HELP ASAP ALGEBRA 2 QUESTION PLEASE!!!

Consider the function f(x)=1/3 x+4.
Find the inverse of f(x) and name it g(x) . Show and explain your work.
Use function composition to show that and are inverses of each other.
Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain how your graph shows that the functions are inverses of each other.

Answers

Answer 1

a)
f(x) is the same as y
y=1/3 x +4

to find inverse, swap and x and y:
x=1/3 y + 4
x-4= 1/3 y
(x-4) x 3 = y
3x -12= y
the inverse(g(x)), is: 3x-12

b) if f(x) and g(x) are inverses of each other, than (f о g)(x) will end up with just "x"

(f о g)(x)=x
(f о g)(x)= f(g(x))
(f о g)(x)= f(3x-12)
(f о g)(x)= 1/3(3x-12)+4
(f о g)(x)= (3x-12)/3 +4
(f о g)(x)= x-4+4
(f о g)(x)= x

c)
You will find that the graphs are mirror images of each other
the graph for f(x) is an oblique line that passes through the points(-12,4)
the graph for g(x) is an oblique line that passes through the points(4,-12)

Related Questions

A student is reading his book at a rate of 15 pages per day.

a. Write the rate in pages per week.

b. Write the rate in pages per hour.

Answers

a) There are 7 days in a week. If the students is reading 15 pages per day, the student is reading 105 pages over the span of one week.

b) There are 24 hours in one day. If the student is reading 15 pages in 24 hours, then the student is reading 0.625 pages in a hour (approximately more than half of a page but less than one full page).

what strategies can be used to divide whole numbers?

Answers

1. Place the numbers so that the dividend is under the division sign and the divisor is in front of the sign.
2. Ask yourself how many times (think multiplication) will the divisor go into the dividend without going over.
3. Bring down the next digit in the dividend.
4. Now divide the divisor to that number.
5. Repeat steps 2 and 3 if necessary until final answer is reached.

if it's still confusing or it doesn't answer your question, you can always use a calculator :)

If AB= BC and BC= CD, then AB= CD

Answers

True, because AB=BC and BC=CD which means that AB=CD. Do I need to explain more?

Isosceles triangle ABC has a perimeter of 96 centimeters. The base of the triangle is and measures 24 centimeters.

What is the measure of ?

12 cm
36 cm
48 cm
72 cm

Answers

Answer:

The measure of length of equal side is 36 cm each.

B is correct.

Step-by-step explanation:

Isosceles triangle ABC has a perimeter of 96 centimeters.

The base of the triangle is BC and measures 24 cm

We need to find the length of equal side of triangle.

AB=AC

The perimeter of triangle is 96 cm

AB + AC + BC = 96

AB + AB + 24 = 96 ( ∵ AB=AC)

2AB = 96-24

2AB = 72

AB = 36

Hence, The measure of length of equal side is 36 cm each.

Use the graph of the function to find its average rate of change from
=x−3
to
=x3
.

PLEASE HELP NO ONE EVER ANSWERS!

Answers

The average rate of change of the function over the interval is 2

Finding the average rate of change

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = -3 to x = 3

The function is a quadratic function

This means that it does not have a constant average rate of change

From the graph

y = -8, when x = -3

y = 4, when x = 3

This means that

f(-3) = -8

f(3) = 4

The average rate is calculated using

Rate = (Change in y values)/(Change in corresponding x values)

So, we have

Rate = (4 + 8)/(3 + 3)

Evaluate

Rate = 2

Hence, the average rate of change is 2

A van travels 150 miles on 5 gallons of gas. how many gallons will it need to travel 630 miles?

Answers

The van would need 21 gallons of gas to travel 630 miles.

At 6 gallons for 150 miles, the van goes 150 / 6 or 25 miles per gallon.

The amount needed to go 575 miles is 575 / 25 or 23 gallons.

LM = JK then JK = LM
What property is this?

Answers

This example is the Symmetric Property.

I hope this helps you!
xo, Leafling

Final answer:

The principle being demonstrated is known as the Symmetric Property, which holds that if an equation or statement is valid, then its switched or flipped version will also be true.

Explanation:

The question refers to a fundamental property in mathematics called the Symmetric Property. The Symmetric Property states that if an equation or statement is true, then its mirror or flipped version will also hold true. In this case, if LM = JK, then under Symmetric Property, it must be true that JK = LM.

For instance: If 5 = 2 + 3, then 2 + 3 = 5.

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Identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of each parabola.

1.) Y=x^2+4x+1

Write each function in vertex form.

1.) Y=x^2+2x+5

A model for a company's revenue from selling a software package is R= -2.5p^2+500p, where p is the price in dollars of the software. What price will maximize revenue? Find the maximum revenue.

Answers

For a quadratic equation y=ax^2+bx+c, use x=-b/(2a) to find out the vertex
#1: a=1, b=4
x=(-4/2*1)=-2
Plug in x=-2 in the equation to find out the value of y: when x=-2, y=-3

so the vertex is at (-2, -3), the symmetry line is x=-2
the equation in vertex form is y=[x-(-2)^2]-3 =>y=(x+2)^2-3
Since the coefficient, a, of x^2, is 1 in this case, a positive number, the parabola opens upward, the equation has a minimum value, which happens at x=-2, and the minimum value is -3

use the same method for the other two questions

Consider the following equation, bh+hr=25 when solving for r

Answers

Solve for r.

You want to get r by itself on one side on the equal sign.

bh + hr = 25

Subtract bh from both sides.

hr = 25 - bh

Divide h on both sides.

r = 25 - bh / h

The two h's cancel each other out.

r = 25 - b

Hope this helps!

Answer:

[tex]r=\frac{25-bh}{h}[/tex]

Step-by-step explanation:

Given : Consider the following equation, [tex]bh+hr=25[/tex]

To find : Solving for r ?

Solution :

The equation is [tex]bh+hr=25[/tex] solve for r,

Subtract 'bh' both side,

[tex]bh+hr-bh=25-bh[/tex]

[tex]hr=25-bh[/tex]

Divide both side by 'h',

[tex]\frac{hr}{h}=\frac{25-bh}{h}[/tex]

[tex]r=\frac{25-bh}{h}[/tex]

Therefore, [tex]r=\frac{25-bh}{h}[/tex]

Which correlation coefficient represents the strongest relationship between two variables?

Answers

a direct correlation between two variables is y = kx where k is a constant. In inverse relationship is y=k/x.

Predict the number of students out of 400 that would pick science(3) as their favorite subject
Math=6
Science=3
English=4
History=7

Answers

We want to find the ratio of students who picked science vs the rest. We would add everything up, totaling to 20. 3 students picked science, so the ratio would be 3/20. We then multiply 400 by 3/20, which is 60.

1. At the grocery store checkout, you watch at the register as it rings up your purchases and coupons. The prices were as follows:
$2.95
$1.19
$4.61
$1.74
$3.04
$8.83
$1.16
– $0.75 (coupon)
– $1.00 (coupon)

The register gives your total bill as $21.77. Estimate the total amount of the bill and use your answer to determine whether the total on the register is reasonable.
Answer:

Answers

estimate by rounded to the nearest dollars

2 +1 +5 +2 +3 +9 +1 = $23

-2

23-2 = 21

yes the amount is reasonable

Answer: 3+1+5+2+3+9+1-1-1=22

The total on the register is reasonable because if you estimate $21.77 to the nearest dollar you would get $22.00.

Step-by-step explanation:

Giving Brainliest! Use graphs and numerical summaries to help you describe how the following three datasets are similar and how they are different (think mean, median, range, and sample standard deviation).
A: 5, 7, 9, 11, 13, 15, 17
B: 5, 6, 7, 11, 15, 16, 17
C: 5, 5, 5, 11, 17, 17, 17

Answers

They are all same because they have the same median. They are all different because they have a different mean.

What is an equivalent expression for 1.5(3x + 4) + 0.25(6x + 8)?

Answers

1.5(3x+4)+0.25(6x+8)
4.5x+6+1.5x+2
6x+8

An expression is defined as a set of numbers, variables, and mathematical operations. An equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as,

1.5(3x + 4) + 0.25(6x + 8)

= 4.5x + 6 + 2.5x + 2

= 7x + 8

Hence, an equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.

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Rewrite 1/x^-3/6 in simplest radical form. show each step of your process

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\\\ \textit{also recall that }a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}}\\\\ -------------------------------[/tex]

[tex]\bf \cfrac{1}{x^{-\frac{3}{6}}}\implies \cfrac{1}{\frac{1}{x^{\frac{3}{6}}}}\implies \cfrac{\frac{1}{1}}{\frac{1}{x^{\frac{3}{6}}}}\implies \cfrac{1}{1}\cdot \cfrac{x^{\frac{3}{6}}}{1}\implies x^{\frac{3}{6}}\implies x^{\frac{1}{2}}\implies \sqrt[2]{x^1} \\\\\\ \sqrt{x}[/tex]

What is the converse of the statement? "If you wash the dishes today, then I will wash the dishes tomorrow." Question 5 options: If I wash the dishes tomorrow, then you will wash the dishes today. If I will not wash the dishes tomorrow, then you will not wash the dishes today. If you wash the dishes today, I will dry the dishes today. If you do not wash the dishes today, then I will not wash the dishes tomorrow.

Answers

If you do not wash the dishes today, then I will not wash the dishes tomorrow.
I Believe that's right

Answer:

Step-by-step explanation:dhdjdbfbd

Write the point-slope form of the line that passes through (-8, 2) and is parallel to a line with a slope of -8. Include all of your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.

Answers

Parallel lines have the same slope, so since you want a line that is parallel to a line with slope -8, your line will also have slope -8.

The slope-intercept form of the equation of a line is

y = mx + b

where m is the slope, and b is the y-intercept.

You already know you have a slope of -8, so m = -8, and you have

y = -8x + b

Now you need to find the value of b.

Use the point you know and substitute it in for x and y, and solve for b.

y = -8x + b

Use x = -8, and y = 2.

2 = -8(-8) + b

2 = 64 + b

-62 = b

b = -62

Now replace b with -62.

y = -8x + b

y = -8x - 62

11.) suppose the correlation between two variables r=0.23. What will the new correlation be if 0.14 is added to all values of the x-variable, every value of the y-variable is double, and the two variables are interchanged?

Answers

it will still be .23.

The correlation coefficient r=0.23 will remain unchanged at 0.23 even after adding a constant to all x-variable values, doubling the y-variable values, and swapping the x and y variables, because the correlation coefficient is unaffected by such transformations.

The correlation between two variables is denoted by the symbol, r, and it measures the strength and direction of a linear relationship between two quantitative variables. When we add a constant to all values of the x-variable or multiply all values of the y-variable by a constant, the correlation coefficient does not change. However, interchanging the x and y variables also does not change the value of r since correlation is symmetrical. Therefore, if r=0.23 initially, after adding 0.14 to all values of x, doubling the y-variable values, and interchanging the two variables, the new correlation will still be 0.23.

True or false: f(x) is a function

Answers

False, since x values cannot have more than one y value.

Answer:

False

Step-by-step explanation:

If f(x) is a function , then for each value of x there should be a single y values

For input 0 there is a output 0

for input 10, the output is 2

for input 15, output is 3

For input 5, we have two output 1 and 3

for single input 5, the function cannot have two outputs 1 and 3

So this f(x) is not a function

Which state of matter has neutral particles that bounce off one another as they collide?

Gas
Liquid
Plasma
Solid

Answers

The answer is gas because gas particles move so fast they bounce off one another when they collide. Plasma has Negatively AND Positively charged particles within it.

Final answer:

Gases are the state of matter where neutral particles bounce off one another as they collide. This is due to their constant, random motion and the elastic nature of their collisions.

Explanation:

The state of matter that has neutral particles that bounce off one another as they collide is a Gas. This is due to the fact that gases are composed of a large number of particles that are in constant, random motion. These particles collide with each other and with the walls of their container. Importantly, these collisions are perfectly elastic, meaning they conserve both momentum and kinetic energy.

In Liquids and Solids, the particles are held together with stronger intermolecular forces which restrict their motion. In Plasma, the particles are ionized and hence, are not neutral.

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Describe the steps in solving the linear equation 3(3x-8)=4x+6

Answers

Here photo with solution

The value of x is 6.

Given,

3(3x-8)=4x+6

We need to solve for x and show steps by steps.

What are the properties used in solving a linear equation?

Distributive property of multiplication over addition.

: a ( b + c ) = a x b + a x c

Distributive property of multiplication over subtraction.

: a ( b - c ) = a x b - a x c

Combining like terms.

: cx + ax + b = x (c + a) + b

: cx - ax - b = x (c - a) + b

We have,

3(3x-8)=4x+6

Removing the brackets.

3x(3x) - 3x8 = 4x + 6

9x - 24 = 4x + 6

Subtracting 4x on both sides.

9x - 24 - 4x = 4x + 6 - 4x

5x - 24 = 6

Adding 24 on both sides.

5x - 24 + 24 = 6 + 24

5x = 30

Dividing 5 into both sides.

5x/5 = 30/5

x = 6

Thus the value of x is 6.

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What are the x and y-intercepts of the line described by the equation? 3x−9y=10.8 Enter your answers, in decimal form, in the boxes.

Answers

3x−9y=10.8

x-intercept when y = 0
3x =10.8
x = 3.6

y-intercept when x = 0
−9y=10.8
y = - 1.2

answer

x-intercept (3.6, 0)
y-intercept (0, -1.2)

Answer: The x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.

Step-by-step explanation: We are given to find the x-intercepts and y-intercepts of the line described by the following equation :

[tex]3x-9y=10.8~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the x-intercept of a line is the point where the y co-ordinate is 0. Similarly, y-intercept is the point where the x co-ordinate is 0.

Substituting y = 0 in equation (i), we get

[tex]3x-9\times0=10.8\\\\\Rightarrow 3x-0=10.8\\\\\Rightarrow 3x=10.8\\\\\Rightarrow x=\dfrac{10.8}{3}\\\\\Rightarrow x=3.6.[/tex]

So, x-intercept is (3.6, 0).

And substituting x = 0 in equation (i), we get

[tex]3\times 0-9y=10.8\\\\\Rightarrow 0-9y=10.8\\\\\Rightarrow 9y=-10.8\\\\\Rightarrow y=-\dfrac{10.8}{9}\\\\\Rightarrow y=-1.2.[/tex]

So, y-intercept is (0, -1.2).

Thus, the x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.

For the following inequality, indicate whether the boundary line should be dashed or solid. 3x ≥ y + 1 dashed solid

Answers

Answer:

The boundary line should be solid because it have a 'great/less than or equal to' sign

Step-by-step explanation:

XY=11d\ YZ=9d-2\ \ xz=5a+22

Answers

XY=11d\ YZ=9d-2\ \ xz=5a+22

D = 2 YZ = 16

A=6 YZ= 38

because that is the answer to the question I hope

What is the difference between a plane (in geometry) and a piece of paper?

Answers

A plane in geometry is a flat surface of infinite size. It has infinite length and infinite width and no thickness at all.
A piece of paper that is lying flat has a finite length and width a some thickness. A piece of paper lying flat is part of a plane.

Which type of angles could be used as a counterexample for the argument all angles are either right obtuse or acute

Answers

I believe it would be a right angle

Answer: You could use straight angles as a counterexample for the argument all angles are either right obtuse or acute .

The number of sides of a polygon that has n vertices is what?

Answers

The equation will be 180(n-2)

The total number of sides in a polygon with n vertices is = n sides.

We have a Polygon with n vertices.

We have to determine the number of sides of this polygon.

What is Polygon?

In geometry, a polygon can be defined as a plane, two-dimensional closed shape bounded with straight sides.

According to the question, we have -

A polygon with n vertices.

The total number of sides in a polygon with n vertices is = n sides.

The sides of the polygon are connected end to end in a cyclic order. The side with endpoints as nth and (n - 1)th vertices is connected to the side with endpoints as (n - 1)th and (n - 2)th vertices and so on.

Hence, the total number of sides in a polygon with n vertices is = n sides.

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Louis spent 12 hours last week practicing guitar. If 1/4 of the time was spent practicing chords, how much time did Louis spend practicing chords?

Answers

Total time spent = 12 hours.

Time spent practicing chords is
(1/4)*(12 hours) = 3 hours

Answer: 3 hours

Final answer:

Louis spent a total of 3 hours practicing chords last week, which is 1/4 of the total 12 hours he dedicated to practicing guitar.

Explanation:

Louis spent 12 hours last week practicing guitar. To calculate the amount of time he spent practicing chords, we need to find 1/4 of 12 hours since 1/4 of the time was dedicated to chords.

Here is the calculation:

Divide the total time by 4 to find 1/4 of 12 hours: 12 hours ÷ 4 = 3 hours.

So, Louis spent 3 hours practicing chords last week.

Factor. 2xy+5x−12y−30

Answers

2xy + 5x -12y -30
x(2y + 5) - 6( 2y + 5)
(2y+5) (x-6)

Answer: The required factored form of the given expression is [tex](x-6)(2y+5).[/tex]

Step-by-step explanation: We are given to factorize the following expression :

[tex]E=2xy+5x-12y-30~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following property :

[tex]a(b+c)+d(b+c)=(a+d)(b+c).[/tex]

From expression (i), we have

[tex]E\\\\=2xy+5x-12y-30\\\\=x(2y+5)-6(2y+5)\\\\=(x-6)(2y+5).[/tex]

Thus, the required factored form of the given expression is [tex](x-6)(2y+5).[/tex]

Which of the following options represents the graph of the function shown below?

ƒ(x) = (x - 3)^3 1 1
ƒ(x) = (x - 3)^3 + 1
ƒ(x) = (x + 3)^3 - 1
ƒ(x) = (x + 3)^3 + 1

Answers

I think the answer is B but not sure about "11" in A

Answer:

The function that best represents the graph of the function which is given is:

[tex]f(x)=(x-3)^2+1[/tex]

Step-by-step explanation:

From the graph that is provided to us we observe that the graph passes through the point (3,1).

Hence, we will check which of the following function satisfies this point.

[tex]f(x)=(x-3)^3-1[/tex]

when x=3 we see that:

[tex]f(x)=(3-3)^3-1\\\\i.e.\\\\f(x)=-1\neq 1[/tex]

Hence, option: a is incorrect.

[tex]f(x)=(x+3)^3-1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3-1\\\\i.e.\\\\f(3)=9^3-1\\\\i.e.\\\\f(3)=729-1\\\\f(3)=728\neq 1[/tex]

Hence, option: c is incorrect.

[tex]f(x)=(x+3)^3+1[/tex]

when x=3 we have:

[tex]f(3)=(3+3)^3+1\\\\i.e.\\\\f(3)=9^3+1\\\\i.e.\\\\f(3)=729+1\\\\f(3)=730\neq 1[/tex]

Hence, option: d is incorrect.

Now we are left with option: b)

i.e.

[tex]f(x)=(x-3)^2+1[/tex]

Also, when x=3 we have:

[tex]f(3)=(3-3)^2+1\\\\f(3)=0+1\\\\f(3)=1[/tex]

Hence, it passes through the point (3,1)

Also, when we will plot this function we observe that it matches the given graph.

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