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4 years ago

10

An expression is shown: martha evaluates the expression using these steps: step 1: step 2: step 3:

1 answer:

earnstyle [38]4 years ago

8 0

Answer:Answer: D Step 3 ; f²k³

Explanation:

(k⁻¹)⁻³ = k³

Step-by-step explanation:

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Freddy is driving from home to his grandfather's house, which is 174 miles away. He drives at an average rate of 58 miles per ho

Liono4ka [1.6K]

If n = number of hours and the equation is 174 + 58n then the answer is 3 hours

174 = 58n

÷ 58

3 = n

5 0

3 years ago

Read 2 more answers

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

Describe the solution of g(x) shown in the graph.

Ugo [173]

Answer:

All real solutions

Step-by-step explanation:

The given graph is a maximum quadratic function.
The solution to the graph is where the graph intersects the x-axis.
We can see from the graph that, the function intersected the x-axis at two different points, hence its discriminant is greater than zero.
Hence the solution of g(x) are two distinct real solutions.
The solutions are not whole numbers because the x-intercepts are not exact.
The solutions are also not all points that lie on g(x)
The first choice is correct.

3 0

3 years ago

Why the great awakening was important to people?

katrin2010 [14]

Well is this like history

4 0

3 years ago

20. I need to find the slope and y-intercept. How do I do that with fractions like that?

stich3 [128]

Answer:

the slope is the fraction and the y int is zero

Step-by-step explanation:

3 0

3 years ago