Just in case you don't know what this is, the explicit formula is the formula that solves for any term in the series without necessarily knowing what came before the term you are solving.

Givens

d = t_(n + 1) - t_n You can take any term and the next term for this part of the formula

d = t_3 - t_2

t_3 = 1

t_2 = -7

d = 1 - - 7 = 8

a = -15

Formula

t_n = a + (n - 1)*d

t_n = -15 + (n - 1)*8

For example find the 5th term.

t_5 = - 15 + (5 - 1)*8

t_5 = - 15 + 4 *8

t_5 = -15 + 32

t_5 = 17 Which is what you have.

Recursive Formula

Computers really like this formula. They use it in what is called a subroutine and they pass values from one part of the program to a subroutine which evaluates the given and sends the result back. I'm telling you all this so you see why you are doing it. The disadvantage of it for humans is that you must know the preceding term to use the recursive formula.

Formula

t_n = t_(n - 1) + d

Example

t_6 = t_(6 - 1) + d

t_6 = t_5 + 8

t_6 = 17 + 8

t_6 = 25

You can check this by using the explicit formula.

4 0

3 years ago

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Which line is parallel to the line shown below?

Travka [436]

<h3>Answer: Choice D</h3>

4x - 3y = 15

====================================================

Explanation:

The two points (-1,-1) and (2,3) are marked on the line

Let's find the slope of the line through those two points.

$(x_1,y_1) = (-1,-1) \text{ and } (x_2,y_2) = (2,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - (-1)}{2 - (-1)}\\\\m = \frac{3 + 1}{2 + 1}\\\\m = \frac{4}{3}\\\\$

The slope is 4/3 meaning we go up 4 and to the right 3.

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Parallel lines have equal slopes, but different y intercepts. We'll need to see which of the four answer choices have a slope of 4/3.

Solve the equation in choice A for y. The goal is to get it into y = mx+b form so we can determine the slope m.

$3x + 4y = -4\\\\4y = -3x-4\\\\y = -\frac{3}{4}x-\frac{4}{4}\\\\y = -\frac{3}{4}x-1$

Equation A has a slope of -3/4 and not 4/3 like we want.

Therefore, this answer choice is crossed off the list.

Follow similar steps for choices B through D. I'll show the slopes of each so you can check your work.

slope of equation B is 3/4
slope of equation C is -4/3
slope of equation D is 4/3

We have a match with equation D. Therefore, the equation 4x-3y = 15 is parallel to the given line shown in the graph.

You can use graphing tools like Desmos or GeoGebra to confirm the answer.

4 0

8 months ago

One end of a ramp is raised to the back of a truck 1 meter

Bogdan [553]

Answer:

26.6°

Step-by-step explanation:

8 0

3 years ago

You bought a pumpkin pie for Friendsgiving. At the end of the part 6/8 of the pumpkin pie was left. The host decided to share ou

ExtremeBDS [4]

The correct answer is D
6/8 divided by 4 is 3/16

6 0

2 years ago

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