least common factor of 12 and 22

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Explanation:

f(x) is continuous when x >= 1. The only discontinuity for f(x) is when x = 0, but 0 is not part of this interval.

f(x) is positive for any valid x value in the domain since x^6 is always positive. In general, x^n is positive for all x when n is any even number.

f(x) is decreasing. You can see this through a table of values or through a graph. For anything in the form 1/(x^k), it will be a decreasing function because x^k gets larger, so 1/(x^k) gets smaller, when x goes to infinity.

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The conditions to use the integral test have been met. So we have to see if [tex]\displaystyle \int_1^{\infty}f(x)dx[/tex] converges or not.

Let's integrate and find out

[tex]\displaystyle \int \frac{1}{x^6} dx = \int x^{-6} dx\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{1+(-6)}x^{-6+1}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{-5}x^{-5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5}*\frac{1}{x^5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5x^5}+C\\\\[/tex]

So we have

[tex]\displaystyle g(x) = \int f(x) dx\\\\\\\displaystyle g(x) = \int \frac{1}{x^6} dx\\\\\\\displaystyle g(x) = -\frac{1}{5x^5}+C\\\\\\[/tex]

Meaning that,

[tex]\displaystyle \int_{a}^{b} f(x) dx = g(b)-g(a)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = \left(-\frac{1}{5b^5}+C\right)-\left(-\frac{1}{5a^5}+C\right)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = -\frac{1}{5b^5}+\frac{1}{5a^5}\\\\\\[/tex]

If we plug in a = 1 and apply the limit as b approaches positive infinity, then the expression [tex]-\frac{1}{5b^5}+\frac{1}{5a^5}[/tex] will turn into [tex]\frac{1}{5}[/tex]

Therefore,

[tex]\displaystyle \int_{1}^{\infty} \frac{1}{x^6} dx = \frac{1}{5}\\\\\\[/tex]

Because this integral converges, this means the series [tex]\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^6}[/tex] also converges as well by the integral test.

Answer:

B and C

Step-by-step explanation:

All others have higher factors than 4

Answer:

B,(4,8) &C,(8,12)

Step-by-step explanation:

A,(2,4)=2=2

4=2^2(GCF of 2&4 is 2)

B,(4,8)=4=2^2

8=2^3(GCF of 4&8 is 4)

C,(8,12)=8=2^3

12=2^2*3(GCF of 8&12 is 4)

D,(8,16)=8=2^3

16=2^4(GCF of 8&16 is 8)

E,(12,24)=12=2^2*3

24=2^3*3(GCF of 12&24 is 12).

i hope it helps you

Answer:

it would me 24 legs

Step-by-step explanation:

hope that helps

Answer:

for example you are given a percentage and numbers you cross multiply

Step-by-step explanation:

hope it helps cause I don't know how to explain the answer

Answer:

13.

Step-by-step explanation:

[tex]42 = a + (a+1) + (a+2) = 3a + 3 = 3(a+1)[/tex]

Then, [tex]a+1 = 14[/tex], so [tex]a=13.[/tex]

Answer:

make each of the supplementary angles 90, then they are equal.                                                                                                                                                                                                                                                                                                                  

Step-by-step explanation:

Answer:

bro are you talking about some picture

Step-by-step explanation:

Answer:

Step-by-step explanation:

A1 = 9 x 4 = 36

A1 = 4 x 3 = 12

Total = 36 + 12

        = 48 in²

Answer:

l=6

b=30

Step-by-step explanation:

b=5l

perimeter= 72

2(l+b)= 72

l+b= 36

l+5l= 36

6l= 36

l= 6

b=5l= 6*6= 30

Answer:

1. True

2. False

3. True

4. False

5. True

Step-by-step explanation:

For 1, you want to see the reduced fraction of 2/6 so you want to divide 2/6 by 2, it is 1/3 and 2/3 is greater than 1/3.

For 2, you want to multiply 5 by 2. and then do the same thing for 6, 6 x 2. Now you want to see if they match.

For 3, you want to make both fractions into decimals so 1/8 is 0.125 and 1/4 is 0.25 and see which is larger.

For 4, you want to see if you can simplify any of them. 2/4 can be simplifed to 1/2. So, it is false because you can see that 2/4 is the same as 1/2

For 5, you want to divide both fractions by 2, so 4/10 would be 2/5 and 4/6 would be 2/3. So it is true.

The answers for the given expressions are given below,

1. True

2. False

3. True

4. False

5. True

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

For 1, you want to see the reduced fraction of 2/6 so you want to divide 2/6 by 2, it is 1/3, and 2/3 is greater than 1/3.

For 2, you want to multiply 5 by 2. and then do the same thing for 6, 6 x 2. Now you want to see if they match.

For 3, you want to make both fractions into decimals so 1/8 is 0.125 and 1/4 is 0.25, and see which is larger.

For 4, you want to see if you can simplify any of them. 2/4 can be simplified to 1/2. So, it is false because you can see that 2/4 is the same as 1/2

For 5, you want to divide both fractions by 2, so 4/10 would be 2/5, and 4/6 would be 2/3. So it is true.

To know more about an expression follow

https://brainly.com/question/13780981

#SPJ2

Answer:

16 cups of water

Answer:

6

Step-by-step explanation:

4x + 3 = 1

4x =-2

x = -1/2 so 4x +8 =4(-1/2) +8=6

$$$$$$$$$$$$$$$$$$$$$$$$$$

Answer:

You must first put the equation into slope-intercept form (y = mx + b). To do this, subtract x from both sides to isolate y. Then, since y will be negative, divide each side by -1, resulting in y = x - 3. Since a 1 is understood to be in front of the x, the slope is 1

How to graph:

x-0 y- -3 or (0,-3)

x- 3 y-0 or (3,0)

If you graph these points you should get your graph

Answer:

209 biology books and 125 psychology books were sold.

Step-by-step explanation:

x = biology books y = psychology books

334 = x + y

x = y + 84

x - y = 84

y = x - 84

Using these systems of equations, we can see that (209,125) is the only possible answer. Elimination, substitution, or guess and check are all viable methods to solve this problem. I can explain further if needed! :)

Answer:

power of for example 4 to the power of 2. 2 means square

Answer:

d

Step-by-step explanation:

Answer:

x=3⋅±  2

​  

=±4.2426

x=0

Step-by-step explanation:

Answer:

I wish I could help you but i have not learn yhat yet. so sorrry :( pleaser forgive jme....... please i beg u plase

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

he can make 4 stacks, leaving 8 chairs as single chairs

Answer:

86 meters

Step-by-step explanation:

27+27+16+16=54+32=86 meters