Write an equation to represent a fraction model below.

Step-by-step explanation:

3:

h(x)=(-3x-15)/5

let y=(-3x-15)/5

interchanging role of x &y

x=(-3y-15)/5

5x+15=-3y

y=-(5x+15)/3

h-1(x)=-(5x+15)/3

not

equal to f(x)=(-3x-6)/4

Given function are not function of each other .

4:

g(x)=2/3x-2/3

let

y=2/3(x-1)

interchanging role of x &y

x=2/3(y-1)

3/2x+1=y

g-1(x)=3/2x+1

not equal to f(x)=½x+1

Given function are not function of each other .

Problem 1

--------------------

Explanation:

One way to see if we have an inverse pair or not is to compute these two composite functions

If both result in x, and just that, then we have shown that they are inverses of one another.

f(x) = (2x)/3

f(x) = (2/3)x

f(g(x)) = (2/3)*g(x)

f(g(x)) = (2/3)*(3/2)x

f(g(x)) = x

The steps to show that g(f(x)) = x are very similar

g(x) = (3/2)x

g(f(x)) = (3/2)*f(x)

g(f(x)) = (3/2)*(2/3)*x

g(f(x)) = x

So this verifies that you have the correct answer.

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

Problem 2

--------------------

Explanation:

We'll use the same idea as problem 1

f(x) = 2 - (3/4)*x

f(g(x)) = 2 - (3/4)*( g(x) )

f(g(x)) = 2 - (3/4)*( (-4/3)x + 8/3 )

f(g(x)) = 2 - (3/4)*(-4/3)x  - (3/4)*(8/3)

f(g(x)) = 2 + x - 2

f(g(x)) = x

So far so good, but we need to check the other way around as well

g(x) = (-4/3)x + 8/3

g(f(x)) = (-4/3)*( f(x) ) + 8/3

g(f(x)) = (-4/3)*( 2 - (3/4)*x ) + 8/3

g(f(x)) = (-4/3)*(2) + (-4/3)*(-3/4)*x + 8/3

g(f(x)) = -8/3 + x + 8/3

g(f(x)) = x

This verifies that f(x) and g(x) are inverses of each other.

Problems 3 and 4 will have similar steps.

Answer:

82

Step-by-step explanation:

6^3/(2x6)+64=?

216/12+64=82

Answer:

82

Step-by-step explanation:

6^3÷2 X 6 + 64= 216/12 + 64 = 18 + 64 = 82

The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

Here, we have,

we know that,

The sum of the angles in a triangle add to 180

x+2x+6x = 180

Combine like terms

9x= 180

Divide by 9

9x/9 = 180/9

x = 20.

Hence, The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.

To learn more on angle click:

brainly.com/question/28451077

#SPJ1

complete question:

The sum of the angle measures in a triangle is 180°. The angles of a certain triangle measure x°, 2x°, and 6x°. Solve for x.

Answer:

\(\huge\boxed{Answer\hookleftarrow}\)

\(_____ x 14.32 = 554.76\)

Let's take '____' as x

\(x \times 14.32 = 554.76 \\ x = \frac{554.76}{14.32} \\ x = \frac{554.76 \times 100}{14.32 \times 100} \\ x = \frac{55476}{1432} \\ x = 38.74\)

⎆ The answer of ____ x 14.32 = 554.76 in 2 decimal places will be ⇻38.74

NOTE:

We multiplied the fraction × 100 to remove the decimal points so that it'll be easier to calculate.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

The mean should be calculated for data sets A, B, C, and D.

It is useful to take into account the nature of the data and any potential outliers when deciding whether to choose the mean or the median as the measure of center in a data set.

When the data is symmetrically distributed with no major outliers, the mean is usually a better choice. It affects extreme values and gives an indication of the average value.

The median, on the other hand, is often preferred when the data is skewed or contains outliers. It represents the middle value when the data is ordered, and it is less affected by extreme values.

Learn more about mean:https://brainly.com/question/31101410

#SPJ1

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

The distance between the two ship based on the angle of depression is 42 meters.

The distance of each ship can be calculated thus:

TanX = opposite / Adjacent

The first ship:

Tan53 = distance/ 82

distance= 108.82 meters

The second ship:

Tan39 = distance/ 82

distance= 66.40 meters

The Difference between the ships are :

Therefore, the distance between the two ships is 42 meters.

Learn more on angles of depression:https://brainly.com/question/17193804

#SPJ1

Using the given formula v² = v₀² + 64h, and plugging the values of v₀ and v, we find the vertical height of drop of roller coaster is 75.53  feet.

The given equation is: v² = v₀² + 64h

Given that given final velocity is  v = 70 ft/s  and initial velocities is v₀ = 8 ft/s.

Substitute the given values into the equation

(70 ft/s)² = (8 ft/s)² + 64h

Simplifying and solving for h

4900 ft^2/s² = 64h + 64 ft²/s²

4836 ft^2/s² = 64h

h = (4836 ft²/s²)/64

h = 75.53 feet (rounded to two decimal places)

Therefore, the vertical drop height is approximately 75.53 feet.

To know more about Vertical height:

https://brainly.com/question/30394460

#SPJ1

--The given question is incomplete, the complete question is given

" ROLLER COASTERS The velocity of a roller coaster as it moves down a hill is v = v , where is the

v^2 = v₀^2 + 64h

v₀ =0 and h is the vertical drop in feet. If v = 70 feet per second and initial velocity v₀ = 8 feet per second, find h. "--

Given:

The recursive formulae are:

(a) \(f(n)=f(n-1)-2; f(1)=8\)

(b) \(f(n)=5+f(n-1); f(1)=0\)

To find:

The explicit equation.

Solution:

A recursive formula of an arithmetic sequence is

\(f(n)=f(n-1)+d\) and f(1) is the first term.

Where, d is the common difference.

The explicit formula is

\(f(n)=a+(n-1)d\)

where, a is first term and d is common difference.

(a)

We have,

\(f(n)=f(n-1)-2; f(1)=8\)

Here, first term is 8 and common difference is -2. So, the explicit formula is

\(f(n)=8+(n-1)(-2)\)

\(f(n)=8-2n+2\)

\(f(n)=10-2n\)

Therefore, the explicit formula is \(f(n)=10-2n\).

(b)

We have,

\(f(n)=5+f(n-1); f(1)=0\)

Here, first term is 0 and common difference is 5. So, the explicit formula is

\(f(n)=0+(n-1)(5)\)

\(f(n)=5n-5\)

Therefore, the explicit formula is \(f(n)=5n-5\).

\((2 + \sqrt{3} ) + (4 - \sqrt{3} ) \\ = 2 + \sqrt{3} + 4 - \sqrt{3} \\ = 2 + 4 \\ = 6\)

Answer:

6

Hope you could get an idea from here.

Doubt clarification - use comment section.

\(\huge \bf༆ Answer ༄\)

Here's the solution ~

Answer:

1025/4

Step-by-step explanation:

x^6 - x

---------------

4y

Let x =-4 and y = 4

(-4)^6 - (-4)

---------------

4*4

4096 +4

------------------

16

4100/16

1025/4

The answer is C. 1025/4

The balance in the account after 13 years is $8233.79.

From the question, we are to use the compound interest formula to compute the balance in the account

From the compound interest formula, we have that

A = P(1 + r/n)^nt

Where A is the amount

P is the principal

r is the interest rate

n is the number of times compounded per year

and t is the time.

From the given information,

P = $7000

r = 3.3%= 0.033

n = 1

t = 13

Putting the parameters into the formula

A = P(1 + r/n)^nt

A = 7000(1 + 0.033/1)^(1×5)

A = 7000(1 + 0.033)^5

A = $8233.79

Hence, the balance is $8233.79

Learn more on Compound interest here: https://brainly.com/question/25545513

#SPJ1

Answer: 7 hours

Step-by-step explanation: Divide 420 by 60 because there are 60 minutes in a hour, or 60 : 1 ratio.

Answer:

7 Hours

Step-by-step explanation:

there are 60 minutes in an hour so take 420 divided by 60=7 Hours.

The points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).

The general equation of a straight line is : y = mx + c.

[m] is called slope and it tells the unit rate of change in [y] with respect to [x].

[c] is called the [y] - intercept.

We have some points that lie on a line that passes through the origin with a slope of −25.

The equation of a straight line that passes through the origin and has slope of -25 will be -

y = - 25x

The points that will lie on the line will be -

(0, 0) , (1, - 25) , (- 1, 25)

Therefore, the points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ1

Answer:

1. x>20   2. x≤1     3.x<4     4.x>9      5.x≥-13

Answer:

C

Step-by-step explanation:

f(r)＝-3r²+30r-75 need to make sure algebra are same

From the table , the insurance cost for the second year based on the prescription given is : $1329

Using the prescription table, the six cylinder compact , second year car with a mileage of 14000 falls in the mid table category with the 13000 mileage label .

The operating cost in insurance for the second year is therefore $1329.

Learn more on insurance :https://brainly.com/question/30291521

#SPJ1

The required amount of water will be saved per year is 9594 gallons per year.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
With a rate of 2.3 gallons per minute, a person consumed 10764 gallons/yr.

Now, the same person replaces the shower head with a low-flow shower head that has a flow rate of 1.5 gallons per minute.
The amount of water that will be saved is given as,
= 10764 - (1.5 × number of weeks in year × time in a day the shower taken)
= 10764 - 1.5×52× 15
= 9594 gallons per year,

Thus, the required amount of water will be saved per year is 9594 gallons per year.

Learn more about arithmetic here:

https://brainly.com/question/11424589

#SPJ1

The person who gets to say the last number, 1000, will be Person 6.

Here, we have,

In this scenario, we have seven people sitting in a circle and counting clockwise. The goal is to determine which person will say the last number when they reach 1000. To solve this problem, we can use the concept of modular arithmetic.

When dividing 1000 by the total number of people (7), we get a quotient of 142 and a remainder of 6 (1000 = 142*7 + 6). This means that after completing 142 full rounds of counting, the group will have reached the number 994 (142*7). In the next round, they will continue counting from 995 to 1000.

Since the remainder is 6, it indicates that the last number (1000) will be spoken by the person sitting 6 positions after the first person in the circle (clockwise). In other words, Person 1 says numbers 1, 8, 15, and so on, while Person 6 will say 6, 13, 20, and so on.

To learn more about modular arithmetic click here

brainly.com/question/29022762

#SPJ1

complete question:

10) Seven people sit in a circle and begin counting clockwise starting from 1.Each person in the group is keeping track of the numbers she is saying (e.g. 1,8, 15...) If they continue in this way, counting on and on, until they reach 1000, which person will get to say the last number

I think 54 is the answer of this puestion

The last part answers the first part for you, just look at the y-values.

In other words:

A' (-8, 2)

B' (-4, 3)

C' (-2, 8)

D' (-10, 6)

Explanation:

When you reflect any point over the x-axis, the y-value of the ordered pair is going to change.

This makes sense especially considering that the x-axis is horizontal, so the only way you could cross is to move up or down. If you were to move left or right, you'd only be able to cross the y-axis, since it's vertical.

Now for the last part, as I mentioned above, if you are reflecting across the y-axis, the x-values of the ordered pair is going to change.

A'' (8, 2)

B'' (4, 3)

C'' (2, 8)

D'' (10, 6)

Take note that the only thing that changes for the respective value is its sign, while the number itself stays the same.

Hello!

We will go tu use the pythagorean theorem!

So:

BA² = BC² + AC²

AC² = BA² - BC²

AC² = 52² - 20²

AC² = 2304

AC = √2304

AC = 48

To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:

Monthly basic salary: Rs 48,000

Social security tax rate: 1%

Income tax rate on income up to Rs 5,00,000: 0% (no tax)

Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%

Dashain allowance: 1 month's salary

Deposit in Citizen Investment Trust (CIT): 10%

Rebate on income tax: 10%

(i) Annual Income:

Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:

Annual Basic Salary = Monthly Basic Salary x 12

= Rs 48,000 x 12

= Rs 5,76,000

Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:

Annual Income = Annual Basic Salary + Dashain Allowance

= Rs 5,76,000 + Rs 48,000

= Rs 6,24,000

Swornima's annual income is Rs 6,24,000.

(ii) Tax Rebate:

Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.

(iii) Annual Income Tax:

First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.

Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000

= Rs 1,24,000

Income Tax in this range = Taxable Income x Tax Rate

= Rs 1,24,000 x 0.1

= Rs 12,400

Now, let's calculate the total annual income tax:

Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000

= Rs 12,400

Next, we calculate the rebate on income tax:

Tax Rebate = Total Annual Income Tax x Rebate Rate

= Rs 12,400 x 0.1

= Rs 1,240

Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.

To summarize:

(i) Swornima's annual income is Rs 6,24,000.

(ii) Swornima's tax rebate is Rs 1,240.

(iii) Swornima should pay an annual income tax of R

Answer:

\(x\geq 4y\\y\leq \frac{x}{4}\)

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

Answer:

Before a variable there is no coefficient.

There is an invisible 1 infront bc there is no real number. so the 1 appears.