if f(x) = x + 7 and g(x) = 1 / x - 13, whaf is the domain of (f°g)(x)?​

If F(x) = X + 7 And G(x) = 1 / X - 13, Whaf Is The Domain Of (fg)(x)?

Answers

Answer 1

Answer: Choice D) x can be anything but 13

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

Explanation:

The domain of [tex](f \circ g)(x) = f(g(x))[/tex] is the same as the domain of g(x)

The domain for g(x) is [tex]\{x|x \ne 13\}[/tex] saying we can plug in any number we want as long as it's not 13. This is to avoid dividing by zero. The same domain applies for the composite function because

[tex]f(x) = x+7\\\\\\f(g(x)) = g(x)+7\\\\\\f(g(x)) = \frac{1}{x-13}+7\\\\\\(f \circ g)(x) = \frac{1}{x-13}+7\\\\\\[/tex]

and we can see that we still need to kick out x = 13 from the domain to avoid the division by zero issue.


Related Questions

find area in square yards of trapezoid 5 yards, 23 yards base and 12 yards height

Answers

Answer:

I found the area its 168, I converted it to square yards 0.12963.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Formula

Area = (b1 + b2) * h /2

Givens

b1 = 5       yards

b2 = 23    yards

h = 12       yards

Solution

Area = (5 + 23)*12 / 2

Area = (28)*12/2        Divide by 2

Area = 28*6               Combine

Area = 168                  Yards^2

The table below shows the number of marbles of each color sold in a single box. There are a total of 25 marbles in the box.
Marbles in the Box
Color
Number
red
11
blue
11
green
3
The likelihood of an event occurring may be described as being certain, more likely, equally likely, less likely, or impossible

Answers

We will find the probability of getting each color of marble, and we will see that getting red and blue is equally likely, while getting green is less likely.

How to find the probabilities for each color of marble?

If we draw a marble at random from the box, all of them will have the same probability of being drawn.

Then the probability of getting a given color is given by the quotient between the number of marbles of that color and the total number of marbles.

Probability of getting red:

P = 11/25 =  0.44  This is really close to 50%, so this is equally likely.

Probability of getting blue:

P = 11/25 =  0.44  This is really close to 50%, so this is equally likely.

Probability of getting green:

P = 3/25 = 0.12 This is really close to 0%, so this is less likely.

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How many 1/4 are in 3

Answers

Answer:

3 ithinks so it lol haha

Answer: 12

Step-by-step explanation:

The are 4 1/4 in 1

3x4=12

Ryan is traveling by car for his vacation. The first day, he travels 80 miles in 2 hours. The second day, he travels 100 miles in 3 hours. Is this a proportional relationship?

Answers

Answer:

No

Step-by-step explanation:

no on the first day he drove 40mph the second day he drove 33 mph

more than one question! Please help me! i have been struggling all day and today i’m on a time limit

Answers

Answer:

2(15 *4)=120

2(5*4)=40

2(15*5)=150

Total = 310mm^2

Second picture:

7k+14

36d+144

Answer:

surface area = 2(5 × 4) + 2(15 × 4) + 2(15 × 5) = 310 mm²

  7(k + 2)

= 7×k + 7×2

= 7k + 14

  12(3d + 12)

= 12×3d + 12×12

= 36d + 144

surface area rectangular prism = 2(4 × 5) + 2(15 × 4) + 2(15 × 5) = 310 cm²

  5x + 7x - 2

= 12x - 2

  4 + 3g - g + 2g

= 4g + 4

  2 + 4g + 7g + 5

= 11g + 7

What amount should you invest now if after 4 years you want a final value of $15000 based on 6%
interest compounded quarterly?

Answers

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$15000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]15000=P\left(1+\frac{0.06}{4}\right)^{4\cdot 4}\implies 15000=P(1.015)^{16} \\\\\\ \cfrac{15000}{1.015^{16}}=P\implies 11820.47\approx P[/tex]

The equation is y=mx+b.

My question is, is ‘b’ supposed to be in decimal form or in fraction form??

Answers

Answer: both ways are acceptable

Step-by-step explanation: When writing equations of lines in this form,

we usually keep the "b" value or the constant term as a fraction.

However, if you prefer decimals, you can absolutely change

it to a decimal to visualize is better if you'd like, it's really your choice.

For example, if the equation of a line was y = -3/4x - 7/4, I could leave

it how it is or I could change the -7/4 to -1.75 giving me y = -3/4x - 1.75.

Julian and two of his friends are going to share 1/4 of a pizza how much will each person get

Answers

Answer:

2

Step-by-step explanation:

because

the pizza will be shared according to the total number of people zo

1/4×2=2

Answer:

it is b

Step-by-step explanation:

just try halfing it

PLEASE HELP ME ASAP
NOT HARD

Answers

Answer:

Step-by-step explanation:

= (3.26 + 9.75) d - 2.65

= 13.01 d - 2.65

Please help I need it asap pls pls pls

Answers

Answer:

1 person = 0.75

1 person = 3/4

Step-by-step explanation:

This answer is at best a guess. It seems to me that you are constructing a circle graph, and I would like that confirmed.

The total number of people in the survey is

Total in survey = 96 + 60 + 24 + 96 + 204

Total in survey = 480

A circle contains 360 degrees.

480 people have 360 degrees of circle room

1  person has x degrees of circle room

480 / 1 = 360 / x

Cross multiply

480 x = 360 *1       Divide both sides by 480

x = 360 / 480

x = 0.75

One person takes 3/4 of a degree of the circle.

So the number of people wanting to go to the UK would be

96 * 0.75 = 72 degrees,

For each part of the table, just use what the frequency is for that entry where 96 is now.

Help me out real quick i just dont understand this question

Answers

Answer:

245

Step-by-step explanation:

The lift can only handle 300lb then subtract the 55lb chair, and the lift will be able to hold a 345lb person in the chair.

Help plz , math equation !!

Answers

Answer:

We are given the table of a linear function

Since we have to find the equation of the function in the slope-intercept form,

we require the slope as well as the y-intercept

Finding the slope:

We know that slope of a line is Rise / Run

Since from the graph, we notice that the difference of 2 consecutive x-coordinates is 1

Hence, we have the x-coordinates at an interval of 1 and since the slope of a line is defined as the units ascended by the line after covering 1 unit in the x-coordinate

change in y = y[tex]_{n}[/tex] - y[tex]_{n-1}[/tex]       (where n is the number of row in the table)

change in y = 31 - 23

change in y = 8 = Rise

Run = 1 (Since the interval in the table is 1)

Slope = Rise / Run

Slope = 8 / 1

Slope  = 8

Finding the y-intercept:

We need the y-coordinate at x = 0

Going up from the third row, we notice that for every unit decreased in the x-coordinate , 8 units of the y-coordinate are decreased (since the slope =8)

In that case, the y-coordinate of every decreased x-coordinate will be 8 less than the last one

so we can say that the y-coordinate of x = 1 will be 8 less than 23 since x=1 is one less than x = 2

similarly, we can also say that the y-coordinate of x = 0 will be 8 less than (23-8) since x = 0 is one less than x = 1

Therefore, the y-coordinate at x =0

y = (23-8-8)

y-intercept  = 7

Making the Equation:

We need to write the equation in the form:

y = ax + b (where a is the slope of the line and b is the y-intercept)

Replacing the known values, we get

y = 8x + 7

Therefore, the equation of the formula shown in the table is y = 8x + 7

rate of change for y=-2x

Answers

Answer: y

=

2

x

2

,  

(

2

,

7

)

Step-by-step explanation:

(

2

(

7

)

2

)

(

2

(

2

)

2

)

(

7

)

(

2

)

A line passes through the point (-8,4) and has a slope of . -5/2

Write an equation in slope-intercept form for this line.

Answers

Answer:

Y= -5/2x +16

Step-by-step explanation:

To solve this, understand that (-8,4) is (x,y)

And Slope intercept form is y=mx +b

Since you have a possible x and y with - 8 and 4, sub that in making it 4=m(-8) + b

We also have the Slope (or M) which is -5/2, sub that in and get 4 = -5/2 (-8) + b

Do the multiplication and get 4= 40/2 +b

Simplify to 4= 20 + b

Then re-arrange to have the unknown (b) on one side and known on the other (when you move a number over the equal sign its sign, positive or negative, becomes the opposite)

B= 20-4

Subtract

B= 16

Now you know the b and can add it to your equation,

Y= -5/2x +16

Answer:

y = -5/2x - 16.

Step-by-step explanation:

First use the point-slope form of a line:

y - y1 = m(x - x1)

y - 4 = -5/2(x - (-8))

y - 4 = -5/2x - 40/2

y =  -5/2x - 20 + 4

y = -5/2x - 16.

How do I solve for D

Answers

Answer:

d = 33

Step-by-step explanation:

cos(ACB) = AC/BC

cos(30°) = 9/BC

BC = 63

AB² + AC² = BC²

d² + 9² = (63)²

d = 33

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

-1/2(-2x+4y) as expaned


please, please help

Answers

Answer:

Your answer is: -2y - x

Factor the polynomial.

Step-by-step explanation:

Hope this helped : )

Try this B E Given: BELO, BOLE Prove ABEL ALOB Complete the Proof Statements 1. 2. BO=LE 3. 4. ∆BEL =∆LOB REASONS 1.GIVEN 2. 3. 4. ​

Answers

The given congruency of the sides [tex]\mathbf{\overline{BE}}[/tex] and [tex]\mathbf{\overline{LO}}[/tex]  and [tex]\mathbf{\overline{BO}}[/tex] and [tex]\mathbf{\overline{LE}}[/tex] as well

as the congruency of the common side [tex]\mathbf{\overline{BL}}[/tex] gives.

ΔBEL ≅ ΔLOB by SSS congruency postulate

Which values correctly completes the table?

The completed two column proof is presented as follows;

Statement [tex]{}[/tex]                                          Reasons

1. [tex]\underline{\overline{BE} \cong \overline{LO}}[/tex]                       [tex]{}[/tex]                  1. Given

2. [tex]\overline{BO}[/tex] ≅ [tex]\overline{LE}[/tex]                       [tex]{}[/tex]                 2.

3. [tex]\underline{\overline{BL} \cong \overline{BL}}[/tex]                       [tex]{}[/tex]                  3. Reflexive property of congruency

4. ΔBEL ≅ ΔLOB                     [tex]{}[/tex]           4. SSS congruency postulate

Side-Side-Side, SSS, congruency postulate states that if three sides of

one triangle are congruent to three sides of another triangle, the two

triangles are congruent.

Learn more about different congruency postulates here:

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write the coordinates of the center and the length of the radius.

Answers

Answer:

Step-by-step explanation:

Center: (7, -13)

Radius = 9

What is the value of x-3

Answers

Answer:

+3

Step-by-step explanation:

Find the 89th term of the arithmetic sequence 25, 35, 45, ...25,35,45,...

Answers

Answer:

895

Step-by-step explanation:

There's a repetitive pattern of adding +10 each time.

A line passes through the point (7,9) and has a slope of 2.

Write an equation in slope-intercept form for this line.

Answers

Answer:   y = 2x - 5

Step-by-step explanation:

slope- intercept form is always written as y = mx + b, where m = slope, and b is the y-intercept.

To find b, substitute the point and the slope into the equations, you will get:

y = mx + b

9 = 2(7) + b

9 = 14 + b

-5 = b

Plug in m and b into the equation, we get:

y = mx + b

y = 2x + (-5)

y = 2x - 5

Solve for k. 2/5k + 3/10k = 42 Enter the answer, as a whole number or as a fraction in simplest form, in the box. k =
i

Answers

Answer:

30k + 1 -1

Step-by-step explanation:

hope this helps

Multiply six times three then divide by two

Answers

6x3=18 18/2 =9 so your answer is 9

The solution when multiplied 6 times 3 and then dividing by 2 is 9.

What is Multiplication?

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

Multiply six times three then divide by two.

First we have to multiply 6 times 3.

6 × 3 = 18

Then we divide the answer by 2.

18 ÷ 2 = 9

Hence the solution is 9.

Learn more about Multiplication here :

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Darryl is a baseball player who has a 0.250 batting average. That means that over some period of time, Darryl had a hit in 1 out of 4 at bats. Consider the experiment where darryl has 4 at bats in a game and observes whether or not he gets a hit each time.

Answers

The number of hits of the baseball player when batting is the average of hit

The expected number of hits in a bat of 4 is 1

How to determine the number of hits

The given parameters are:

The battling average, p = 0.250

The number of bats, n = 4

The number of hits in the bat is the average of hit, and it is calculated as:

[tex]E(x) = np[/tex]

This gives

[tex]E(x) = 4 * 0.250[/tex]

Evaluate the product

[tex]E(x) = 1[/tex]

Hence, the expected number of hits in a bat of 4 is 1

Read more about expected number at:

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Rayna Prater's gross biweekly pay is $2,420. Her earnings to date for the year total
$58,080. What amount is deducted from her pay for Social Security, which is taxed at
6.2%? What amount is deducted for Medicare, which is taxed at 1.45%?

Answers

Answer:

$35.09

Step-by-step explanation:

If f(x) = 2x and g(x) = 5x, what is f(g(x)) when x = 3?​

Answers

Hey there!

RANDOM FACTOID:

‘‘f(x)’’ or ‘‘g(x)’’ is understood to be “y”


f(x) = 2x

f(x) = 2(3)

f(x) = 2 + 2 + 2

f(x) = 4 + 2

f(x) = 6


Therefore, your answer is: f(x) = 6


g(x) = 5x

g(x) = 5(3)

g(x) = 5 + 5 + 5

g(x) = 10 + 5

g(x) = 15


Therefore, your answer is: g(x) = 15


OVERALL ANSWER: f(x) = 6 or g(x) = 15


Good luck on your assignment & enjoy your day!



~Amphitrite1040:)

a cell phone tower services about 1,256sq. miles what is the radius?

Answers

Start with the formula for finding the area of a circle.

A=πr2

First, substitute the given information in the equation. You have the area and you know that pi is 3.14.

153.86=(3.14)r2

Next, divide the area by pi. This will help to get one step closer to figuring out the radius.

3.14)153.86¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Remember, when you divide decimals, to move the decimal two places in the divisor and the dividend.

314)15386¯¯¯¯¯¯¯¯¯¯¯¯¯¯

314)15386¯¯¯¯¯¯¯¯¯¯¯¯¯¯  49− 1256  ––––––––  2826  − 2826–––––––0

So far, the answer is 49, but that is not the radius because r2 is on the right side of the equal sign.

49=r2

Then, you need to figure out which number times itself is equal to 49. You can figure this out by finding the factors of 49.

7×7=49

Now, you know that the radius is 7 inches because 7×7=49.

The radius is 7 inches.

Finally, to figure out the diameter, which is twice the radius, multiply the radius by 2.

7×2=14

The diameter is 14 inches.

hope this helps.

The radius covered by the tower will be 20 miles.

What is an area?

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that a cell phone tower services about 1,256sq. miles. The area of the circle will be calculated by the formula,

Area = πr²

1256 = π x r²

r² = ( 1256 / π )

r² = 400

r = √400

r = 20 miles

Hence, the radius of the circle will be 20 miles.

To know more about an area follow

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In a two digit number. the unit digit is thrice the tens digit. if 36
is added to the number, the digits interchange their place. find the number​

Answers

Answer:

Step-by-step explanation:

answer: the original number is 62.

Given :

Units digits is thrice the tens digit

The digits interchange when - 36 is added

To find :

The number

Solution :

Let the digits be -

   Units place as 3y

   Tens place as 10(y)

⇒ 10(y) + 3y

⇒ 10y + 3y

⇒ 13y --------- (Orignal Number)

Let the digits be -

   Units place as y

   Tens place as 10(3y)

⇒ 10(3y) + y

⇒ 30y + y

⇒ 31y --------- (Number with reversed digits)

The number gets reversed when 36 is added to it.

⇒ 13y + 36 = 31y

⇒ 13y - 31y = - 36

⇒ 18y = 36

⇒ y = 36/18

⇒ y = 2

⇒ 13y

⇒ 13(2)

⇒ 26

The units place should be thrice of the tens place,

⇒ 2 × 3 = 6

Units place is 6

Reversed digits are 62,

⇒ 26 + 36 = 62

⇒ 62 = 62

The Orignal Number is 62.

Alex skated 5 meters in 4 seconds. How fast was Alex skating per second? ​

Answers

1.25 meters

5 divided by 4 = 1.25

HOW TO DO IT
Divide 5 and 4 and you’ll get 1.25

ANSWER
1.25 per second

Sergio found 4 pennies on the ground his sister said that she found 2times as many pennies Sergio figured out that his sister found 6 pennies .what did Sergio do wrong

Answers

Answer:

12 pesos

Step-by-step explanation:

Answer:

Sergio added 2 instead of multiplying 2

Step-by-step explanation:

If Sergio's sister found 6 pennies that means that Sergio should've found 3 but instead of multiplying 2 he added 2.

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