Simplify the expression. 6(7n – 5m) 8m

1 answer:

4 0

Simplifying
6(7n + -5m) + 8m = 0

Reorder the terms:
6(-5m + 7n) + 8m = 0
(-5m * 6 + 7n * 6) + 8m = 0
(-30m + 42n) + 8m = 0

Reorder the terms:
-30m + 8m + 42n = 0

Combine like terms: -30m + 8m = -22m
-22m + 42n = 0

Solving
-22m + 42n = 0

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-42n' to each side of the equation.
-22m + 42n + -42n = 0 + -42n

Combine like terms: 42n + -42n = 0
-22m + 0 = 0 + -42n
-22m = 0 + -42n
Remove the zero:
-22m = -42n

Divide each side by '-22'.
m = 1.909090909n

Simplifying
m = 1.909090909n

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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