Find the domain of the function.
1-
X
O all real numbers such that x ≥ -7 and x ≤ 0
O all real numbers except x > -7 and x ≤ 0
O all real numbers except x = -7 and x = 0
O only x = -7 and x = 0
O all real numbers
g(x) =
=
Need Help?
4
x+7
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Find The Domain Of The Function.1-XO All Real Numbers Such That X -7 And X 0O All Real Numbers Except

Answers

Answer 1

The domain of the given function is all real numbers expect x> -7 and x ≥ 0.

What is domain?

The entire range of independent variable values is the domain of a function.

According to this definition, it means:

The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.

Keep these things in mind when locating the domain:

A fraction's denominator (bottom) cannot be 0.

In this section, the integer following a square root symbol must be positive.

Given,

g(x) = 1/x- 4/x+7

Applying the definition of rational function that denominator is non zero

x ≠ 0 and x+7 ≠ 0

solving the inequality,

x ≠ 0 and x ≠ -7

Combining the values,

x < -7 or -7 < x< 0 or x> 0.

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Related Questions

2. A car is going 65 miles per hour down the highway.
a. How far does it travel in 1.5 hours?
b. How long does it take the car to travel 130 miles?
c. Mai wrote the equation y = 65x, with a representing
the time traveled, in hours, and y representing the
distance traveled, in miles. Explain why Mai's equation
matches the story.
C
t
a
m
e
th
d
d

Answers

a. A car travels 97.5 miles in 1.5 hours.

b. A car takes 2 hours to travel 130 miles.

c. Mai's equation matches the story because it is algebraic form of the formula of speed.

In this question, we have been given a car is going 65 miles per hour down the highway.

Part a.

A car is going 65 miles per hour.

This means, in 1 hour car traveled 65 miles.

Let car travels 'm' miles in 1.5 hours.

So, m = 1.5 × 65

m = 97.5 miles

Thus, a car travels 97.5 miles in 1.5 hours

Part b.

Suppose that it will take t hours to travel 130 miles.

We have been given 1 hour = 65 miles

So, we get an equation,

t = 130 / 65

t = 2 hours

This means, a car takes 2 hours to travel 130 miles.

Part c.

Mai wrote the equation y = 65x, with x representing the time traveled, in hours, and y representing the distance traveled, in miles.

We know that the formula of speed.

speed = distance / time

⇒ distance = speed × time

here, speed = 65 miles per hour

⇒ distance = 65 × time

Assuming distance = y  and time = x

y = 65x

This means,  Mai's equation matches the story.

Therefore, a. A car travels 97.5 miles in 1.5 hours.

b. A car takes 2 hours to travel 130 miles.

c. Mai's equation matches the story because it is algebraic form of the formula of speed.

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over the set of integers factor the expression 4x^3 - x^2+16x-4 completely

Answers

The factorized expression of the equation of the function given as lf(x) = 4x³ - x² + 16x - 4 is f(x) = (x² + 4)(4x - 1)

How to determine the factor of the expression?

The equation of the function is given as

f(x) = 4x³ - x² + 16x - 4

Factor out x from the equation of the function

So, we have

f(x) = 4x³ - x² + 16x - 4

Group the terms in 2's

f(x) = (4x³ - x²) + (16x - 4)

Factorize the expression in the bracket

So, we have

f(x) = x²(4x - 1) + 4(4x - 1)

Factor out 4x - 1

So, we have

f(x) = (x² + 4)(4x - 1)

Hence, the factorized expression is f(x) = (x² + 4)(4x - 1)

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Algebra Question, please provide a step-by-step explanation.

Answers

Answer:

4 seconds

Step-by-step explanation:

First I substitute the Y with 0 and then I move the 16x^2 to the left side of the equation and then I divide both sides with 16 leaving me with x^2 then I get the square root of both sides and then I evaluate it and then I got the answer x = 4

Answer:

4 seconds

Step-by-step explanation:

We have a quadtratic equation, that is, we have a function to the highest degree of x^2.

When solving this, we can either solve using the quadratic equation, or by solving for X which would be the easiest and quickest way to do it.

256 -16x^2=0

-16x^2=-256

x^2=16 (divide both sides by -16)

[tex]\sqrt{x} =\sqrt{16}[/tex]

Which leaves x=4 as your answer.

To check this, we can simply input 4 back into the equation, and we will find that it does indeed equal 0.

To further visualize this, when we solve the equation for x, we are finding where the x value that intersects the x axis.  We are finding where x=0, or when it touches the ground.

an executive in an engineering firm earns a monthly salary plus a christmas bonus of 5700 dollars. if she earns a total of 83500 dollars per year, what is her monthly salary in dollars?

Answers

The monthly salary of an executive is $6483.

What is monthly salary?

A salary is the amount of money that an employee receives from their employer each month, particularly when they work in a profession like education, law, or medical.

Given: An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 5700 dollars. She earns a total of 83500 dollars per year.

To find the salary for each month.

First to subtract the Christmas bonus from the total amount.

83500 - 5700 = 77800.

So, the salary from each month is,  77800/12 = 6483

Therefore, the salary for each month is, $6483.

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11.04 = 1/2 (a + 0) 1.5

Answers

Answer: the value of a = 14.72 and if you evaluate it.

Have a good day

plss someone help me asap!!

Answers

By analyzing the geometric system, the measure of the angle RSP is equal to 49°.

What are the variables behind the angles of the system of triangles and one of the internal angles

In this problem we find a geometric system formed by two triangles, in which the line segment QR is parallel to the line segment PS. Then, we can obtain the following system of linear equations:

Intern alternate angles between parallel line segments

m ∠ QRP = m ∠ RPS

5 · y + 14 = 8 · y - 13

27 = 3 · y

y = 9

Internal angles of a triangles

m ∠ RPS + m ∠ PRS + m ∠ RSP = 180°

(8 · y - 13) + 3 · x + (2 · x + 1) = 180

8 · y + 5 · x - 12 = 180

8 · y = 180 + 12 - 5 · x

5 · x = 192 - 8 · y

x = (192 - 8 · y) / 5

x = (192 - 8 · 9) / 5

x = (192 - 72) / 5

x = 120 / 5

x = 24

Finally, the measure of the angle RSP is:

m ∠ RSP = 2 · x + 1

m ∠ RSP = 2 · 24 + 1

m ∠ RSP = 49

The measure of the angle RSP is equal to 49°.

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Determine the value of y in the inequality.

18 + 6y < 42

y < −7
y > −7
y < 4
y > 4

Answers

Answer:

y>-7

Step-by-step explanation:

Answer:

the answer is option 3

Step-by-step explanation:

18+6y<42

6y<42-18

6y<24

y<4

i need help, what is 4x+14≤38

Answers

Answer:

x ≤ 6 I think!

Answer: [tex]x\leq 6[/tex]

Step-by-step explanation: [tex]4x\leq 38-14[/tex]. Move the 14 to the right side first.

Then you would get [tex]4x\leq 24[/tex]

Divide 4 on both side

[tex]x\leq 6[/tex]

Ajay is working two summer jobs, making $8 per hour washing cars and $11 per hour
tutoring. Last week Ajay worked 2 more hours tutoring than hours washing cars and
earned a total of $60. Write a system of equations that could be used to determine
the number of hours Ajay worked washing cars last week and the number of hours he
worked tutoring last week. Define the variables that you use to write the system.
Let
Let
System of Fiquations

Answers

Using equation, the number of hours Ajay spent washing car and tutoring are 2 and 4 hours respectively.

How to represent system of equation?

Ajay is working two summer jobs working $8 per hour washing cars and $11 per hour tutoring.

Last week Ajay worked 2 more hours tutoring than hours washing cars and earned a total of $60.

The system of equation that could be used to determine the number of hours Ajay worked washing cars last week and the number of hours he worked tutoring last week can be calculated as follows:

let

x = number of hours washing cars

y = number of hours tutoring

Therefore,

y = 2 + x

Hence,

8(x) + 11(2 + x) = 60

8x + 22 + 11x = 60

19x  = 60 - 22

19x = 38

x = 38 / 19

x = 2

Therefore,

y = 2 + 2

y = 4

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Answer:

variables :

Let = w = The number of hours washing car.

let = t = The number of hours tutoring.

system of equations:

8w + 11t = 60

t = w + 2

Step-by-step explanation:

Which statement is true
A)Only graph A is a function
B)Only graph B is a function
C)Both graphs are functions
D)Neither graph is function

Answers

Answer:wish i could help

Step-by-step explanation:......

Only graph A is a function

Solve for x 6 + 2x = 2(x - 3)

Answers

Answer:

No solution

Step-by-step explanation:

6 + 2x = 2(x - 3)

6 + 2x = 2x-6

No solution

how many solutions does the equation 7x+3-8=2(5x-4) have

Answers

The number of solutions in the equation where the equation is given as 7x + 3 - 8 = 2(5x - 4)  is one solution

How to determine the number of solutions in the equation?

The equation is given as

7x + 3 - 8 = 2(5x - 4)

The above equation is a linear function with one variable

So, we have

7x + 3 - 8 = 2(5x - 4)

Open the brackets

So, we have

7x + 3 - 8 = 10x - 8

Subtract 10x from both sides of the equation

So, we have

-3x + 3 - 8 = - 8

Subtract (3 - 8) from both sides of the equation

So, we have

-3x = - 3

Divide by -3

x = 1

The above equation is true because it has a definite solution

Hence, the number of solutions in the equation is one

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Give a real-life representation of loudness and sound using exponential function.

Answers

Using an exponential function, the sound intensity of a noise that is 130 dB is of I = 10 watts/m².

Sound level

The sound level, in dB, of a sound of intensity given by I is given according to the following equation:

[tex]B = 10\log{\left(\frac{I}{I_0}\right)}[/tex]

In which [tex]I_0[/tex] is the smallest sound heard by the human ear, which is of [tex]I_0 =  10^{-12}[/tex] watts/meter.

Hence, for a sound of 130 db, the intensity I is found as follows:

[tex]130 = 10\log{\left(\frac{I}{10^{-12}}\right)}[/tex]

Isolating the logarithm, the equation is:

[tex]\log{\left(\frac{I}{10^{-12}}\right)} = 13[/tex]

The power of 10 and the logarithm are inverse functions, hence the power of 10 is applied to both sides of the equation to isolate the intensity creating the exponential function given as follows:

[tex]10^{\log{\left(\frac{I}{10^{-12}}\right)}} = 10^{13}[/tex]

[tex]\frac{l}{10^{-12}} = 10^{13}[/tex]

[tex]l = 10^{-12} \times 10^{13}[/tex]

Multiplying two terms with the same base and different exponents, we keep the base and add the exponents, hence the intensity is given as follows:

I = 10 watts/m².

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a steamer sails 100 miles east and then 40 miles on a bearing of n60°e. how far is the steamer from its starting point, and at what angle has it traveled from its starting point? round your answer to the nearest thousandth.

Answers

how do i delete an answer?

The population of a village is 6400. The population is decreasing exponentially at a rate of r% per year. After 22 years, the population will be 2607. Find the value of r.

Answers

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$2607\\ P=\textit{initial amount}\dotfill &6400\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\dotfill &22\\ \end{cases} \\\\\\ 2607=6400(1 - \frac{r}{100})^{22} \implies \cfrac{2607}{6400}=\left( \cfrac{100-r}{100} \right)^{22} \implies \sqrt[22]{\cfrac{2607}{6400}}=\cfrac{100-r}{100}[/tex]

[tex]\cfrac{r-100}{100}=-\sqrt[22]{\cfrac{2607}{6400}}\implies r-100=-100\sqrt[22]{\cfrac{2607}{6400}} \\\\\\ r=100-100\sqrt[22]{\cfrac{2607}{6400}}\implies {\Large \begin{array}{llll} r\approx 4 \end{array}}[/tex]

Rory has a handful of Skittles. He has 5 red, 8 yellow, 6 purple, 4 green, and 11 orange.
What is the ratio of red and orange to the other Skittles?

Answers

The most appropriate choice for ratio will be given by-

Ratio of red and orange to the other Skittles  = 8 : 9

What is ratio?

Ratio determines how many times one number is bigger than the other number, provided both the numbers has the same unit.

The first part of the ratio is called antecedent and the second part of the ratio is called consequent

Here,

Number of red Skittles Rory has = 5

Number of yellow Skittles Rory has = 8

Number of purple Skittles Rory has = 6

Number of green Skittles Rory has = 4

Number of orange Skittles Rory has = 11

Total number of red and orange skittles = 5 + 11

                                                                   = 16

Total number of other skittles = 8 + 6 + 4

                                                  = 18

Ratio of red and orange to the other Skittles = 16 : 18

                                                                         = 8 : 9

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Factorise 12x raise to power of 2 and y raise to power of 2 +11xy-5

Answers

According to the solving the factorized value of the given equation is:

(4x-5). (3x+1).

What is factorization?

Writing a number or any mathematical object as the sum of several factors—typically smaller or simpler objects that use the same known as factorization or factoring. For instance, 3 5 factors the polynomial x2 - 4 as well as the integer 15.

Why do we factor?

Factoring is a crucial procedure that aids in our understanding of our equations. We factorize our polynomials to create a simpler form, and when we factorize equations, we obtain a wealth of important information.

According the given data:

Detailed explanation:

12x² - 11x-5

12x²+4x-15x-5

4x(3x+1) - 5(3x+1)

(4x-5). (3x+1)

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A projectile is fired vertically upward and can be modeled by the function h(t)=−16t2+900t+175. During what time interval will the projectile be more than 9000 feet above the ground? Round your answer to the nearest hundredth.

Answers

Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.  12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.

Given that,

Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.

We have to find how long will the projectile be above the ground at a height more than 9000 feet.

Answers should be rounded to the closest hundredth.

The function is

h(t)=-16t²+900t+175

-16t²+900t+175>9000

-16t²+900t+175-9000>0

-16t²+900t-8825>0

The simplest method for locating a quadratic equation's roots is the quadratic formula. There are some quadratic equations that are difficult to factor, and in these cases we can quickly discover the roots by using the quadratic formula.

Gives the roots of a quadratic equation ax² + bx + c = 0.

x = [-b ± √(b² - 4ac)]/2a.

Now, We get

t= [-900 ± √((900)² - 4(-16)(-8825))]/2(-16)

t=[-900 ± √(810000-564800)]/-32

t=[-900 ± √(245200)]/-32

t=[-900 ± 495.17]/-32

First,

t=[-900 + 495.17]/-32

t=[-404.83]/-32

t=12.65

Second,

t=[-900 - 495.17]/-32

t=[-1395.17]/-32

t=43.59

Therefore, 12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.

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PLEASE HELP!! PICTURE INCLUDED!!

Please explain how to find angle R!!

Answers

Answer:

∠ R = 75°

Step-by-step explanation:

you are correct with answers to a, b, c

d

the sum of the 3 angles in Δ QRS = 180° , that is

∠ Q +∠ R + ∠ S = 180° , so

55° + ∠ R + 50° = 180°

∠ R + 105° = 180° ( subtract 105° from both sides )

∠ R = 75°

Make g the subjest of a=g+h/2

Answers

g = a - [tex]\frac{h}{2}[/tex]

Find the distance between the two points rounding to the nearest tenth (if necessary).
(4, -4) \text{ and } (9, -2)
(4,−4) and (9,−2)

Answers

The distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

As per the question statement, two points having coordinates (4, -4) and

(9, -2) plotted on the cartesian plane.

We are required to calculate the distance between the above mentioned two points, rounded to the nearest tenth.

To solve this question,  we need to know the Distance-formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by √[(x₂ - x₁)² + (y₂ - y₁)²]"

Assuming that [(x₁, y₁) = (4, -4)] and [(x₂, y₂) = (9, -2)], and substituting these values in the above-mentioned distance formula, we get,

√[(9 - 4)² + {(-2) - (-4)}²]

= √[(9 - 4)² + {(-2) + 4}²]

= √[(9 - 4)² + (4 - 2)²]

=√[(5)² + (2)²]

=√(25 + 4)

=√29

= 5.38 units.

Therefore, rounding (5.38) to the nearest tenth, we get, 5.40.

That is, the distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

Distance: In Mathematics, physics or daily life, distance is a numerical or occasionally qualitative measurement of how far objects or points are from each other.Coordinates: In geometry, coordinates are a pair of numbers that can uniquely determine the position of points or other geometric elements on a Euclidean or Cartesian Plane.

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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.


Please use a picture to show where they are plotted if you can.

Answers

The slope of the line in the given diagram = rise/run = 1/2.

How to Determine the Rise and Run of a Line to Determine its Slope?

The slope of a line is determined as the ratio of the rise of the line to the run of the line.

The rise of a line = change in y

The run of a line = change in x.

The red line in the image attached below shows the rise of the line which is, 1 units.

The blue line represents the run, which is, 2 units.

The slope of the line = 1 units/2 units = 1/2.

Therefore, we can state that the slope of the line = 1/2.

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Find the length of WY if WZ=128 ft and WX=YZ

Answers

Answer: 91 ft

Step-by-step explanation:

Since WZ=1287ft .XY=54ft

WX is congruent to YZ

so WX= 1/2 (128-54)

= 1/2 x(<—times) 74

=37ft

WY= WX + XY

=37+54

= 91ft

Sonia takes a 4/5-mile walk every day. What part of her walk has she completed once she has walked 3/5 mile?

Answers

 3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.

As given in the question,

Sonia takes a walk everyday which is equal to

= 4/5 mile

Moreover, she has completed a part of her daily targeted distance =  3/5 mile

We need to find, what part of the total distance which Sonia covers daily, has she covered just now by covering 3/5 mile of distance.

Part of the total distance which Sonia covers daily, from the distance she has covered just now by covering 3/5 mile of distance

= (Distance covered by Sonia)/ (Total distance covered by Sonia)

= (3/5) / (4/5)

= (3/5) × (5/4)

= 3/4 mile

Therefore,,   3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.

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irections: Find the missing endpa
D. R(-9, 4) and S(2, -1); Find T.

Answers

The coordinates of T are (13, -6) which s is the midpoint of rt r(-9,4) and s(2,-1).

What is Midpoint?

A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.

Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,

M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2

Assuming that S is the midpoint of the line segment RT, where point R's coordinates are (-9, 4) and S's coordinates are (2, -1).

We have to determine the coordinates of point T.

The midpoint is the average of both endpoints. i.e., (x₁, y₁) and (x₂, y₂).

In this case, the midpoint is given by M = S(2, -1).

Let R(x₁, y₁) = R(-9, 4) and we will determine T(x₂, y₂).

2 = (-9 + x₂)/2

-9 + x₂ = 4

x₂ = 13

-1 = (4 + y₂)/2

4 + y₂ = -2

y₂ = -6

Therefore, the coordinates of T are (13, -6).

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The question seems to be incomplete the correct question would be

Find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T

23. graph 6x=-90
pls anwser need to turn in asap

Answers

Answer:

Step-by-step explanation:

Step: 1

-Graph the 6x: It will start at (0,0) and will have a rise of 6 and a run of 1

Step: 2

-Graph the 90: From what I understand it should be a horizontal line with its point on 90y

Sorry if this doesn't help very late where I am.

I need help with this question. Please help

Answers

A linear function which has the same y-intercept of 5 as the one that is represented by the graph is: table 1.

How to calculate the slope of a linear function?

Mathematically, the slope of any linear function can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

At points (-3, -4) and (-1, 2), the slope of the line is given by:

Slope, m = (2 + 4)/(-1 + 3)

Slope, m = 6/2

Slope, m = 3.

Note: The y-intercept of the line shown on the graph is 5.

At points (-3, -4), the y-intercept of this line can be calculated by using the slope-intercept form:

y = mx + c

Where:

x and y represents the points.m represents the slope.c represents the y-intercept.

Making y-intercept (c) the subject of formula, we have:

y-intercept, c = y - mx

y-intercept, c = -4 - 3(-3)

y-intercept, c = -4 + 9

y-intercept, c = 5.

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Complete Question:

Which linear function has the same y-intercept as the one that is represented by the graph?

Ryan invests $7,000 for 9 months at a simple interest rate of 8.3%. The amount of interest received is found by
I=PRT
Since R=0.083,
I=0.083 x P x T
What are P and T?

Answers

P, which is the principal invested is $7,000 whereas the T is 0.75

What is simple interest?

The simple interest on an investment such as that of Ryan, can be determined as the principal multiplied by the simple interest  rate and the time whose formula is as given below:

I=PRT

I=simple interest amount in dollars=unknown

P=principal investment=actual amount invested on simple interest basis=$7000

R=annual simple interest rate=8.3%

T=period of investment measured in years=9/12=0.75(9months divided by 12months in a year gives 0.75 years)

I=$7000*0.083*0.75

I=$435.75

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Ashley babysits for 6 hours for $73.50 on Friday and for 3 hours for $36.75 on Sunday. What constant of proportionality relates the number of hours and total pay?

Group of answer choices

$13.50

$12.25

$11.75

$14.25

Answers

Answer:

12.25

Step-by-step explanation:

Armand plans to save money every month for the next six months. The function f(x)=2x−1 represents the amount of money, in dollars, Armand will deposit into his savings account at the end of x months since the time he started saving. Which of the following represents the amount of money, in dollars, Armand deposits into his savings account at the end of 3 months since the time he started saving? Select all that apply. Responses f⋅3f times 3 f(3)f of 3 3f(x)3 f x 23−12 cubed minus 1 3(2x−1)3 times open paren 2 to the x th power minus 1 close paren

Answers

AAnswer:

Step-by-step explanation:

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