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konstantin123 [22]
3 years ago
15

Find Sn for the given arithmetic series a1=-26 d=-9 n=24

Mathematics
1 answer:
ryzh [129]3 years ago
5 0

Answer:

- 3108

Step-by-step explanation:

The sum to n terms of an arithmetic series is

S_{n} = \frac{n}{2} [ 2a_{1} + (n - 1)d ]

Substitute the given values into the formula

S_{24} = \frac{24}{2} [ (2 × - 26) + (23 × - 9) ]

                          = 12 ( - 52 - 207 )

                         = 12 × - 259 = - 3108

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How far is 7 from 0 and in which direction?
muminat

Answer: On a number line, 0 is in the middle, to the right , 7 is 7 spaces away from 0

5 0
3 years ago
Please show work 3d – 4 + d = 8d – (-12)
balandron [24]

Answer:

d = -4

Step-by-step explanation:

3d – 4 + d = 8d – (-12)

3d - 4 + d = 8d + 12

4d - 4 = 8d + 12

(4d - 4d) - 4 = (8d - 4d) + 12

-4 = 4d + 12

-4 - 12 = 4d (+ 12 - 12)

-16 = 4d

-16/4 = 4d/4

d = -4

4 0
2 years ago
Read 2 more answers
Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29
hram777 [196]

Answer:

\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }

Step-by-step explanation:

Hello,

I assume that we are working in \mathbb{C}, otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

   p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }

Now, we need to find the zeroes of the second factor, meaning finding x so that:

x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4}  \\ \\  x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\  x = 2+5i \ \text{ or } \ x = 2-5i

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0
3 years ago
Type the correct answer in the box.
Pepsi [2]

Answer:

f(g(-64)) = -190

Step-by-step explanation:

The functions are not well written.

Let us assume;

f(x) = x+1

g(x) = 3x+1

f(g(x)) = f(3x+1)

Replace x with 3x+1 in f(x)

f(g(x)) = (3x+1) + 1

f(g(x)) = 3x + 2

f(g(-64)) = 3(-64) + 2

f(g(-64)) = -192+2

f(g(-64)) = -190

<em>Note that the functions are assumed but same method can be employed when calculating composite functions</em>

8 0
2 years ago
I have been stuck on the problem for so long. please help me:
Xelga [282]

Answer:

D-2

Step-by-step explanation:

You can use elimination to get the value of y. Move numbers to one side and x and ys to the other side. To use elimination, multiply the first equation with 2. You will get 2x+2y=24. add it with the equation below. y will be eliminated and you will get the value of x. X=10. Plug in x and get the y value. Y=2

6 0
3 years ago
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