Question 21
Let's complete the square
y = 3x^2 + 6x + 5
y-5 = 3x^2 + 6x
y - 5 = 3(x^2 + 2x)
y - 5 = 3(x^2 + 2x + 1 - 1)
y - 5 = 3(x^2+2x+1) - 3
y - 5 = 3(x+1)^2 - 3
y = 3(x+1)^2 - 3 + 5
y = 3(x+1)^2 + 2
Answer: Choice D
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Question 22
Through trial and error you should find that choice D is the answer
Basically you plug in each of the given answer choices and see which results in a true statement.
For instance, with choice A we have
y < -4(x+1)^2 - 3
-7 < -4(0+1)^2 - 3
-7 < -7
which is false, so we eliminate choice A
Choice D is the answer because
y < -4(x+1)^2 - 3
-9 < -4(-2+1)^2 - 3
-9 < -7
which is true since -9 is to the left of -7 on the number line.
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Question 25
Answer: Choice B
Explanation:
The quantity (x-4)^2 is always positive regardless of what you pick for x. This is because we are squaring the (x-4). Squaring a negative leads to a positive. Eg: (-4)^2 = 16
Adding on a positive to (x-4)^2 makes the result even more positive. Therefore (x-4)^2 + 1 > 0 is true for any real number x.
Visually this means all solutions of y > (x-4)^2 + 1 reside in quadrants 1 and 2, which are above the x axis.
After 6 years the investment is $5555.88
Step-by-step explanation:
A principal of $3600 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 6 years?
The formula used to find future value is:
where A(t) = Accumulated amount
P = Principal Amount
r = annual rate
t= time
n= compounding periods per year
We are given:
P = $3600
r = 7.5 %
t = 6
n = 1
Putting values in formula:
So, After 6 years the investment is $5555.88
Keywords: Compound Interest formula
Learn more about Compound Interest formula at:
#learnwithBrainly
Step-by-step explanation:
take the right triangle
15^2 = 9^2 + x^2
225 = 81 + x^2
x = 12
area of square b = 144
If you have a Scientific calculator you can type this in
