(X+2) (x+8) <br> expand and simplify

Please help i have 2 questions thank you very much.

Rudik [331]

Hello!

Question 1
We first have to convert everything to yards since the concrete is charged by the cubic yards

15 feet = 5 yards
15 feet = 5 yards
3 inches = 0.08333

Multiply these to find the volume

5 * 5 * 0.08333 = 2.08325

Multiply this by the cost

2.08325 * 46 = 95.83

The answer is C) $95.83
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Question 2

You have to find the volume of the first pyramid

The equation we use is $V = \frac{lwh}{3}$

V is volume
l is length
w is width
h is height

Put in the values we know

$V = \frac{16 * 16 * 28}{3}$

Multiply

$V = \frac{7168}{3}$

Divide

V = 2389.3333

Now we use this to find the side length of the second pyramid

$2389.333 = \frac{lw * 112}{3}$

Multiply both sides by 3

<span>7167.999 = lw * 112
</span>
Divide both sides by 112

63.9999 = lw

Since it is a square pyramid we know that sides are equal

63.999 = l^2

Take the square root of both sides

8 = l

The answer is B) 8in

Hope this helps!

8 0

3 years ago

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: