Answer:
$2147.36
Step-by-step explanation:
The first value can be modeled by ...
b1 = 1000·(1 -0.005)^t
After 10 years, that balance is ...
b1 = 1000·0.995^10 = 951.11
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The second value can be modeled by ...
b2 = 1000·(1 +0.018/2)^(2t)
After 10 years, that balance is ...
b2 = 1000·1.009^20 = 1196.25
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The total of the two investments after 10 years is ...
$951.11 +1196.25 = $2147.36
2ˣ = 2³
Since 2ˣ is EQUAL to 2³ and since 2 is equal to 2, then the solution is a must that the 2 exponents are equal.
Then x = 3
Answer:
3sqrt2
Step-by-step explanation:
If a side length is a, then a^2 + a^2 = 36
2a^2 = 36
a^2 = 18
a = 3sqrt2
Or, you can remember that in a square, if you cut it in half diagonally, you get a 45-45-90 triangle, so the sidenglth is diagonal/sqrt2
Answer: Choice D)
S(x) = 6x^2 - 20x
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Explanation:
x = side length of base
x*x = x^2 = area of base
The top also has an area of x^2 since the base and top are both congruent squares. The total base area is x^2+x^2 = 2x^2
The height h is 5 inches shorter than the base, so
h = (base length) - 5
h = x-5
Each lateral side is of area h*x = (x-5)*x = x^2-5x
There are 4 lateral sides
Total lateral area = 4*(area of one lateral side)
Total lateral area = 4*(x^2-5x)
Total lateral area = 4*x^2-4*5x
Total lateral area = 4*x^2-20x
Add the total lateral area (4x^2-20x) to the total base area (2x^2)
Doing so gets us
S(x) = Total Surface Area
S(x) = (Area of bases) + (area of lateral sides)
S(x) = (2x^2) + (4x^2-20x)
S(x) = (2x^2+4x^2) - 20x
S(x) = 6x^2 - 20x
which is why the answer is choice D
