f(x )= ?
g(x) = ?
Neither function can be the identity function.
(There may be more than one correct answer.)

Problem 1

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Explanation:

Add the equations straight down.

The x terms add to 5x+(-3x) = 2x

The y terms cancel out since 3y+(-3y) = 0y = 0

The right hand sides add to -7+3 = -3

After adding the equations you should get 2x = -4 which solves to x = -2

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Problem 2

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Explanation:

Since 5x = 0, this means x = 0 after dividing both sides by 5.

Use this to find y

y = -4x+4

y = -4(0)+4

y = 4

If you want the value of z, then

x = -3y+z+6

0 = -3(4)+z+6

0 = z-6

6 = z

z = 6

Answer:

50

Step-by-step explanation:

i asked alexa so yeaaa

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:

each bus has cost $2 thats it

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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.

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

Answer: 5) 2, -8, 32, _,_

I believe that it would be -64, then 128

Step-by-step explanation:

Bc its positive then negative and its being multiplied by -4 each time so when you mutiply a negative to a negative its a positive which is were the positives and negatives come from. :)

Answer:

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

Answer:

y=3 the answer is 9 to the equation

Answer:

b, controlled variables are constant and unchanged

A controlled variable is what is held constant. When doing an experiment, it is ideal to only focus on one variable at a time while keeping everything else in check. This way you can compare two items effectively.

In contrast, a manipulated variable is one that is intentionally changed to see how it affects the subject. For example, if you're testing various fertilizers, then the fertilizer brand would be the manipulated variable. The soil, moisture, amount of sunlight, and other environmental factors are kept the same (each subject gets the same about of each) making them to be controlled variables.

Answer:

18,28,38,48,58,68

Step-by-step explanation:

You are adding by 10 every time

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:

there are 8 girl students

Step-by-step explanation:

28-4= 24

28 divided by 3 is 8

8x2=16

16+4=20

20+8= 28

therefore... there are 8 girls in the class

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:

d

Step-by-step explanation:

Answer:

Geometry so easy

Step-by-step explanation:

You can do it..

Answer:

i dont no hindi ko alam eh

Step-by-step explanation:

-Given

-4

-Divison Property Of Equality

-3

Answer:

x=6

Step-by-step explanation:

The picture is a little unclear but I hope this is true...

To find the perimeter you need to add the sides of the triangles and the question says that the perimeters of the triangles are equal. So,...

(2x+4)+(2x)+(2x+3)=(3x+1)+(2x)+(2x)

2x+4+2x+2x+3=3x+1+2x+2x

4+2x+3=3x+1

7+2x=3x+1

2x-3x=1-7

-x=-6

x=6

Answer:

16 cups of water

Answer:

9

Step-by-step explanation:

3x3=9

its nine bruhhhhhhhhhhhhh

Answer:

100.40

Step-by-step explanation:

if 6 members has paid, then the remaining 8 will be 8 x 12.55 = 100.4

Answer:

The answer is $100.40

Step-by-step explanation:

ok. their are 14 members. 6 members payed their dues in week 1. so, subtract 6 from 14.    14 - 6 = 8.    Now, the due is $12.55. 8 members payed their dues in week 2, so multiply 8 by 12.55.     8 x 12.55 = 100.50    the answer SHOULD be $100.50 i would think, but there is not an option for that. so, i would pick option 4, because that is .10 off from 100.50. Good luck!!

Answer:

Step-by-step explanation:

Explaining the Basic Concept:

This is a piecewise function, which means that it is made up of several different functions which all have different domains

In this question, we have 3 'pieces' in our piecewise function

the domain of each piece is:

1.   x < -1

2.  -1 ≤ x ≤ 2

3.  x > 2

we will use the function related with the respective domain

Finding the values of the function:

h(-4)

Here, our input value is -4

we notice that -4 is in part of the first domain

therefore, -4 is in the domain of the first function

So, we will use the first function

h(x) = -(x/4) + 2           (for x < -1)

replacing x with -4

h(-4) = -(-4/4) + 2

h(-4) = 1 + 2

h(-4) = 3

h(1):

Here, our input value is 1

we notice that 1 is a part of the second domain

Hence, 1 is in the domain of the second function

So, we will use the second function

h(x) = -(x-1)² + 2            (for -1 ≤ x ≤ 2)

replacing x with 1

h(1) = -(1-1)² + 2

h(1) = -(0)² + 2

h(1) = 2

h(2):

Here, out input value is 2

We notice that 2 is a part of the second domain

Hence, 2 is a part of the domain of the second function

So, we will use the second function

h(x) = -(x-1)² + 2            (for -1 ≤ x ≤ 2)

replacing x with 2

h(2) = -(2-1)² + 2

h(2) = -(1)² + 2

h(2) = - 1 + 2

h(2) = 1

Therefore:

h(-4) = 3

h(1) = 2

h(2) = 1

Answer:

the third one im pretty sure

Step-by-step explanation:

Answer:

[tex]Solution: f(x)\ge-5\\Interval:[-5,\infty)[/tex]

Step-by-step explanation:

Equation: [tex]\frac{1}{4} x^2-5 = y[/tex]

1). [tex]\frac{1}{4} x^2-5 = y[/tex] →[tex]\frac{x^2}{4}-5=y[/tex]

2). [tex]\frac{x^2}{4}-5=y[/tex] ∴ [tex]a=\frac{1}{4}, b=0, c=-5[/tex]

3). [tex]x_v=-\frac{b}{2a}[/tex]

         [tex]=-\frac{0}{2(\frac{1}{4})}[/tex]

         [tex]=0[/tex]

4). now plug [tex]x_v[/tex] into [tex]y_v[/tex]

[tex]y_v=\frac{0^2}{4}-5[/tex]

    [tex]=-5[/tex]

5). Minimum (0,-5) ∴ [tex]f(x)\ge-5[/tex]

Answer:

it is 82.53 round to 82.50 ithink

Answer:

2 3/5

Step-by-step explanation:

Answer:

In math, prime numbers are whole numbers greater than 1, which have only two factors – 1 and the number itself. Prime numbers are divisible only by the number 1 or itself. For example, 2, 3, 5, 7, and 11 are the first few prime numbers.

Step-by-step explanation:

hope this helps :)

Answer:

  y = -5/4x -19

Step-by-step explanation:

It is often convenient to simplify a point-slope form of the equation.

  y = m(x -h) +k . . . . . line with slope m through (h, k)

  y = -5/4(x -(-8)) -9 . . . . fill in given values

  y = -5/4x -10 -9

  y = -5/4x -19