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gregori [183]
3 years ago
6

What is the sum of this arithmetic series?

Mathematics
2 answers:
ValentinkaMS [17]3 years ago
7 0

Answer:

52

Step-by-step explanation:

The ' easiest' method here is to substitute k = 1, 2, 3, 4 into the expression and sum the terms, that is

(- 2 + 6(1) ) + ( - 2 + 6(2) ) + ( - 2 + 6(3) ) + (- 2 + 6(4) )

= (- 2 + 6) + (- 2 + 12) + (- 2 + 18) + (- 2 + 24)

= 4 + 10 + 16 + 22

52

MrMuchimi3 years ago
6 0
The sum of this arithmetic series is 52.
You might be interested in
Factor the trinomial. You many need to check the discriminant to make sure it can be factored. SHOW YOUR WORK.
lbvjy [14]
Check the discriminant (always a good idea).

b^2 - 4ac 
b = -19
c = -15
a = 10

(-19)^2 - 4(10)(-15)
361 + 600
961

Yes it can be factored, but if you like, you could use the quadratic formula.
x = [- (-19) +/- sqrt(961)]/(2 * 10)
x = [19 +/- 31 ] / 20
x = (19 + 31/20
x = (50)/20
x = 5/2

x = [19 - 31] / 20
x = [- 12]/20
x = -3/5

Getting the factors is a little tricky.
(x - 5/2)(x + 3/5) = 0
The first factor is found by putting 
x - 5/2 in that form and multiplying through by 2
1/2 (2x - 5) The 1/2 comes from multiplying by 2. 

The second factor is
1/5 (5x + 3)

So the equation will look like 
1/2(2x - 5)1/5(5x + 3) = 0 If you multiply by 2 you get
(2x - 5)1/5(5x + 3) = 0 and now multiply by 5 you get
(2x - 5) (5x + 3) 

Check
2x*5x - 25x + 6x - 15
10x^2 - 19x - 15 = 0

So everything works out. 
6 0
3 years ago
Do this please please?!?!​
Shalnov [3]

Answer:

1. 6

2. 27

3. 158

4. 9

5. 380

6. 108

7. 48

8. 10

9. 115

10. 57

Step-by-step explanation:

3 0
3 years ago
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
dybincka [34]

What you should do first is simplify the equation into the y = mx + b format. Move 2x to the other side. Know that in doing this, 2x must become the opposite of what it currently is (-2) in order for the equation to remain true. We also have to take away the '10' because the line is parallel, not exactly the same, which means a different y intercept. This looks like:

5y = -2x + b

Next, simplify y to make things easier. This can be done by dividing both sides by 5, like so:

\frac{5}{5}y = -\frac{2}{5}x + b

What you should also know is that if a line is parallel to another, then this means the slope has to be the same because they both have the same changes in rise and run. With this in mind, simply plug in the x and y values.

(-4) = -\frac{2}{5} * (5) + b

--> -4 = \frac{10}{5} + b

---> -4 = -2 + b

Add 2 to both sides to isolate b.

-4 + 2 = b

Which means that -2 = b.

Now that we have the y intercept, we can write the equation of the line, which is y = -\frac{2}{5}x - 2.

Hope this was helpful.

3 0
3 years ago
Determine the equations of the vertical and horizontal asymptotes if any for h(x)=(x+1)^2/x^2-1
shepuryov [24]

ANSWER

Vertical asymptote:

x=1

Horizontal asymptote:

y=1

EXPLANATION

The given rational function is

h(x) =  \frac{ {(x + 1)}^{2} }{ {x}^{2} - 1 }

h(x) =  \frac{ {(x + 1)}^{2} }{ ({x}  - 1)(x + 1)}

h(x) =  \frac{ (x + 1)(x + 1) }{ ({x}  - 1)(x + 1)}

h(x) =  \frac{ x + 1}{ {x}  - 1}

The vertical asymptote occurs at

{x} - 1 = 0

x = 1

The vertical asymptotes is x=1

The degree of the numerator is the same as the degree of the denominator.

The horizontal asymptote of such rational function is found by expressing the coefficient of the leading term in the numerator over that of the denominator.

y =  \frac{1}{1}

y=1

8 0
3 years ago
Determine the next three terms in the following sequence
tia_tia [17]

Answer:

A

Step-by-step explanation:

4 0
3 years ago
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