Use the given functions to find f (g(x)), and give the restrictions on x.
F(x)= 1/x-3 and g(x) = 3/x +3

F(g(x)) = ?

Where x(doesn’t = ?

Answers

Answer 1

Answer:

[tex]f(g(x)) = \frac{10x-9}{3 + 3x}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{x} - 3[/tex]

[tex]g(x) = \frac{3}{x} + 3[/tex]

Required

Find f(g(x))

If: [tex]f(x) = \frac{1}{x} - 3[/tex]

Then:

[tex]f(g(x)) = \frac{1}{3/x + 3} -3[/tex]

Solve the denominator (take LCM)

[tex]f(g(x)) = \frac{1}{\frac{3+3x}{x}} -3[/tex]

[tex]f(g(x)) = \frac{x}{3 + 3x} - 3[/tex]

It can be solved further as:

[tex]f(g(x)) = \frac{x-3(3 + 3x)}{3 + 3x}[/tex]

[tex]f(g(x)) = \frac{x-9 + 9x}{3 + 3x}[/tex]

[tex]f(g(x)) = \frac{10x-9}{3 + 3x}[/tex]


Related Questions

5 times a number is 14 less than the square of that number. Find the negative solution.​

Answers

Answer:

x=-2

Step-by-step explanation:

5x=x^2 - 14

x^2-5x-14=0

(x-7)(x+2)=0

x=7,-2

A box has 70 cookies . 10% are broken (a) What fraction is broken ?
(b) What fraction remained whole?​

Answers

Answer:

Step-by-step explanation:

70(10/100)=7 broken cookies.

7/70=1/10 is the fraction broken

(70-7)/70=63/70 is the fraction remaining whole

Answer:

(a) 1/7 are broken

(b) 6/7 remain whole

Step-by-step explanation:

70 is a nice number to deal with in terms of percentages and fractions. If 10% of the cookies are broken, do 10/70. That fraction simplified gets you 1/7. To find the remaining whole cookies. Do 7/7 - 1/7 = 6/7 (or if you already know that in your head that works too)

In a triangle with all sides equal, what is the degree measure of any of the
angles? Write one number. *

Answers

answer:

the degree measure would be 60°

60 + 60 + 60 = 180

therefore, 60 is the answer.

1/3 1/4 3/8 7/24 5/12 which is the biggest

Answers

Answer: 5/12

Step-by-step explanation:

Answer:

Step-by-step explanation:

5/12 is the biggest

120g:5kg in simplest form

Answers

the correct answer is 24g : 1kg

An angle measures 154º more than the measure of its supplementary angle. What is the
measure of each angle?


Answers

Answer:

167 & 13

Step-by-step explanation:

(180-154)/2=

26/2=13

154+13=167

true or false. the cross section of a rectangular prism is a prism

Answers

true is the answer me adding extra words to reach the 20 character minimum okay have a good day❤️

Answer:

true

Step-by-step explanation:

It takes Naomi 4 minutes to run 5 laps. How long does it take her to run 30 laps? Use a table, double number line, tape diagram or another strategy to show your thinking.

(Please hurry I'm being timed)​

Answers

Answer:

24 minutes

Step-by-step explanation:

5x6=30

4x6=24

How many tens are in the number 639

Answers

Answer:

63 tens are in 639 are in that number

Answer:

There are 63 full tens in 639.

Step-by-step explanation:

639÷10=63.9

Hope this helps! :)

2. What is an interest that is computed on the
principal and then added to it?
A. Simple Interest
B. Compound Interest
C. Interest
D. Principal​

Answers

Answer:

Step-by-step explanation:

What are two fractions equivalent to 2/8?

Answers

Hm, any two? 1/4 and 4/16 are equal to 2/8.

Hope this helps.

Question

A random sample of SAT scores has a sample mean ofă = 1060 and sample standard deviation of s = 195. Use the

Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865.

Answers

Answer:

The approximate percentage of SAT scores that are less than 865 is 16%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 1060, standard deviation of 195.

Empirical Rule to estimate the approximate percentage of SAT scores that are less than 865.

865 = 1060 - 195

So 865 is one standard deviation below the mean.

Approximately 68% of the measures are within 1 standard deviation of the mean, so approximately 100 - 68 = 32% are more than 1 standard deviation from the mean. The normal distribution is symmetric, which means that approximately 32/2 = 16% are more than 1 standard deviation below the mean and approximately 16% are more than 1 standard deviation above the mean. So

The approximate percentage of SAT scores that are less than 865 is 16%.

help pls

Find the volume of the composite solid.

Answers

Answer:

80cm3

Step-by-step explanation:

volume of the composite solid=volume of the

pyramid+

volume of the

cuboid

volume of the pyramid=1/3* base area*height

=1/3*5*4*6

=40cm3

volume of the cuboid=base area *height

=5*4*2

=40cm3

volume of the composite solid=40cm3+40cm3

=80cm3

7 cm
10.5 cm
13 cm
Your Turn!
3 m
15 m
11 m
5m

Answers

Answer:  number 1 . 6688.5 then rounded is 6689.

Number 2.  2475

Step-by-step explanation:

A small theater head six rows of 26 chairs each an extra seven chairs have just been brought in how many chairs are in the theater now

Answers

6 rows x 26 chairs each
6 x 26 = 156
7 chairs brought in
156 + 7 = 163 chairs

0.4 divided by 2.3 plzz fast

Answers

it’s 0.17 rounded to two digits

Answer:

divided by 2.3 plzz fastdivided by 2.3 plzz fast

Step-by-step explanation:

divided by 2.3 plzz fast

divided by 2.3 plzz fastdivided by divided by 2.3 plzz fast plzz fast

The time to complete a project varies inversely
with the number of employees. If 3 people can
complete the project in 7 days, how long will it
take 5 people?
O 4.2
O 21
O 11.7
O 2.1

Answers

Answer:

4.2

Step-by-step explanation:

T = K/N

K= TN

= 3×7

K= 21

Therefore the time required for 5 employees can be calculated as follows

T= 21/5

= 4.2

1. The cost of a fish dinner for a restaurant is $7.95. If they sell it for $11.95, what is the percent markup?

Answers

Answer:

the answer will be

50.3144 %

Jerome won the lottery! He donated 1/2 of the money to charity and gave his parents 1/6 of the winnings. The remaining 1/3 was divided equally among his 5 friends. The expression given represents the part of the lottery money for each friend received. "1/3 (divided by) 5" Which expression is equivalent to the amount of money each friend received? A: 1/5 (divided by) 1/3 B: 1/5 x 1/3 C: 1/3 (divided by) 1/5 D: 5/1 x 1/3

Answers

Answer:

B: 1/5 x 1/3

Step-by-step explanation:

how to find the interest for a 2% interest rate loan of $3000 for 1 year, BUT instead of the 2% in the example, switch it to 3% interest on a $3500 loan.

Answers

Answer: See Explanation

Step-by-step explanation:

Simple interest is calculated as:

= principal × rate × time.

The interest for a 2% interest rate loan of $3000 for 1 year will be:

= principal × rate × time.

= $3000 × 2% × 1

= $3000 × 2/100 × 1

= $3000 × 0.02 × 1

= $60

The interest for a 3% interest rate loan of $3500 for 1 year will be:

= principal × rate × time.

= $3500 × 3% × 1

= $3500 × 3/100 × 1

= $3500 × 0.03 × 1

= $105

find the equation for the line that passes through the point (4,-3), and that is perpendicular to the line with the equation y= -3/4x-3​

Answers

Answer:

hi

Step-by-step explanation:

Answer

Slope between two given points (1,3) and (2,7) is

m=  

2−1

7−3

​  

=4

Then perpendicular slope is m  

1

​  

=  

4

−1

​  

 

The line equation with this slope is given by

y=  

4

−1

​  

x+c.......(1)

Now, the above line passes through the point (−4,−3)

⇒−3=  

4

−1

​  

×(−4)+c

⇒c=−4

Therefore required line is 4y+x+16=0 (Substitute  

c  

 in (1) and simplify)

PleSee help!!! 10 points for it

Answers

If you count the squares you should get 22.75, might be wrong but give it a try

a. [(-28)-(+42)] - (-13)​

Answers

Answer:

= -57 is answer

Step-by-step explanation:

−28−42−(−13)

have a good day!

What is the slope of the line that passes through the points (2, -3) and (5, 1)

Answers

Answer:

Answer is (4) 4/3

Step-by-step explanation:

[tex]\frac{1- -3}{5-2}[/tex]

[tex]\frac{4}{3}[/tex]

Answer:

slope is 4/3

Step-by-step explanation:

1-(-3)/5-2

4/3

Using only addition what is 20 - 9 + 8 -7

Answers

Answer:

12

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

I don't know if you mean using the Complements Method but I really wouldn't recommend using this method for all problems unless your teacher asked you to specifically.

Here is how to:

1. take the "complement" of the number we are subtracting (The "complement" is the number to add to make 10 (or 100, 1000, etc, depending on how many digits we have)

2. add it to to the number we are subtracting from

3. discard the extra "1" on the left

If you mean to do it mentally, think about it like this:

20 + (-9) = 11 You are essentially adding negative nine to twenty, not subtracting nine. If you want to see this better, try using a number line.  When you add a negative number, you move to the left on the number line.

Same thing with 8 + (-7) = 1

You are adding negative seven to eight.

All that is left to do is adding both of the results together, and you get twelve.

11 + 1 = 12

The graph shows your elevation during a bike ride. Which statement is true about your bike ride?

Answers

Answer:

You were running downhill for the first 15 minutes.

help pleaseeeeeee!!!!!!

Answers

Answer:

5x + 100

Step-by-step explanation:

(2x + 6) x 2 = 4x + 12

14x + 8 - 4x + 12 =

10x + 20 / 2 =

5x + 100

Hope that helps!

Select the statement that describes this expression: 32 ÷ 4 + ( fraction 1 over 2 x 16) − 2

Answers

Answer:

Step-by-step explanation:

32 ÷ 4 + ([tex]\frac{1}{2}*16) - 2[/tex] =   8 + (1*8) - 2

                                 = 8 + 8 - 2

                                 = 16 - 2

                                 = 14

Answer:

The quotient of 32 and 4 added to the product of fraction 1 over 2 and 16, then subtract 2

Step-by-step explanation:

Which answer is an equation in point-slope form for the given point and slope?
Point (1, 9), Slope: 5

(A) y - 9 = 5(x + 1)
(B) y+9 -5(x - 1)
(C) y-9=5(x - 1)
(D) y-1-5(x +9)

Answers

Answer:

Step-by-step explanation:

Point-slope equation for line of slope m that passes through (x₀,y₀):

y-y₀ = m(x-x₀)

In your case, m=5 and (x₀,y₀)=(1,9):

y-9 = 5(x-1)

туре or Movie
Number or
Students
36
Horror
Drama
26
Comedy
30
Sci-Fi
28
Based on the data in the table, what is the probability that a random

Answers

Answer:  3/4,  because the probability of renting a comedy is 1/4

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

Explanation:

We have 36+26+30+28 = 120 students. 30 of which rented a comedy.

The probability of renting a comedy is 30/120 = (30*1)/(30*4) = 1/4

The probability of not renting a comedy is 1 - (1/4) = 4/4 - 1/4 = (4-1)/4 = 3/4.

Or you could say that 1/4 = 0.25, so 1-0.25 = 0.75 which converts to the fraction 3/4.

If you had 4 people and 1 of them rents a comedy, then the other 3 hasn't rented a comedy.

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