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4 years ago

15

What is the function g(x) created from f(x) = x2 by moving the graph left 4 units, vertically stretching it by a factor of 5, an

d shifting the graph down 2 units?

2 answers:

IRISSAK [1]4 years ago

7 0

Answer:

$f(x) =5 (x+4)^2 -2$

Step-by-step explanation:

A = 5

B = 1

h = 2

k = -2

Use ABhk

vesna_86 [32]4 years ago

4 0

Answer is g(x) = 5(x + 4)2 − 2

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Find the point on the line 5x+7y+1=0 which is closest to the point (−4,3).

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$5x + 7y + 1 = 0$

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3 years ago

A water tank is in the shape of a right circular cylinder with a height of 20 feet and a volume 320π of cubic feet. What is the

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To solve for radius use the volume formula and solve for r.

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4 years ago

Read 2 more answers

What multiple of 7 is also a factor of 7

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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:

$\displaystyle \large{r=\frac{a_{n+1}}{a_n}}$

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

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

Above should be applied for series that have common ratio not equal to 1.

$\displaystyle \large{S_n=a_1 \cdot n}$

Above should be applied for series that have common ratio exactly equal to 1.

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Topics

Sequence & Series — Geometric Series

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

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7 0

3 years ago