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3 years ago

Use the given functions to find f (g(x)), and give the restrictions on x.

Mathematics

1 answer:

torisob [31]3 years ago

4 0

Answer:

$f(g(x)) = \frac{10x-9}{3 + 3x}$

Step-by-step explanation:

Given

$f(x) = \frac{1}{x} - 3$

$g(x) = \frac{3}{x} + 3$

Required

Find f(g(x))

If: $f(x) = \frac{1}{x} - 3$

Then:

$f(g(x)) = \frac{1}{3/x + 3} -3$

Solve the denominator (take LCM)

$f(g(x)) = \frac{1}{\frac{3+3x}{x}} -3$

$f(g(x)) = \frac{x}{3 + 3x} - 3$

It can be solved further as:

$f(g(x)) = \frac{x-3(3 + 3x)}{3 + 3x}$

$f(g(x)) = \frac{x-9 + 9x}{3 + 3x}$

$f(g(x)) = \frac{10x-9}{3 + 3x}$

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What additional information is required in order to know what triangles are congruent

aev [14]

Answer:

C. RS=IS

Step-by-step explanation:

To use ASA the side between the two congruent angles must be equal as well. Given one set of congruent angles, we can assume the other congruent angles to be the vertical angles in the middle. In order for ASA to work, the side between those angles must also be congruent.

7 0

3 years ago

Read 2 more answers

1. Find the sum of the series (IMAGE) . Show your work.

pav-90 [236]

QUESTION 1 ANSWER

The series is

$\sum_{n=1}^{15}{ (2n-1)}$

So the nth term of this sequence is

$U_n=2n-1$

We generate some few terms of the sequence as follows:

When $n=1$ ,

The first term of the sequence becomes,

$U_1=2(1)-1$

$U_1=1$

When $n=2$ ,

$U_2=2(2)-1$

$U_2=3$

When $n=3$ ,

$U_2=2(3)-1$

$U_2=5$

The constant difference is $d=2$ .

The sum of the series is given by,

$S_n=\frac{n}{2}(2a+(n-1)d)$

There are 15 terms in the series, therefore $n=15$

$S_{15}=\frac{15}{2}(2(1)+(15-1)2)$

$S_{15}=\frac{15}{2}(2+14(2))$

$S_{15}=\frac{15}{2}(30)$

$S_{15}=15\times 15$

$S_{15}=225$

ANSWER TO QUESTION 2

The bottom row has $23$ boxes. This means $a=U_1=23$

a) Since each row has 3 fewer boxes $d=-3$ .

The nth row is given by,

$U_n=23+(n-1)\times(-3)$

$U_n=23+-3n+3$

$U_n=23-3n$

The top row is the 6th row, meaning $n=6$ .

$U_6=23-3(6)$

$U_6=23-18$

$U_6=5$

b) The number of boxes in the entire display is given by

$S_n=\frac{n}{2} (a+l)$

Where $a=23$ , the first term(row) and $l=5$ , the last term(row).

Since there are 6 rows,

$S_6=\frac{6}{2} (23+5)$

$S_6=3 (28)$

$S_6=84$

ANSWER TO QUESTION 3

The number of visitors in the first week is $a=5$ .

Since the number of visitors each week is doubled the number of visitors in the subsequent weeks, the sequence is a geometric progression with a common ratio of $r=2$ .

The general term of a geometric sequence is

$U_n=ar^{n-1}$

So in the 8th week, we have

$U_8=5\times 2^{8-1}$

$U_8=5\times 2^{7}$

$U_8=5\times 128$

$U_8=640$

Hence 640 people visited the website in the 8th week

4 0

3 years ago

Which of the following amounts is greater than 4 yards? Select all that apply.

Bezzdna [24]

Answer:

is c

Step-by-step explanation:

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3 years ago

Read 2 more answers

Mandy and Pete have a biased spinner numbered 1, 2, 3, 4, 5. They each want to find an estimate for the probability that the spi

kotykmax [81]

Answer:

Pete

Step-by-step explanation:

Given that:

Mandy's Estimate :

Number of spins , n = 20

Pete's Estimate:

Number of spins, n = 200

A good probability estimate is one which has narrow margin of error with a high degree of confidence. These two variables are affected by sample size.

A high sample size give a narrower margin of error and increases the confidence level probability

Based on the sample size used by each of Pete and Mandy, we can conclude that, Pete's probability estimate would be better due to its significantly higher sample size.

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3 years ago

Three consecutive even integers that add up to -6. What are these integers?

Gekata [30.6K]

Answer:

-1, -2, -3 Are all consecutive

Step-by-step explanation:

-1 + -2 + -3 = -6

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3 years ago