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2 years ago

(gof)(x) = x2 + x + 1

Mathematics

1 answer:

Sever21 [200]2 years ago

8 0

Answer:

$the \: answer \: is \: b$

Step-by-step explanation:

$(gof)x = {(x + 1)}^{2 } = {x}^{2} + 2x + 1$

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What is the perimeter of a rectangle with an area of 2x^2+11x+5 in^2?

kirza4 [7]

Answer:

6x + 14

Step-by-step explanation:

Area = side x side

Factor the quadratic:

2x^2 +10x / +1x +5

2x(x+5) 1 (x+5)

(2x + 1) (x+5)

^These are your two sides

Perimeter =2L + 2W

(2(2x+1)) + (2(x+5))

4x+4+2x+10 = final answer 6x + 14

6 0

2 years ago

Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

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

Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

---------------------

The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$

The sum of the first ten terms is -85

-----------------------

As a check for $S_{10}$ , here are the first ten terms:

t1 = 5
t2 = 2
t3 = -1
t4 = -4
t5 = -7
t6 = -10
t7 = -13
t8 = -16
t9 = -19
t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that $S_{10} = -85$ is correct.

6 0

2 years ago

What’s the answer to this question?

steposvetlana [31]

Answer:

its x^4

Step-by-step explanation:

its x^4

5 0

2 years ago

PLEASE HELP ME!! FIND THE VOLUME OF X

sineoko [7]

Answer:

x = 6

Step-by-step explanation:

So thee cube is just x^3

The cube root of 216 is 6

7 0

3 years ago

Drag and drop the correct answer into each box to complete the proof.

Rudiy27

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4 0

3 years ago