How to find the endpoint when given the midpoint and one of the end points

For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions.

Rufina [12.5K]

Answer:

The value of $(f \circ g)(x)$ is 17-18x and $(g \circ f)(x)$ is -7-18x.

Step-by-step explanation:

It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.

It is required to find $(f \circ g)(x)$ and $(g \circ f)(x)$ .

To find $(f \circ g)(x)$ , substitute g(x) for x in f(x) and simplify the expression.

To find $(g \circ f)(x)$ , substitute f(x) for x in g(x) and simplify the expression.

Step 1 of 2

Substitute g(x) for x in f(x) and simplify the expression.

$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$

Step 2 of 2

Substitute f(x) for x in g(x) and simplify the expression.

$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$

5 0

2 years ago

Sears editing ‘company is a small editorial services company owned and operated by deloris Sears. On January 31, 20Y1 , the end

Valentin [98]

1. Preparation of the adjusting entries for

Sears editing ‘company

Sears editing ‘company Adjusting Entries

a. Dr Insurance expense $1,800

($7,200-$5,400)

Cr Prepaid insurance $1,800

(To record insurance expense)

b. Dr Supplies expense $1,605

($1980 - $375)

Cr Supplies $1,605

(To record supplies expense)

c. Dr Depreciation expense $6,000

Cr Accumulated depreciation-building $6,000

(To record depreciation expense on building)

d. Dr Depreciation expense $3,000

Cr Accumulated depreciation-equipment $3,000

(To record depreciation expense on equipment)

e. Dr Unearned rent $5,400

($6,750-$1,350)

Cr Rent revenue $5,400

(To record rent earned from unearned rent)

f. Dr Salaries and wages expense $2,900

Cr Salaries and wages payable $2,900

(To record salaries and wages expense)

g. Dr Accounts receivable $18,600

Cr Fees earned $18,600

(To record accrued revenue)

2. Preparation of an adjusted trial balance.

Sears editing ‘Company Adjusted Trial balance

Debit side

Cash $7,500

Account Receiveble $57,000

Prepaid Insurance $5,400

Supplies $375

Land $112,500

Building $150,250

Equipment $135,300

Drawing $15,000

Salaries and wages expense $196,270

Utilities expense $42,375

Advertising expense $22,800

Repair expense $17,250

Depreciation expense-Building $6,000

Depreciation expense-Equipment $3,000

Insurance expense $1,800

Supplies expense $1,605

Miscellaneous expense $6,075

Total Debit side $780,500

Credit side

Accumulated Depreciation-Building $93,550

Accumulated Depreciation-Equipment $100,950

Account payable $12,150

Unearned rents $1,350

Salaries and wages payable $2,900

Capital stock $221,000

Fees earned $343,200

Rent revenue $5,400

Total Credit side $780,500

Learn more here:brainly.com/question/21304366

4 0

2 years ago

Sample spaces For each of the following, list the sample space and tell whether you think the events are equally likely:

Schach [20]

Answer and explanation:

To find : List the sample space and tell whether you think the events are equally likely ?

Solution :

a) Toss 2 coins; record the order of heads and tails.

Let H is getting head and t is getting tail.

When two coins are tossed the sample space is {HH,HT,TH,TT}.

Total number of outcome = 4

As the outcome HT is different from TH. Each outcome is unique.

Events are equally likely since their probabilities $\frac{1}{4}$ are same.

b) A family has 3 children; record the number of boys.

Let B denote boy and G denote girl.

If there are 3 children then the sample space is

{GGG,GGB,GBG,BGG,BBG,GBB,BGB,BBB}

The possible number of boys are 0,1,2 and 3.

Number of boys Favorable outcome Probability

0 GGG $\frac{1}{8}$

1 GGB,GBG,BGG $\frac{3}{8}$

2 GBB,BGB,BBG $\frac{3}{8}$

3 BBB $\frac{1}{8}$

Since the probabilities are not equal the events are not equally likely.

c) Flip a coin until you get a head or 3 consecutive tails; record each flip.

Getting a head in a trial is dependent on the previous toss.

Similarly getting 3 consecutive tails also dependent on previous toss.

Hence, the probabilities cannot be equal and events cannot be equally likely.

d) Roll two dice; record the larger number

The sample space of rolling two dice is

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Now we form a table that the number of time each number occurs as maximum number then we find probability,

Highest number Number of times Probability

1 1 $\frac{1}{36}$

2 3 $\frac{3}{36}$

3 5 $\frac{5}{36}$

4 7 $\frac{7}{36}$

5 9 $\frac{9}{36}$

6 11 $\frac{11}{36}$

Since the probabilities are not the same the events are not equally likely.

4 0

3 years ago

Which expression is equivalent to [(3xy^-5)^3/(x^-2y^2)^-4]^-2?

Mademuasel [1]

Answer:- a.The given expression is equivalent to $\frac{x^{10}y^{14}}{729}$

Given expression:- $[\frac{(3xy^{-5})^3}{(x^{-2}y^2)^{-4}}]^{-2}$

$=[\frac{(3)^3x^3y^{-5\times3}}{x^{-2\times-4}y^{2\times-4}}]^{-2}.........(a^m)^n=a^{mn}$

$=[\frac{27x^3y^{-15}}{x^8y^{-8}}]^{-2}$

$=[27x^{3-8}y^{-15-(-8)}]^{-2}............\frac{a^m}{a^n}=a^{m-n}$

$=[27x^{-5}y^{-7}]^{-2}=(27)^{-2}(x^{-5})^{-2}(y^{-7})^{-2}.........(a^m)^n=a^{mn}$

$=\frac{1}{(27)^2}(x^{10}y^{14})=\frac{x^{10}y^{14}}{729}$

Thus a. is the right answer.

6 0

3 years ago

Read 2 more answers

4 gallons of paint cost a total $22.00. How much will 14 gallons cost? A. $60.50 B. $242.00 C. $82.00 D. $77.00

Nana76 [90]

The answer is D. $77.00. To get the cost for a single gallon you divide $22 by 4 gallons you get $5.50. To get the cost for 14 gallons you multiply $5.50 by 14 and you get the answer $77.00.

4 0

3 years ago