what is the inverse of cube root x/3 +1

Answers

Answer 1

Answer:

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

Step-by-step explanation:

We want to find the inverse of

[tex] y = \sqrt[3]{ \frac{x}{3} + 1} [/tex]

We interchange x and y to get:

[tex]x= \sqrt[3]{ \frac{y}{3} + 1} [/tex]

We solve for y;

[tex] {x}^{2} = \frac{y}{3} + 1[/tex]

Multiply through by 3

[tex]3 {x}^{2} = y + 3[/tex]

Subtract 1 from both sides:

[tex]y = 3 {x}^{2} - 3[/tex]

Therefore the inverse is

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


Related Questions

what is x? 1.5x - 6 = 7.5

Answers

Answer:

x=9

Step-by-step explanation:

1.5x - 6 = 7.5

       +6    + 6

1.5x = 13.5

1.5x divided by 13.5 then equals 9

Choose the best graph that represents the linear equation:

4x + y = 0

i need help please

Answers

Answer:

graph A

Step-by-step explanation:

Answer:

Graph B

Step-by-step explanation:

I did the practice on edg

PLEASE ANSWERRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR

Answers

The equations for the regular cost is [tex]y=18.50 x[/tex] and

The equation for the party special is  [tex]y=15 x+28[/tex],

where y is the total cost in dollars and x is the number of students in the group.

Step-by-step explanation:

Step 1:

The regular cost per person is $18.50 per person.

So to calculate the total cost, all we need to do is multiply the number of students in the study group with the cost per person i.e. $18.50.

So the equation is [tex]y=18.50 x[/tex].

If x = 5, [tex]y=18.50(5)[/tex] = $92.50,

If x = 10, [tex]y=18.50(10)[/tex] = $185.00.

Step 2:

The party special costs $15 per person but has an additional fee of $28 for a private room where they can have lunch.

So to calculate the total cost we multiply the number of students in the group with the cost per person i.e. $15 and add it with the private room fee i.e. $15.

So the equation is [tex]y=15 x+28[/tex].

If x = 5, [tex]y=15 (5)+28[/tex] = $103.00

If x = 10, [tex]y=15 (10)+28[/tex] = $178.00.

Four families are planning to make a joint purchase at a warehouse club in order to purchase no more than 15 pounds of potatoes for each family how many potatoes should they buy?

Answers

Answer:

x < 15.  

Step-by-step explanation:

Solving Inequalities Word Problems

Let X is the total pounds of potatoes that four families should buy

To purchase no more than 15, so they should buy 0< x < 15

Because four families are planning to make a joint purchase and we dont know their specific proportion  so we take x as the number on be haft.

A linear equation exists for the following sets of ordered pairs: {(-1, 1), (0, 3), (-1/3, 7/3)}. The rule for the linear equation states that y is three more than twice x. Set up a linear equation that satisfies the rule, and use the set of ordered pairs to prove that your equation satisfies the set of coordinates. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.

Answers

Answer:

Part 1) [tex]y=2x+3[/tex]

Part 2) The equation satisfy the set of coordinates (see the explanation)

Step-by-step explanation:

step 1

Find the linear equation

The rule for the linear equation states that y is three more than twice x.

so

The variable y is equal to the number 2 multiplied by x plus the number 3

[tex]y=2x+3[/tex]

step 2

Prove that the equation satisfies the set of coordinates

substitute the value of x and the value of y in the linear equation and then compare the results

a) (-1, 1)

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

[tex]1=1[/tex] ----> is true

so

The equation satisfy the ordered pair

b) (0, 3)

[tex]3=2(0)+3[/tex]

[tex]3=3[/tex] ----> is true

so

The equation satisfy the ordered pair

c) (-1/3,7/3)

[tex]7/3=2(-1/3)+3[/tex]

[tex]7/3=7/3[/tex] ----> is true

so

The equation satisfy the ordered pair

therefore

The equation satisfy the set of coordinates

Triangle M R N. Angle N is 98 degrees. Side N M extends to form exterior angle with a measure of 109 degrees.
16 degrees
19 degrees
71 degrees
87 degrees

Answers

Answer:

16 degrees

Step-by-step explanation:

The question is

Find the measure of angle R

we know that

An exterior angle of a triangle is equal to the sum of the opposite interior angles

so

In this problem

[tex]m\angle N+m\angle R=109^o[/tex]

we have

[tex]m\angle N=93^o[/tex]

substitute

[tex]93^o+m\angle R=109^o[/tex]

[tex]m\angle R=109^o-93^o=16^o[/tex]

Answer: 16 degrees

Step-by-step explanation: 109-93 is 16

Which statement best describes what happened to average gas prices from week 2 to week 4?
A They fell.
B They rose and then fell.
C They stayed the same.
D They rose.

Answers

Answer:

Is there a graph that we need to look at


Kay is drawing a triangle. Two of the sides have an equal length of 8 cm, and the angle between those sides measures 68°. Which could be the measure of each base angle?

Answers

The measure of each base angle is 56°.

Step-by-step explanation:

The isosceles triangle has two base angles that are congruent (same measure).Let the measure of each base angle is 'x'.The sum of angles in a triangle add to 180°.

base angle + base angle + 68° = 180°

2x + 68° = 180°

2x = 112°

x = 112/2

x = 56°

Therefore, the measure of each base angle is 56°.

The required measure of each base angle is equal to 56°.

It involves understanding the properties of an isosceles triangle, which is the key to solving the problem. In an isosceles triangle, if two sides are equal, the angles opposite those sides are also equal.

Given that Kay is drawing a triangle with two equal sides of 8 cm and the angle between these sides measures 68°, the triangle is isosceles, and we know that the other two angles (the base angles) are equal due to this property.

The sum of all angles in any triangle equals 180°. Therefore, to find the measure of each base angle, we subtract the given angle from 180° and then divide by 2 (since the base angles are equal):

The sum of angles in a triangle = 180°.

The measure of the angle between the two sides = 68°.

The sum of the two base angles = 180° - 68° = 112°.

Measure of each base angle = 112° / 2 = 56°.

Therefore, the measure of each base angle in Kay's triangle is 56°.

The area of a square whose side measures four units is added to the difference of eleven and nine divided by two.

Answers

Answer:

The correct answer is D. 17.

Correct statement and question:

The area of a square whose side measures four units is added to the

difference of eleven and nine divided by two. What is the total value?

a. 9

b. 16

c. 5

d. 17

Source:

Previous question that can found at brainly

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Side of the square = 4 units

Area of the square = 4 * 4 = 16 units

2. What is the total value?

Difference of eleven and nine divided by two = (11 - 9)/2

Difference of eleven and nine divided by two = 2/2 = 1

Area of a square whose side measures four units is added to the

difference of eleven and nine divided by two = 16 + 1

Area of a square whose side measures four units is added to the

difference of eleven and nine divided by two = 17

The correct answer is D. 17

Final answer:

The combined result of the area of a square with a side of four units and the arithmetic expression (11 minus 9) divided by 2 is 17.

Explanation:

Calculating the Combined Area and Arithmetic Expression

To solve the given problem, we need to calculate the area of a square with a side of four units and add this to the arithmetic expression (11 minus 9) divided by 2. First, let's find the area of the square. The area of a square is found using the formula area = side × side. Therefore, the area of our square is 4 units × 4 units = 16 square units.

Next, we calculate the arithmetic expression. The difference of eleven and nine is 11 - 9 = 2, and dividing this by two gives us 2 / 2 = 1.

Finally, we add the area of the square to this result: 16 square units + 1 = 17. The final answer is 17.

Alina is flying a kite. The kite string is fully extended and measures 100 feet in length. The kite is 45 feet east of Alina. Which equation can be used to find the height of the kite? How high is the kite? Select two answers

Answers

Answer: I chose A and D but I'm not sure.

Answer:

The answers are A and D since A is the right equation and 89.3 is the right answer

Step-by-step explanation:

Identify the point from the equation: y + 5 = 3(x - 2)

Answers

Answer:

The point is [tex](2,-5)[/tex]

Step-by-step explanation:

we have

[tex]y+5=3(x-2)[/tex]

This is the equation of the line written in point slope form

so

[tex]y-y1=m(x-x1)[/tex]

where

The slope is equal to

[tex]m=3[/tex]

The point (x1,y1) is

[tex](2,-5)[/tex]

therefore

The point is [tex](2,-5)[/tex]

Consider the equation x=-2y+7 what is the x-intercept

Answers

Answer:

7

Step-by-step explanation:

The x-intercept is the x-value when y=0, so we plug in y=0,

x=-2(0)+7

x=0+7

x=7

So the x-intercept is 7

Answer:

X intercept is 7

Step-by-step explanation:

9(2x + 10) = 2(9x+ 45)

Answers

Answer:

infinitely many solutions

Step-by-step explanation:

1) distribute 9 to each term inside parenthesis on left side of equation

18x+90=2(9x+45)

2)now distribute 2

18x+90=18x+90

these equations are exactly the same! this means that this equation has infinitely many solutions

Hope this helps!

Answer:

infinite solutions

Step-by-step explanation:

9(2x + 10) = 2(9x+ 45)

Distribute

18x+90 = 18x +90

Subtract 18x from each side

18x-18x+90 = 18x-18x+90

90=90

Since this is always true, the equation has infinite solutions.

X can be any number

You travel 150 miles on 5 gallons how far did you travel per gallon?

Answers

Answer:

Step-by-step explanation:

Answer:

You travel 30 miles per (1) gallon!!!!! please give brainliest!!

Step-by-step explanation:

150/5=30

help and hurry plzzzzzzzzzzzzz

Answers

Answer:

The equation of the line in the slope-intercept form is y = [tex]\frac{4}{3}[/tex] x + 4A

Step-by-step explanation:

The slope-intercept form is y = m x + b, where

m is the slope of the lineb is the y-intercept (y at x = 0)

The formula of the slope of a line which passes through points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

∵ The line passes through points (-6 , -4) and (0 , 4)

∴ [tex]x_{1}[/tex] = -6 and [tex]x_{2}[/tex] = 0

∴ [tex]y_{1}[/tex] = -4 and [tex]y_{2}[/tex] = 4

- Substitute them in the formula of the slope

∴ [tex]m=\frac{4--4}{0--6}=\frac{8}{6}[/tex]

- Simplify it by divide up and down by 2

∴ [tex]m=\frac{4}{3}[/tex]

∵ The slope-intercept form is y = m x + b

- Substitute the value of m on it

∴ y = [tex]\frac{4}{3}[/tex] x + b

∵ b is value y at x= 0

∵ At x = 0 , y = 4 ⇒ given point

∴ b = 4

- Substitute the value of b in the equation

∴ y = [tex]\frac{4}{3}[/tex] x + 4

The equation of the line in the slope-intercept form is y = [tex]\frac{4}{3}[/tex] x + 4

Wavelength varies inversely with frequency. Let k be the product of wavelength and frequency. Complete
the table using the inverse variation relationship.
Visible Light
Wavelength (m)
Frequency (THz)
Blue
450
301,500
Green
520
580
Yellow
540
302,400
Red
635
304,800
480
a=
b = 301,
c=_
DONE

Answers

Answer:

A=670

B=301,600

C=560

Step-by-step explanation:

A is K divided by the wavelength (m) 301,500 / 450

B is wavelength(m) multiplied by the Frequency (Thz) 520x580

C is K divided by the Frenquency (Thz) 302400 / 540

The value of a is 670, b is 301,600, and c is 560.

What is Inverse Variation?

When a variable varies inversely with the other variable, i.e. on increasing one variable the other decreases is called Inverse Variation.

The table consists of data of wavelength, frequency and k, the product of wavelength and frequency.

The missing values of a, b, and c has to be determined.

The wavelength is in inverse relation to frequency, on increasing the wavelength, the frequency decreases.

Wavelength ∝ ( 1 / frequency)

Wavelength * Frequency = k

For determining a,

450 * a = 301500

a = 301500/450 = 670

a = 670

For determining b,

520 * 580 = b

b = 301600

For determining c,

c * 540 = 302400

c = 302400 / 540

c = 560

To know more about Inverse Variation

https://brainly.com/question/11592410

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Absolute value equation |x-3|=5​

Answers

Answer:

x = - 2, x = 8

Step-by-step explanation:

The absolute value function always returns a positive value, but the expression inside can be positive or negative, thus

x - 3 = 5 OR - (x - 3) = 5

Solving both equations

x - 3 = 5 ( add 3 to both sides )

x = 8

OR

- x + 3 = 5 ( subtract 3 from both sides )

- x = 2 ( multiply both sides by - 1 )

x = - 2

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are solutions.

x = 8

| 8 - 3 | = | 5 | = 5 = right side

x = - 2

| - 2 - 3 | = | - 5 | = 5 = right side

Thus the solutions are x = - 2, x = 8

The equation given is the same as x - 3 = 5 or -(x - 3) = 5

Steps to solve:

x - 3 = 5

x - 3 + 3 = 5 + 3

x = 8

Steps to solve:

-(x - 3) = 5

-x + 3 = 5

-x + 3 - 3 = 5 - 3

-x = 2

-x/-1 = 2/-1

x = -2

Therefore, the solutions are x = 8 and x = -2

Best of Luck!

The length of a rectangular piece of sheet metal is 3 times it’s width. What is its length if it’s area is 192 square centimeters

Answers

To find the missing number, you will need to divide the numbers you already have.

192 divided by 3 = 64

Your answer/length will be 64.

Area = 192

Width = 3

Length = 64

64 x 3 = 192

                                                                                Hope this helps :)

To determine the length of the rectangular piece of sheet metal with an area of 192 square centimeters and a given length-to-width ratio, solve for the width using the area formula, then use the ratio to find the length. The calculated length is 24 centimeters.

The problem involves finding the length of a rectangle given the area and the relationship between the length and width. Let's denote the width of the rectangle as w and the length as L. We are given that L = 3w and the area (A) of the rectangle is 192 square centimeters. The area of a rectangle is calculated by multiplying its length and width.

A = L x w

Substituting L from the given relationship into the area equation:

192 cm² = (3w) x w

Now we can solve for w:

192 cm² = 3w²

w² = 192 cm² / 3

w² = 64 cm²

w = 8 cm

Now, use the value of w to find L:

L = 3 x 8 cm

L = 24 cm

Therefore, the length of the rectangular piece of sheet metal is 24 centimeters.

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find the area of the complex figure.
Not drawn to scale.​

Answers

Answer:

1863 [tex]meters^{2}[/tex]

Step-by-step explanation:

( 23 x 12 ) x 2 = 552

69 x 19 = 1311

 1311

+552

= 1863 [tex]meters^{2}[/tex]

The area of the complex figure is 1,863 square meters

To find the area of the complex figure, break it down into individual rectangles and then sum up their areas. The complex figure consists of two smaller rectangles and one larger rectangle.

For the first two rectangles:

- Length = 23 m

- Width = 12 m

The area of each of the first two rectangles is:

Area = Length × Width = 23 m × 12 m = 276 square meters

Now, for the larger rectangle:

- Length = 69 m

- Width = 19 m

The area of the larger rectangle is:

Area = Length × Width = 69 m × 19 m = 1,311 square meters

To find the total area of the complex figure, sum up the areas of the three rectangles:

Total Area = Area of the first two rectangles + Area of the larger rectangle

Total Area = (276 square meters + 276 square meters) + 1,311 square meters

Total Area = 552 square meters + 1,311 square meters

Total Area = 1,863 square meters

So, the area of the complex figure is 1,863 square meters. This approach demonstrates how to find the area by breaking down the complex figure into simpler shapes and summing their individual areas.

For more such questions on complex figure:

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A colony of 300,000 bacteria doubles in size every 35 minutes what will the population be 70 minutes from now ?

Answers

Answer:

1,200,000

Step-by-step explanation:

300,000 x 4

It doubles every 35 minutes so you multiply by 4

Answer:

X=600000

Step-by-step explanation:

Let the unknown value for 70minutes be x

So let's solve the given question

300000 bacteria is double in every 35minutes

So to solve we will have

300000 bacteria=35minutes

X bacteria=70 minutes

So let's cross multiply

35x=300000×70

Let's make x the subject of formula by dividing both sides by 35

X=300000×70/35

X=300000×2

X=600000

Therefore the population in 70 minutes is 600000

Simplify the expression

7.) -3.5 - 2.1 x 1.8​

Answers

1. Simplify 2.1 * 1.8 to 3.78

-3.5 - 3.78

2. Simplify

-7.28

Answer: -7.28

Step-by-step explanation:

A cone with a height of 14 feet has a volume of 405.63 cubic feet

Answers

Answer:

R=5.26

Step-by-step explanation:

What is the measure of it

Answers

Answer:My guess is 185

Step-by-step explanation:

There are 2 bags, each containing red blocks and yellow blocks. Bag 1 contains 1 red block and 3 yellow blocks. Bag 2 contains 4 red blocks and 12 yellow blocks. Tom says he is more likely to pick a red block out of bag 2 than out of bag 1 because bag 2 has more red blocks than bag 1. Is this correct? Explain your reasoning.

Answers

Answer:

No

Step-by-step explanation:

Bag 1:

P(red) = 1/4

Bag 2:

P(red) = 4/16 = 1/4

Same probability so equally likely

A triangle has an area of 80 yd² and a height of 10 yd. How long is the base of the triangle?
Plz help this is my unit test

Answers

Answer:

16 yd. is the answer. Good luck with the test.

Step-by-step explanation:

A=b×h÷2

80=10×y÷2

160=10×y

16=y

16 yd.

Answer:

he base length of triangle = 16 yd

Explanation:

he base length of triangle = 16 yd

Step-by-step explanation:

Formula:-

Area of triangle

area A = bh/2

b - base of triangle

h - height of triangle

To find the area of triangle

It is given that,A triangle has an area of 80 yd^2 and a height of 10 yd.

here, b = ?, A = 80 yd^2  and h = 10 yd

A = bh/2

80 = (b*10)/2

5b = 80

b = 80/5 = 16

Therefore the base length of triangle = 16 yd

solve the equation 14z=224

Answers

Step-by-step explanation:

[tex]14z = 224[/tex]

To solve for [tex]z[/tex] in this equation, we need to isolate [tex]z[/tex] by itself on one side of the equation.

To do this, we need to get rid of the [tex]14[/tex] that is being multiplied by the [tex]z[/tex] on the left-hand side of the equation. This can be done by dividing both sides by [tex]14[/tex]:

[tex]14z = 224[/tex]

[tex]\frac{14z}{14} = \frac{224}{14}[/tex]

[tex]z = 16[/tex]

Therefore, the solution to the equation is [tex]z = 16[/tex].

Answer:

Step-by-step explanation:

14z = 224

divide both sides by 14

[tex]z=\frac{224}{14}\\\\z=16[/tex]

PLEASE HELP NOW!! Will grant brainliest

Answers

(f·g)(x) is x^5 - 5x^4 + 4x³ - x² + 5x - 4

Step-by-step explanation:

Step 1: Given, f(x) = x² - 5x + 4 and g(x) = x³ - 1 Find (f·g)(x)

(f·g)(x) = f(x)·g(x) = (x² - 5x + 4)(x³ - 1)

                          = x^5 - 5x^4 + 4x³ - x² + 5x - 4

                          = x^5 - 5x^4 + 4x³ - x² + 5x - 4

What is the value of d?

Answers

Answer:

d=5

Step-by-step explanation:

1 + 1 2 ⋅ (4x − 6) = −2

Answers

1.4375

Step-by-step explanation:

Step 1:

Let the given equation be     [tex]1+12(4X-6)=-2[/tex]

To find X simplification of terms using BODMAS ( Brackets Orders Division Multiplication Addition Subtraction) is done as follows.

Step 2:

Let us expand the equation as [tex]1+ (12*4X)-(12*6)=-2[/tex]

Step 3:

Let us expand it further as [tex]1+48X-72=-2[/tex]

Step 4:

To find X segregate X in one side and all other remaining terms in other side as follows

[tex]48X=-2+72-1[/tex]

After the simplification the numerical value is

[tex]48X=69[/tex]

Step 5:

Keep X along one side and bring 48 to the denominator of another side to find X as follows

[tex]X=69/48[/tex]

And the value of X is 1.4375

Answer:

x = 1 7/16

Step-by-step explanation:

1 + 1 2 ⋅ (4x − 6) = −2

Subtract 1 from each side

1-1 + 1 2 ⋅ (4x − 6) = −2-1

1 2 ⋅ (4x − 6) = −3

Distribute the 12

48x -72 = -3

Add 72 to each side

48x-72+72 = -3+72

48x =69

Divide by 48

48x/48 = 69/48

x =1 21/48

x = 1 7/16

!!!!!!!!!!!Help please!!!!!!!!!!!!!!!

Answers

Answer:

Option D

Step-by-step explanation:

A radical equation has only a radical itself, with an additional multiplier.

Answer:

7√x=14

Step-by-step explanation:

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A)Using Coupons to Save Money at the Grocery StoreB)Plan Your Weekly Food Menus and Lose Weight C)Save Time, Money, and Hassle at the Grocery Store D)How to Get the Best Deal at the Grocery StoreE)The Link Between Grocery Lists and Weight Loss Write the expression in simplest form.(-11/2 x + 3)-2(-11/4 x - 5/2) Solve this questiongiving 5 points Describe the trends and potential advances in health care treatments over the next few decades and identify associated careers that may emerge From the 1920s to the 1970s, about 1 out of 1,000 Americans was in prison at any point in time. By 2008, due largely to changes in drug laws and drug enforcement, that rate: A. decreased to about 0.5 per 1,000. B. increased to about 1.5 per 1,000. C. doubled to about 2 per 1,000. D.increased to about 5 per 1,000. determine area under the standard normal curve given the z score, z less than 1.25 Which of the following is NOT true about an ATM? A. ATM stands for "Access or Transfer Money". B. An ATM is available virtually 24 hours a day. C. You can make a deposit at your bank's ATM. D. You can transfer money between your own accounts. According to the timeline, which of these events preceded the Boston Tea Party?A. the signing of the Declaration of IndependenceB. the Battles of Lexington and Concordc. the Boston MassacreD.the Continental Congress what indication is there that religious tolerance was already fairly common in new york at the time Kalm made his visit An object's mass is a measure of how much matter makes it up. An object's weight is a measure of the gravitational force that acts on it. An object's mass is always _______ its weight. A. double B. equal to C. half of D. proportional to During the past decades, the College Board has worked to diversify its reading lists for its Advanced Placement Exams to reflect works by women, people of color, and writers from Asia, Africa, and Latin America. Such efforts on the part of the College Board reflect which approach to multicultural education? solve the question of what is 2 + 3 What is the specific heat for the aluminum wire?J/gCWhat is the specific heat for the steel wire?J/gCWhat is the specific heat for the lead pellets?J/gC On August 1, Greene Company purchased merchandise inventory on account with a list price of $25,000 and credit terms of 2/10, n/30. What is the correct journal entry to record the August 1 purchase? Muhammad, a 21-year old computer engineer, is opening an individual retirement account (IRA) at a bank. His goal is to accumulate $2.5 million in the IRA by the time he retires in 46 years. Muhammad expects his IRA to receive 8% nominal annual interest, compounded semiannually, throughout the 46 years. As a computer engineer, Muhammad believes his salary will increase at a constant 4% annual rate during his career. Muhammad wishes to make annual deposits into his IRA account over the 46 years. He wishes to start his IRA with the lowest possible deposit and then increase his deposit amount at a constant 4% rate each year. Assuming end-of-year deposits, how much should she deposit the first year?