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3 years ago

Solve for r: -5 = 7 + 3r

Mathematics

2 answers:

larisa86 [58]3 years ago

8 0

$-5=7+3r\ \ \ \ \ \ |combine\ like\ terms\\\\-5-7=3r\\\\-12=3r\ \ \ \ \ \ \ |:3\\\\r=-4$

Setler79 [48]3 years ago

6 0

So,

-5 = 7 + 3r
(subtract 7 from both sides)
-12 = 3r
(divide both sides by 3)
-4 = r

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Which graph represents the sequence: 1/2, 1, 2, 4, 8...?

Aleonysh [2.5K]

The graph represents the sequence is Option D.

<h3>Further explanation </h3>

A function defined in the set of natural numbers is called a sequence.

Allow $\boxed{a_n \ as \ n^{th} \ term}$ , or general term.

In a sequence, n should always represent a natural number, i.e.,

n > 0, n = 1, 2, 3, ...,

but the value of $\boxed{a_n}$ may be any real number depending on the formula for the general term of the sequence.

A sequence is considered geometric if the ratio between each consecutive term is common.

In our problem, the sequence is $\boxed{ \ \frac{1}{2}, 1, 2, 4, 8, ... \ }$

The ratio of each term $\boxed{a_{n+1}}$ to the previous term $\boxed{a_n}$ is equal 2, so we can formalize the sequence as

$\boxed{\frac{a_{n+1}}{a_n} =2}.$

The consecutive terms of the sequence have a common ratio r = 2, so this sequence is geometric.

The general term of a geometric sequence $\boxed{a_n}$ with common ratio r is $\boxed{\boxed{ \ a_n = a_1 \cdot r^{n-1} \ }}.$

Presently we go back to the question. The graph shows the horizontal axis as n and the vertical axis is the general term $\boxed{a_n}$ . The relationship between n, the terms, and the coordinates as written below:

$\boxed{n = 1 \rightarrow the \ 1st \ term \ a_1 = \frac{1}{2} \rightarrow \bigg( 1, \frac{1}{2} \bigg)}$

$\boxed{n = 2 \rightarrow the \ 2nd \ term \ a_2 = 1 \rightarrow (2, 1)}$

$\boxed{n = 3 \rightarrow the \ 3rd \ term \ a_3 = 2 \rightarrow (3, 2)}$

$\boxed{n = 4 \rightarrow the \ 4th \ term \ a_4 = 4 \rightarrow (4, 4)}$

$\boxed{n = 5 \rightarrow the \ 5th \ term \ a_5 = 8 \rightarrow (5, 8)}$

Therefore, the graph representing the sequence is Option D.

The general term of a geometric sequence is exponential.
From the common ratio (r > 1) and graph, the type is an increasing sequence.

<h3>Learn more </h3>

Combining two functions to create a geometric sequence brainly.com/question/1695742
A word problem about arithmetic and geometric sequences brainly.com/question/3395975
Drawing graph of the geometric sequence brainly.com/question/3166290

Keywords: which, the graph, geometric sequences, common ratio, general term formula, natural numbers, The consecutive terms, arithmetic

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3 years ago

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 ? 9x2 ? 108x + 2, [?3, 4]

SVEN [57.7K]

Assuming the question marks are minus signs
to find max, take derivitive and test 0's and endpoints

take derivitive
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if we make a sign chart to find the change of signs
the sign changes from (+) to (-) at x=-2 and from (-) to (+) at x=3
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test entpoints

f(-3)=83
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3 years ago

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myrzilka [38]

Answer: 7

Step-by-step explanation:

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3 years ago

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