the y coordinate of the vertex.
Overall, the vertex is (h,k) = (-2,10)
Meaning that we go from this general vertex form
y = a(x-h)^2 + k
to this
y = -3(x - (-2))^2 + 10
y = -3(x+2)^2 + 10
39 hours, 13 minutes and 50 seconds
Answer:
Coordinates of P: (10,2)
Step-by-step explanation:
Slope of ST = (2-(-5))/(-4-3) = -1
angle S = 90° so Slope of SP = 1
P(10,2)
I’m assuming you mean 7.2% for the annual interest rate and not 72%. If the annual interest rate is 7.2% then the interest after 6 months is $54.
To solve this problem, you us the equation A=P(1+rt)
A stands for the amount of money accumulated after t years
P stands for principal
r stands for annual interest rate
t stands for time (in years)
Next you need to plug it into your formula which should look like this...
A=1500(1+(0.072*0.5))
When you plug in your annual interest rate, you have to move your decimal place 2 places to the left. That is why 7.2% is 0.072 in the formula above.
The reason that I plugged in 0.5 for the time instead of 6 months is because the time in this formula is calculated in years. For example, if the question told you the time was 12 months, 12 months is one year, so you would plug in a 1 for t. Since your question asked for 6 months, 6 months is equal to half a year or 0.5 of a year. That is why t is 0.5 in the formula.
Now that you have your problem, the next step is to solve. I will show you what that looks like down below.
A=1500(1+(0.072*0.5))
A=1500(1+(0.036))
A=1500(1.036)
A=1554
From this problem, we just solved for how much money is in this account after 6 months which is $1554. But we’re not done yet, we are looking for how much interest was earned after 6 months.
To find this, all you have to do is subtract the amount earned after 6 months ($1554) by the principal amount ($1500) using this formula (the I stands for Interest).
A-P=I
1554-1500= 54
The interest earned after 6 months is $54.
(If the annual interest rate is 72% and not 7.2%, you can still use the formulas and my lesson to solve it yourself)
<C = 1/2(135 - 59)
<C = 1/2(76)
<C = 38
answer
A. 38°
