How do you prove inverse?

Answers

Answer 1

To prove the inverse :

In the equation expressing the function, swap out f(x) for y.Swap out x and y. To put it another way, swap out every x for a y and vice versa.Solve for y.Change y to [tex]f^{-1}[/tex] (x).

You assemble the functions (that is, insert x into one function, plug that function into the suggested inverse function, then simplify) and check that you end up with simply "x" to establish (or refute) that two functions are the inverses of one another. The functions are inverses if you get x; otherwise, they are not.

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Related Questions

Which government tax policy is most likely to result in an increase in consumer demand? A - an increase in personal income tax B - a decrease in corporate tax C - a decrease in personal income tax D - an increase in corporate tax

Answers

The correct answer is "C" - a decrease in personal income tax is most likely to result in an increase in consumer demand.

Define Tax.

Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.

What is VAT?

A value-added tax, often referred to as a goods and services tax in some nations, is a kind of tax that is imposed gradually. At every stage of manufacture, distribution, or sale to the final customer, it is added to the cost of a good or service.

There is an increase in consumer demand when personal income taxes are cut because people have more money that they can spend on products and services.

On the other hand, a rise in personal income taxes would reduce the amount of disposable money that consumers have, which will result in a drop in demand from consumers.

In a similar vein, a rise in company tax would result in higher business costs and lower profits, both of which would reduce consumer demand. Conversely, a drop in corporate tax would not directly influence consumer spending.

So the correct answer is C.

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100 points + Brainliest Let C represents the cost in dollars and R represents the revenue in dollars. What is the break-even point? Use a table to help if necessary.

C=36x+200
R=76x
Break-even point: (,)

Answers

Answer:

  (x, {C and/or R}) = (5, 380)

Step-by-step explanation:

You want the break-even point when cost (C) and revenue (R) are given by ...

C = 36x +200R = 76x

Profit

Profit is the difference between revenue and cost. The break-even point is the point at which profit is zero:

  P = R -C

  0 = 76x -(36x +200)

  0 = 40x -200 . . . . simplify

  0 = x -5 . . . . . . . . . divide by 40

  x = 5 . . . . . . . . . add 5

The break-even point is at x=5. Revenue and cost are both 380 at that point.

Table

If you prefer to look at these values in a table, you can consider ...

  [tex]\displaystyle \begin{array}{ccc}x&C&R\\\cline{1-3}\vphantom{\^B}3&308&228\\4&344&304\\5&380&380\\6&416&456\end{array}[/tex]

We notice that cost and revenue are the same for x=5. They are both 380 for that value of x.

Graph

Another way to find the break-even point is to use a graph to plot cost and revenue on the same vertical axis. The point at which the lines cross is the break-even point. The break-even point coordinates are (5, 380).

one leg of a right triangle is 8 cm what could the other length be justify your answer

Answers

Answer:

6-L2


10-hypotenuse

Step-by-step explanation:

Pythagorean theorem

How many ways can we put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together

Answers

On solving the provided question, we can say that the permutation will bw  , N = (4!)(5!)(3!)(3!)= 103,680

what is permutation?

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.

we can put 3 math books and 5 English books on a shelf if all the math books must stay together and all the English books must also stay together will be , N = (4!)(5!)(3!)(3!)= 103,680

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Find the measures of the angles

Answers

Answer:

(1):

angle1/2/3/4=90

angle6=51

angle7=40

angle8=89

angle9=51

angle10=40

angle12=50

angle13=130

angle14=50

Step-by-step explanation:

Q1:

angle1 2 3 4 divided 360 into four equal parts

so 360/4=90

angle11=110degree

so angle12 is 180-130=50 degree

because angle 12 3 10 are in triangle

their sum is 180

so angle 10=180-90(angle3)-50(angle12)=40

because angle 10 5 6 sum is 180

so angle 6 is=180-89(angle5)-40(angle10)=51

because angle 5 6 7 sum is 180

angle7=180-51(angle6)-89(angle5)=40

angle8=angle5=89

angle9=angle6=51

angle12 &13sum is 180

so angle13=180-50=130

angle14=angle12=50

OMG PLEASE HELP FAST, Write the equation of the line in fully simplified slope-intercept form.

Answers

The equation of the line in the attached graph in slope intercept form is written as

y = -6x + 2

How to write the equation of the line

The slope, m of the linear function is calculated using the points on the graph (1, -4) and  (2, -10)

m = (y₀ - y₁) / (x₀ - x₁)

plugging in the values and evaluating

m = (-10 + 4) / (2 - 1)

m = (-6) / (1)

m = -6

equation passing through point (2, -10), using the point slope formula

(y - y₁) = m (x - x₁)

y - (-10) = -6(x - 2)

y + 10 = -6x + 12

rearranging the equation

y = -6x + 12 - 10

y = -6x + 2

The equation of the line in slope intercept form is written as y = -6x + 2

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how do i do this qustion

Answers

The slope of the line is 20.

The slope represents the rate of change in the price per hour is $20.

What are coordinates in a graph?

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Two coordinates from the graph.

(1, 60) and (3, 100)

Slope.

= (100 - 60) / (3 - 1)

= 40 / 2

= 20

The slope represents the rate of change in the price per hour.

Thus,

The value of the slope is 20.

The slope denotes that the rate of charge per hour is $20.

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If $x$ is a positive multiple of 8 and $x^2>100$, but $x<20$, what is $x$?

Answers

Answer:

16

Step-by-step explanation:

16 is a positive multiple of 8, in which 16²=256>100 and 16<20 are true statements.

Answer:

[tex]$x=\boxed{16}$[/tex]

Step-by-step explanation:

Since $x$ is a positive multiple of 8, it must be at least 8. Since $x^2>100$ and $x$ is at least 8, the only solution is $x=16$.

To verify this, note that $x=8$ does not satisfy the inequality $x^2>100$, but $x=16$ does, so $x=16$ is the only solution that works.

Therefore, $x=\boxed{16}$.

Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers,n,of hourse he could read on each of the 5 weekdays this week. The graph is shown. Which describes the solution set of the inequality.

Answers

Answer:

It appears that the solution set of the inequality 5n + 1.5 ≥ 4 is the set of all real numbers greater than or equal to -0.3. This can be determined by looking at the graph and noting that the region to the right of the vertical line x = -0.3 is shaded, which indicates that all values of x in that region are included in the solution set.

To verify this, we can substitute -0.3 into the inequality in place of n to see if the inequality is satisfied:

5(-0.3) + 1.5 ≥ 4

This simplifies to:

-1.5 + 1.5 ≥ 4

Which further simplifies to:

0 ≥ 4

Since this is not true, -0.3 is not a solution of the inequality. However, all values of x that are greater than or equal to -0.3 are solutions, as indicated by the shaded region on the graph.

Step-by-step explanation:

Perform the calculation then round to the appropriate number of significant digits

Answers

Answer:

315

Step-by-step explanation:

88.2 × 3.5742 = 315.24444

Answer: 315

Solve for x.

x2=14


Responses

x=±18
x equals plus or minus 1 eighth

x=±12
x equals plus or minus 1 half

x=±116
x equals plus or minus 1 sixteenth

x=±2

Answers

The solution for x in the equation given as x² = 1/4 is (b) x = ±1/2

How to determine the solution for x

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

An equation

The equation as poorly stated in the question is represented as

x2=14

When written properly

We have the following representation

x² = 1/4

Solving further, we need to take the square root of both sides of the equation

So, we have the following representation

√x² = ±√1/4

Evaluate the exponents on the left-hand side

So, we have the following representation

x = ±√1/4

Evaluate the exponents on the right-hand side

So, we have the following representation

x = ±1/2

Hence, the solution is (b) x = ±1/2

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Awatch which loses a half a minute was set to read the correct time at 0445h on Monday. determine the time in 12 hour clock system,the watch will show on the following Friday at 1845h

Answers

The Correct answer is 5.50 p.m

Explanation

Time between Monday 0445h and Friday 1845h

= 4 x 24 + 14 = 110h

Time lost = 0.5 x 110

= 55min

Time shown in 12 hour system

1845 – 55 = 1750 h

= 5.50 p.m

What is a 12-hour Clock system?

On an analogue clock, the 12-hour clock is most frequently displayed as the digits 1 through 12; on a digital clock, it is typically followed by either a.m. (ante meridiem, Latin for "before noon") or p.m. (post meridiem, Latin for "after noon").

What is a 24-hour Clock system?

Digital clocks are more frequently used to display the 24-hour clock, which is printed in a 4-digit format with the first two numbers denoting the hour and the final two denoting the minutes.

No need for a.m. or p.m. is necessary because each time represents one of the 24 hours in a day. For instance, 0300 is the third hour of the day, or 3am; 1400 is the fourteenth hour of the day, or 2pm; and 1830 is the thirty-minute mark after the eighteenth hour of the day, or 6.30pm.

How can we change 12-hour time format into a 24-hour clock format?

Children can be taught to add 12 to the hours after noon in order to change a 12-hour clock to a 24-hour one. For instance, 3pm becomes 15:00 since 3 + 12 = 15.

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The time shown on 19:45h Fridays is 06: 55 pm Friday.

What is meant by clock system?

A collection of synchronized clocks that can communicate with one another and display the exact same time every single time is known as a clock network or clock system. A constant pulse known as a system clock or system timer aids the computer clock in maintaining accurate time. It keeps track of how many seconds have passed since the epoch and utilizes that information to determine the current date and time.

A piece of electronic equipment inside a computer that continuously emits a high-frequency signal to keep everything in sync. electrical gadget type. a piece of equipment that operates electronically. a computerized time-of-day clock.

Given: Watch loses = 1/2 minute every hour

Time difference = 19: 45 h Friday - US:45 h Monday

=4 days 14 hours

=24 × 4+14 hours

=96+14

=110 hours

Time lost [tex]$= & 144^{55} \times \frac{1}{2} \mathrm{~min} \\[/tex]

= 55 min

Time shown on 19:45h Fridays

= 19: 45 - 0: 55

= 18: 55 h Friday

= 06: 55 pm Friday

Hence, 06: 55 pm Friday

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What is dual expression?

Answers

The Dual of Boolean Expression is defined as an expression that is obtained by interchanging the addition and multiplication and interchanging the 0's and 1's .

What is a Boolean Expression ?

The Boolean Expression is defined as an logical statement which results in the Boolean value which can either be True or False.

Sometimes, the synonyms is used to express statement such as ‘Yes’ for ‘True’ and ‘No’ for ‘False’. and also, 1 and 0 are used for digital circuits for True , False .

If in the Boolean expression , the addition and multiplication are interchanged and the binary 0 and 1 are also interchanged then the resulting expression will be called as a Dual Of Boolean Expression .

The given question is incomplete , the complete question is

What is Dual Boolean Expression ?

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what is x if 2/6+x=11/18

Answers

Answer:

multiply top and bottom of 2/6 to get 6/18, then subtract the answer by 6/18 , you get 5/18

Step-by-step explanation:

Answer:

x = 5/18

Step-by-step explanation:

what is x if 2/6+x=11/18

2/6 + x = 11/18

x = 11/18 - 2/6

x = 5/18

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

check

2/6 + 5/18 = 11/18

11/18 = 11/18

The answer is good

F18) if y varies jointly as x and the inverse of z, and y = -5 and z = 6, find y when x = 5 and z = -8

Answers

Answer:

gfifhdrtjttt9668ztjt*

At a recent graduation at a naval flight school, 18 Marines, 10 members of the Navy, and 3 members of the Coast Guard got their wings. Choose three pilots at random to feature on a training brochure. Find the probability that there will be

Answers

Probability measures how probable something is to occur.

What  the probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.

Probability is a measure of how likely something is to happen.

18 Marines, 10 Navy personnel, and 3 Coast Guard troops received their wings at a recent naval aviation school graduation.

Total: 18 + 10 + 3 = 31

a. 1 of each.  P = C 18 * C 10 * C 3  / C 3 31  

= (18 * 10 * 3) / 4495 = 0.120

b: 0 members of the navy = (C_{21} ^ 3)/(C_{21} ^ 3) = 1330/4495 = 0.296

c: 3 Marines.

p = (G ^ 3)/(C_{31} ^ 3) = (8 + 6)/4495 = 0.182

The complete question is

At a recent graduation at a naval flight school, 18 Marines, 10 members of the Navy, and 3 members of the Coast Guard got their wings. Choose three pilots at random to feature on a training brochure. Find the probability that there will be

a.1 of each 0.120  b.  members of the Navy 0.296 c.  Marines 0.182.

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Please hurry it's timed i need help

Answers

The solution of the given function cosx - √(3 - 3cos³x) = 0 is C. 30° + 360° n, 330° + 360°n

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are given the function as;

cosx - √(3 - 3cos³x) = 0

cosx = √(3 - 3cos³x)

Taking square root on both sides.

cos ²x = √(3 - 3cos³x) ²

cos ²x = (3 - 3cos³x)

For solving for x in

cos ²x = (3 - 3cos³x)

cos ²x = 3 (1 - cos³x)

(1 - cos³x) = cos ²x/3

x= π/6 + 2πn

or

x=11π/6 + 2πn

where n is an integer.

30° + 360° n, 330° + 360°n

The correct answer is C.

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Select all the expressions that are equivalent to 16x - 12- 24x+ 4 16 x − 12 − 24 x + 4. Explain or show your reasoning.

1. 4+16x-12(1+2x)4 + 16 x − 12 ( 1 + 2 x )


2. 40x-1640 x − 16


3. 16x-24x-4+1216 x − 24 x − 4 + 12


4. -8x-8- 8 x − 8


5. 10 (1. 6x - 1. 2 - 2. 4x + 4)

Answers

1) 16x - 12(1 + 2x) + 4 is the expression that are equivalent to 16x-12-24x+4.

what is expression?

An expression is a mathematical phrase that can contain numbers, variables, and operators. It can be a combination of these elements and can be evaluated to a specific value or a mathematical function.

An expression can be a simple mathematical statement such as 2x+3, or a more complex one involving multiple operations such as

(3x^2 - 4x + 5) / (2x +1). Expressions are used to represent mathematical operations, equations and relations between variables.

so we need to evaluate option 1 :

16x - 12 -24x +4

=> 16x - 12 -24x +4

the above expression is same as the expression mentioned in the question so option 1 is correct.

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Complete question :

Select all expressions that are equivalent to 16x−12−24x+4. Show or explain your reasoning.

1. 16x - 12(1 + 2x) + 4

2. 40x - 16

3. 4 - 12 + (2x - 3x)

4. -8(x+1)

The length and the breadth of a rectangular room is in 3:2 and its area is 96m². Find the length and breadth of the room. [Ans: 12m, 8m]​

Answers

Answer:12m,8m

Step-by-step explanation:BREAADTH

Write a rule for g that represents the indicated transformations of the graph of f.
f(x)=x³-6; translation 3 units left, followed by a reflection in the y-axis.

Answers

The function obtained after transformation is given as -x³ + 9x²- 27x + 21.

How to transform a graph of the function?

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

For left shifting it is f(x + a).

The function is given as f(x) = x³- 6.

The translation of 3 units towards left can be written as,

f(x + 3) = (x + 3)³ - 6

⇒ x³ + 9x² + 27x + 21

For reflection across y axis replace -x with x as below,

⇒ (-x)³ + 9(-x)² + 27 × -x + 21

⇒ -x³ + 9x²- 27x + 21

Hence, the required form of the transformed function is -x³ + 9x²- 27x + 21.

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Two alien pacehip tart traveling toward each other from pace tation that are 710,000 km apart. The firt pacehip tarted an hour before the econd pacehip and i traveling at 110,000 km/hr. In how many hour will the two pacehip meet if the econd pacehip i traveling at 90. 000 km/hr?

Answers

The two spaceships will meet in 8 hours if the second spaceship is traveling at 90. 000 km/hr.

To calculate the time it will take for the two spaceships to meet, you must use the equation Distance = Rate x Time. Since the first spaceship has a higher rate of speed, it will reach the second spaceship in less time than it would take the second spaceship to reach the first.

This means that the time it takes for the two spaceships to meet will be equal to the time it takes for the first spaceship to travel the distance between the two space stations. We can use the equation to solve for time: Time = Distance/Rate. In this case, the distance is 710,000 km and the rate is 110,000 km/hr, so the time is 6.45 hours.

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how do i solve -2.4>b/-2.5 step by step

Answers

Step-by-step explanation:

hope this helps....see above for answer

a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes
pls help explanation required

Answers

Answer:

$68

Step-by-step explanation:

Let x = original price.

The sale price is 75% of the original price, so the sale price is 75% of x.

75% as a decimal is 75/100 = 0.75

75% of is the same as 0.75x

We are told the sale price is $51, so 0.75x must equal $51.

0.75x = 51

Divide both sides by 0.75 to find the value of x.

x = 51/0.75

x = 68

Answer: $68

Answer:

Step-by-step explanation:

$51 is 75% of 100%

75% = 3/4

51 / 3 = 17

17 = 1/4

51 + 17 = 68

$68 is the original price of the shoes

Jeremy made nine out of twelve basketball shots in P.E. class. What decimal and percent represents the number of shots he made?​

Answers

3/4 shots were made so 75% or .75 of his total shots were made.

Jay and kevin are shoveling the snow off a driveway. working together, they can clear the driveway of snow in 14 minutes. working alone, it would take kevin 21 minutes longer to clear the driveway of snow than it would take jay working alone. when j is the number of minutes it would take jay to clear the driveway of snow when working alone, the situation is modeled by this rational equation: how long would it take jay to clear the driveway of snow working alone?
a. 7 minutes
b. 21 minutes
c. 35 minutes
d. 42 minutes

Answers

Therefore, As a result, the answer to the given equation problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.

Define equation .

A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation. Word illustration The product of 8 and 3 is 11.

Here,

The formula is: 1/j +1/j+ 21 = 11/ 4.

LCM = j+21+j / j(j+21)=1/14

Thus, 2j+21 / j(j+21) = 1/14 is obtained.

14(2j+21) times itself yields j(j+21).

28j+294 expanded to j²+21j

Gather comparable terms

j²+21j-28j-294=0

j²- 7j-294=0

With the use of a graphing calculator, we have:

j = 21 or j= -14

Due to the context,

j's value cannot be negative.

As a result, the answer to the given equation's problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.

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What is the equation for the linear relationship in slope intercept form?

Answers

Answer:

y=1/2x-3

Step-by-step explanation:

y=mx+b

y=1/2x-3

A recipe for 3 people uses 150 g of flour. How much flour is needed to
make the same recipe for 6 people? Give your answer in grams (g).

Answers

To make the same recipe for 6 people you need 300 grams (g)

600 g flour is needed to make the recipe which needs 150 g flour for 3 people, for 6 people.

Given that a recipe for 3 people uses 150 g of flour.

We know that the relation between quantity of flour and number of people for whom recipe will be prepared is directly proportional.

So if the number of people will increase so the quantity of flour will be needed more.

The flour needed to make the recipe for 1 people is = 150/3 = 50 g.

The flour needed to make the recipe for 6 people will be = 50 * 6 = 300 g.

Hence 600 g flour is needed to make the same recipe for 6 people.

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What critical value of t* should be used for a 95% confidence interval for the population mean based on a random sample of 15 observations

Answers

A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The critical t-value is what?

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

How do we determine the appropriate value of T *?

Using a standard t-test and the following formula, you can determine a t-value: t is equal to (X - ц0) / (s / √n), where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The critical t-value is what?

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

How do we determine the appropriate value of T?

Using a standard t-test and the following formula, you can determine a t-value: t is equal to [tex](X - ц0) / (s / √n)[/tex], where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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HI!!

can someone help with ts

Answers

Function Notation: another way of representing the relation between two variables, y is denoted as f(x) and x remains.

x is the input and f(x) is the output

This question is essentially asking what is the output of the function when the input is equal to 5.

[tex]f(5) = (5)^2-2(5)[/tex]

[tex]f(5) = 25-10[/tex]

[tex]f(5) = 15[/tex]

Solve for x.

3 1/2 ≥ 1.4x

A. x ≥ 2 1/2

B. x ≤ 2 1/2

C. x ≥ 4 9/10

D. x ≤ 4 9/10

Answers

To solve for x, we need to get x by itself on one side of the equation. To do this, we can start by subtracting 1.4x from both sides of the equation. This gives us:

3 1/2 - 1.4x ≥ 0

Next, we can simplify the left side of the equation to get:

7/2 - 7/5x ≥ 0

Now we can divide both sides of the equation by -7/5 to get:

-5/2x ≤ -7/2

Finally, we can multiply both sides of the equation by -2/5 to get:

x ≥ 4 9/10

Therefore, the solution is x ≥ 4 9/10, which corresponds to answer choice C.

Answer:
x ≥ 4 9/10 C:)

Step-by-step explanation:

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