What is the inverse of f(x)= 1/3x + 2?

Answer:

y=-7x-2

Step-by-step explanation:

I assume you need the equation for the line, so that's what I'm solving for here.

1. Start by putting the slope and the coordinates into point slope form, which is y-y1=m(x-x1)

y+30=-7(x-4)

2. Distribute -7 to (x-4) (or multiply x and -4 by -7).

y+30=-7x+28

3. Subtract 30 from both sides to get y by itself.

y=-7x-2

Student A is incorrect. The student started at 0 on the y-axis, did not need to move horizontally on the graph, and so moved horizontally to 2 on the x-axis. The student should have started at 0 on the x-axis, moved horizontally to the graph, and then moved vertically to -6, which student B did.

The value of x at which we want to find the numeric value of the function is given as follows:

x = 2.

Tracing a vertical line through x = 2, it will cross the graph of the function at y = -6, hence the numeric value is given as follows:

f(2) = -6.

Meaning that student B is correct.

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Answer:

c. Yes because ∠2 and ∠6 are congruent.

Step-by-step explanation:

From the picture attached,

m(∠2) = m(∠3) = m(∠6) = 40°

m(∠1) = 140°

Since (∠2 ≅ ∠6) (corresponding angles)

Therefore, by the converse theorem of corresponding angles lines c and d are parallel.

Option c is the answer.

The coordinates of the midpoint M of segment JK are (-0. 3). The distance between the endpoints of JK is sqrt(104) or approximately 10.198.

To find the coordinates of the midpoint M of segment JK, we can use the midpoint formula, which states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, for segment JK with endpoints J(3, -6) and K(-3, 2), the x-coordinate of the midpoint is (-3+3)/2 = 0 and the y-coordinate of the midpoint is (-6+2)/2 = -2. Therefore, the coordinates of the midpoint M are (0, -2).

To find the distance between the endpoints of JK, we can use the distance formula, which states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by the square root of [(x2-x1)^2 + (y2-y1)^2]. So for segment JK with endpoints J(3, -6) and K(-3, 2), the distance is sqrt[(-3-3)^2 + (2-(-6))^2] = sqrt[36 + 64] = sqrt(100) = 10. Therefore, the distance between the endpoints of JK is approximately 10.198.

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Answer:

2 pints

Step-by-step explanation:

1 pint = 2 cups

Answer:

2 pints

Step-by-step explanation:

There are 2 cups in one US pint. This means that the cup would have 2 pints in total.

4 cups/2 cups per pint = 2 pints.

Hope this helps.

The resulting religion Islam belongs to the class monotheism.

Monotheism is the class of religion where they believe in only one God.

Monotheism is the belief that there is one and only supreme power that is referred to as the universal God.

Given that according to Muslim tradition, the prophet Muhammad received his revelations from the only true God, whose name is Allah.

So there is only one God Allah that Islam believes in.

So Islam is a monotheistic religion.

Hence Islam is a monotheism.

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Answer: 17.5%

Step-by-step explanation:

Percentage of chips given to Jackie = 20%

Percentage of chips given to Ronald = 20%

Percentage of chips given to Mark = 1/4 × 100 = 25%

From the above calculation, we can see that Ms Johnson has given out ((20% + 20% + 25%) = 65% worth of chips out. The percentage she'll have left will be:

= 100 - 65

= 35%

Since Susan takes half of what's left, the percent that Ms. Johnson has left to eat will be:

= 1/2 × 35%

= 17.5%

She has 17.5% left to eat.

The number of unicycles on a labeled set of vertices {1, 2, ..., n} can be found using the formula: (1/2)(n-1)![(n-2)! - (n-3)! + (n-4)! - ... + \((-1)^{(n-1)}*1\)!]

This formula is based on the fact that a unicycle can be formed by choosing any vertex as the starting point, and then arranging the remaining n-1 vertices in a cycle.

This can be done in (n-1)! ways. However, we must subtract the number of cases where there are disconnected components, which can occur when we exclude one or more edges from the cycle.

To do this, we can use the principle of inclusion-exclusion. The term (n-2)! represents the number of ways to arrange the remaining vertices in a cycle when one edge is excluded, and we subtract this from the total count.

However, we must add back the cases where two edges are excluded and there are two disconnected components. This is given by (n-3)!, and we continue this alternating pattern until we add back or subtract 1!, depending on whether n-1 is odd or even.

Thus, the final formula for the number of unicycles is given by the above expression.

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Step-by-step explanation:

W^2 = 46.

We know that 6^2 = 36 and 7^2 = 49.

Therefore W should be between 6 and 7.

Answer:

Step-by-step explanation:

The vertex form of an equation of the parabola:  

                                                      f(x) = a(x - h)² + k

the vertex is (4, -4)  ⇒   h = 4,  k = -4

so:

  f(x) = a(x - 4)² + (-4)

    f(x) = a(x - 4)² - 4

So the right answer is the first one.

One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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The counterclockwise circulation around c is 12 and the outward flux through c is zero.

Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.

In this case,

we have a field f=(7x−4y)i+(9y−4x)j and

a square curve c bounded by x=0, x=4, y=0, y=4.

To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.

The curl of f is given by (0,0,3), so the line integral evaluates to 12.

To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.

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On solving we got that. he shorter pieces will therefore be 3 feet long and the longer pieces will therefore be 8 feet long.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

The lengths of the shorter and longer pieces of a board should be determined.

the case

Let's say that the shorter parts are x in length.

as stated

Jared has an 11-foot wooden board with him.

In order for the longer piece to be 4 feet less than 4 times as long as the shorter piece, he wants to cut it into two pieces.

The length of the longer pieces is then equal to 4x - 4.

The equation then becomes

\(x + 4x - 4 = 11\\ 5x = 11 + 4\\ 5x = 15\\ x = 3 ft\)

The shorter pieces will therefore be 3 feet long.

The longer pieces' length -

\(4x - 4\\ = 4 X 3 - 4\\ = 12 - 4\\ = 8 ft\)

The longer pieces will therefore be 8 feet long.

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Reason:

There are 500 integers in the set {1,2,3,...,499,500}. Only one of which is what we care about (the 441). So the chances of randomly getting "441" is 1/500.

In decimal form this is exactly 1/500 = 0.002 which converts to a 0.2% chance.

The probability of selecting a specific integer, such as 441, from a range of 1 to 500 (inclusive) using a random number generator is 1/500.

We have,

There are a total of 500 possible outcomes (integers from 1 to 500), and only one of those outcomes corresponds to selecting the number 441.

This means,

The probability of selecting 441 specifically is 1 out of the total number of possible outcomes.

= 1/500

Thus,

The probability of selecting a specific integer, such as 441, from a range of 1 to 500 (inclusive) using a random number generator is 1/500.

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Therefore the answer is 11 + x = x + 11.

11 + x

With the option

A) 11x

B) 11 + x

C) 11 minus x  ⇒  11 - x

D) Negative x + 11  ⇒  -x + 11

We have A and D aren't the same (A is multiplication, not addition, and D has a negative x instead of a positive x).

C is actually the same as D, if you switch the places of 11 and -x:

11 - x = -x = 11.

What is the commutative property?

x+a=a+x

Therefore

answer choice B is correct

because by the Commutative Property of Addition,

11 + x = x + 11.

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To check which point is lying on the given graph, we can just put the values in the equation in input x, and see if y comes out same as that specified y ordinate of the given point.

The points that lie on the graph of y = 1. 5 ⌈x⌉ are:

(–4. 5, –2. 5), (7. 9, 9. 5) and (1. 3, 3. 5)

The graph is of y = 1. 5 + ⌈x⌉

Putting x = -4.5, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil -4.5 \rceil\\y = 1.5 + -4 = -2.5\)

The specified point too has y ordinate as -2.5, thus, this point lies on the graph of given function.

Putting x = 0.8, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil 0.8 \rceil\\y = 1.5 + 1 = 2.5\)

But specified point's y ordinate is 0.5, thus, this point doesn't lie on the graph of given function.

Putting x = 7.9, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil 7.9 \rceil\\y = 1.5 + 8 = 9.5\)

The specified point too has y ordinate as 9.5, thus, this point lies on the graph of given function.

Putting x = 4.5, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil 4.5 \rceil\\y = 1.5 + 5 = 6.5\)

But specified point's y ordinate is 6, thus, this point doesn't lie on the graph of given function.

Putting x = 1.3, we get:

\(y = 1.5 + \lceil{x}\rceil\\y = 1.5 + \lceil 1.3 \rceil\\y = 1.5 + 2 = 3.5\)

The y ordinate of given point too is 3.5, thus, this point lies on the graph of given function.

Thus, the points (–4. 5, –2. 5), (7. 9, 9. 5), (1. 3, 3. 5) lie on the given graph.

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Repeated measures study is a technique used in statistics that involves taking multiple measures from the same individual or group. The major concern with a repeated-measures study is the possibility of carry-over effects.

What is a repeated-measures study?A repeated-measures study is a design used in statistics, where all the members of a given sample group are evaluated on two or more occasions. In other words, the repeated-measures study can be viewed as a test-retest design.In this type of study, participants undergo a specific treatment or intervention, and then their responses or measurements are evaluated at various intervals to examine any effects of the intervention. The repeated measures are then compared, and statistical tests are used to determine whether there are any significant differences in the results.

The possibility of carry-over effects: When conducting a repeated-measures study, the possibility of carry-over effects is a major concern. This occurs when the effects of the first treatment are still present when the second treatment is applied, resulting in an unintended impact on the second set of results. For example, if an experimental group is treated with a medication and then evaluated, and the same group is treated with a different medication and then evaluated, the results may be influenced by the residual effects of the first medication.

A carry-over effect can result in an inaccurate representation of the study's effect and can decrease the validity of the results. As a result, researchers must establish an appropriate washout period to reduce the impact of the carry-over effects before conducting a repeated-measures study.

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The numbers in order are 7, 8, 9, 11, 11, and 11.

Mode:

The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all

Here we have to arrange the number in order.

Range:

The difference between the lowest and highest values.

Pu the six numbers in order from small to large.

7,8,9,11,11,11

So the median of the number is = (9 + 11) /2

= 10

The mode of these numbers is = 11

As 11 is three times in the series.

The range of the numbers is = 11-7 =4

Therefore the order is 7, 8, 9, 11, 11, 11.

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We have that the angle is 330°

Now

When converted from active voice to passive voice, the sentences read as follows:

Active Voice refers to a sentence construction where the subject is performing the action described by the verb. It emphasizes the doer of the action.

On the other hand, Passive Voice refers to a sentence construction where the action is performed on the subject, rather than the subject performing the action. It emphasizes the action or the object affected by the action.

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Answer: $725.4

Step-by-step explanation:

The charity raffles can be arranged in ascending order of their expected values to the player based on the chances of winning and the potential prize value.

Arranging the charity raffles in ascending order of expected values allows players to determine which raffle offers the most favorable outcome for their investment. The expected value of a raffle ticket can be calculated by multiplying the probability of winning by the value of the prize.  

In this case, since all the raffles cost $2 per ticket, the expected value can be simplified by comparing the prizes alone. The raffle with the highest prize value would have the highest expected value, assuming the probabilities of winning are equal for all raffles. Therefore, the raffle with the lowest prize value would have the lowest expected value.

By arranging the raffles in ascending order of their expected values, players can make an informed decision on which raffles to participate in based on their desired outcome and potential return on investment.

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The taxable income of Marcel and Stephanie is less than their annual salary because they are allowed to make deductions from their income before calculating their taxable income.

These deductions include contributions to retirement plans, health insurance premiums, and other eligible expenses. The amount of deductions varies depending on factors such as the type of expense and the individual's tax filing status.

Thus, the taxable income is the amount of income that is subject to taxation, and it is generally lower than the individual's annual salary. In the case of Marcel and Stephanie, their taxable incomes are calculated by subtracting their deductions from their respective annual salaries.

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Complete Question:

Why are Marcel's and Stephanie's taxable incomes less than their annual salary? Marcel's annual salary is $30,000 and his income is $17,450. Stephanie's annual salary is $50,000 and her income is $37,600.