Need help with these---
30. Suppose the area of a square is x^2 - 6x + 9. What is the perimeter of the square?
33. Factor the expression: k^2 + k^f - 2f^2
38. Find the final amount of an investment if $2,000 is invested at an interest rate of 8% compounded quarterly for eight years.
Thanks
-MC
30. If we factorise x^2 - 6x + 9, we get (x-3)^2.
So the perimeter is 4(x-3) = 4x -12
I'll need to figure out the others yet in a minute.
Wouldn't the perimeter be 4(x-3)^2?
Why? x-3 is the length of ONE side. To calculate
the perimeter of a square, the 4 identical sides are added. But maybe I'm wrong, I dunno....why do you want to square it?
Jazzie, you're correct. Thanks
-MC
30. 4x-12 is correct
33. You probably meant to type
k^2 + kf - 2f^2 which is
=(k+2f)(k-f)
38.
Amount = 2000(1.02)^32
= .....
Sure! I can help you with these problems. Let's go through each one step by step.
30. Suppose the area of a square is x^2 - 6x + 9. What is the perimeter of the square?
To find the perimeter of a square, we need to know the length of one side of the square. The area of the square given is x^2 - 6x + 9. We can find the side length by taking the square root of the area.
Taking the square root of x^2 - 6x + 9 gives us:
√(x^2 - 6x + 9)
Since the square root of a number squared cancels out the square, it simplifies to:
x - 3
Now that we know the side length of the square is x - 3, we can find the perimeter by multiplying it by 4. The perimeter of a square is 4 times the length of one side.
So, the perimeter of the square is:
4(x - 3)
33. Factor the expression: k^2 + k^f - 2f^2
To factor this expression, we need to look for common factors or patterns that can be factored. In this case, there doesn't seem to be any common factors or patterns that can be factored out easily.
So, we have:
k^2 + k^f - 2f^2
Since there are no common factors, we can use the quadratic formula to factor the expression. The quadratic formula is:
k = (-b ± √(b^2 - 4ac)) / (2a)
For our expression, we have a = 1, b = 1, and c = -2f^2.
Substituting these values into the quadratic formula, we get:
k = (-(1) ± √((1)^2 - 4(1)(-2f^2))) / (2(1))
Simplifying further:
k = (-1 ± √(1 + 8f^2)) / 2
So, the expression k^2 + k^f - 2f^2 cannot be factored further.
38. Find the final amount of an investment if $2,000 is invested at an interest rate of 8% compounded quarterly for eight years.
To find the final amount of the investment, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, P = $2,000, r = 8% (or 0.08 as a decimal), n = 4 (quarterly compounding), and t = 8 years.
Substituting these values into the formula, we get:
A = 2000(1 + 0.08/4)^(4*8)
Simplifying:
A = 2000(1 + 0.02)^(32)
A = 2000(1.02)^(32)
Calculating further:
A ≈ 2000 * 1.913145
A ≈ $3,826.29
So, the final amount of the investment after eight years is approximately $3,826.29.
I hope this helps! Let me know if you have any more questions.