Please help me with this question

The correct pairs of the functions and their inverses are given by the image at the end of the answer.

To find the inverse function, we exchange x and y in the original function, then isolate y.

The first function that we want to find the inverse is:

f(x) = (2x - 1)/(x + 2).

Hence:

x = (2y - 1)/(y + 2)

(y + 2)x = 2y - 1

xy + 2x = 2y - 1

xy - 2y = -1 - 2x

y(x - 2) = -1 - 2x

y = (-1 - 2x)/(x - 2) (which is the inverse function).

The second function which we want to find the inverse is:

y = (x + 2)/(-2x + 1)

Then:

x = (y + 2)/(-2y + 1)

x(-2y + 1) = y + 2

-2yx + x = y + 2

-2yx - y = 2 - x

-y(2x + 1) = 2 - x

y = (x - 2)/(2x + 1)  (which is the inverse function).

The third function which we want to find the inverse is:

y = (x - 1)/(2x + 1)

Then:

x = (y - 1)/(2y + 1)

2yx + x = y - 1

2yx - y = -1 - x

y(2x - 1) = -1 - x

y = (-x - 1)/(2x - 1) (which is the inverse function).

The fourth function which we want to find the inverse is:

y = (2x + 1)/(2x - 1)

Then:

x = (2y + 1)(2y - 1)

2yx - x = 2y + 1

2yx - 2y = 1 + x

2y(x - 1) = (1 + x)

y = (x + 1)/(2(x - 1)) (which is the inverse function).

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Given: The velocity function of a moving particle as

To Determine: The time at which the acceleration equals to zero

Solution

Note that at time t=0, the particle is at origin, so

Determine the acceleration function

The acceleration of a particle is the rate of change of velocity or the derivative of the velocity function. Therefore,

When the acceleration is equal to zero, then we have

Let us plot the graph of the acceleration function

The time for given interval for which the acceleration is zero are

ence, thre first time the acceleration is zero is π/2 or 1.571

Answer: A.

Step-by-step explanation:

Answer:

the perimeter of a triangle is 84 cm and its area is 336 cm? if one of its side is 30 cm find the length of reamining two side

The distance between the points E = (-4,5) and L = (1,-3) in the coordinate plane is  [tex]\sqrt{89}[/tex]

The points are E = (-4,5) and L = (1,-3)

We know the distance between the two points d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Where d is the distance between two points

[tex](x_{1},y_{1} )[/tex] and [tex](x_{2},y_{2} )[/tex] are the coordinates of the points

Here the given points are E = (-4,5) and L = (1,-3)

To find the distance between the given points, we have to substitute the values in the equation

d = [tex]\sqrt{1-(-4))^{2}+(-3-5)^{2} }[/tex]

d = [tex]\sqrt{5^{2}+(-8)^{2} }[/tex]

d = [tex]\sqrt{25+64}[/tex]

d = [tex]\sqrt{89}[/tex]

Hence, the distance between the points E = (-4,5) and L = (1,-3) in the coordinate plane is  [tex]\sqrt{89}[/tex]

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We will employ the z score table in this problem.

The shaded part is our area of interest.We will be required to seek the value of the z score at 0.11.

when we ahave a probability of 0.11 or 11%

This corresponds with a z-score of -1.225.

We then substitute into our z-score equation:

where

Therefore, we have

In a case whereby Tammy has 4 more then five times the amount of dimes than nickels in her pocket and have total of $1.50 in her pocket the equation that could be used to determine the number of nickels(x) she has in her pocket is (0.05)(X+3) = 1.50.

The  number of nickels(x) that can be found her pocket be determined by  adding the the number of times the amount of dimes is than nickels, which can be expressed as :

let x will be number of dimes

let x+4 will be number of nickels

Therefore the number of nickels(x)  that is required will be (0.10)X + (0.05)(X+3) = 1.50

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The numerical value of 4.9 in the equation of the regression line

[y = (4.9x - 198)] determines "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.

As per the question statement, the equation of the regression line goes as [y = (4.9x - 198)], where "x" represents the height and "y" is the predicted walking speed.

We are required to determine, what the numerical value of 4.9 expresses in the regression line.

To solve this question, first we need to know about the formula to express the point-slope form of a line, which goes as, [(y - y₁) = m(x - x₁)], where (x₁, y₁) is a point through which the line passes, and "m" is the slope of the line, and compare this standard form to our question mentioned equation, to establish the numerical significance of 4.9.

Now, [y = (4.9x - 198)] can be written as [(y - 0) = 4.9(x - 40.41)], and comparing it to the standard point-slope form of a line, we get (m = 4.9), i.e., the slope of our concerned line of regression is 4.9.

Hence, 4.9 in 4.9x signifies "for every unit change in height, walking speed increases by 4.9 m/min" since, "x" represents the height and "y" is the predicted walking speed.

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Answer:

For every 1 inch increase in height, walking speed increases by 4.9 m/min.

Step-by-step explanation:

Just took it, hope this helps.

Answer:

Step-by-step explanation:

The value of 8 in 8.260 is 8 units.

Answer:

$0.14 per kg

Step-by-step explanation:

A 18-kg bag of cherries for $2.65

for 1 kg

[tex] \frac{2.65}{18} = 0.14 \\ [/tex]

so, the answer is $0.14

The specific thing about this graph is it forms a straight line, and it extends to point of origin. The time x is on the x-axis and the distance y is on the y-axis. The coordinates on the graph are the same as the pairs in the table. (2, [tex]6\frac{2}{3}[/tex]) means Sam's mother ran  [tex]6\frac{2}{3}[/tex] km in 2 hours.

Relationships between two variables are called as proportional when you see that their ratios are equal. One variable in a proportional connection is always a constant value multiplied by the other. "Constant of proportionality" is the name that is given to this constant.

The graph of a proportionate connection is a straight line that passes through the origin and rises steadily. The graph's unit rate can be represented by the point on this graph.

The graph depicting this proportional relationship formed in the table can be seen in the image attached.

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The complete question is:

"Sam's mother has entered a 10K race. Sam and his family want to show their support of their mother, but they need to

figure out where they should go along the race course. They also need to determine how long it will take her to run the

race so that they will know when to meet her at the finish line. Previously, his mother ran a SK race with a time of

hours. Assume Sam's mother ran the same rate as the previous race in order to complete the chart.

Create a table that shows how far Sam's mother has run after each half hour from the start of the race, and graph it on

the coordinate plane to the right.

a) What are some specific things you notice about this graph?

b) What is the connection between the table and the graph?

c) What does the ordered pair (2,6 [tex]\frac{2}{3}[/tex]) Represent in the context of this problem?"

The equation in the slope-intercept form will be y = (-2/5)x + 4.4.

So, point is (-20, 4) and line is 2x + 5y = 10, then the equation will be:

Now, solve for b as follows while inserting the values of x and y:

So, equation will be y = (-2/5)x + 4.4

Therefore, the equation in the slope-intercept form will be y = (-2/5)x + 4.4.

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To convert 2.21 x 10⁻⁶, place 6 zeros before 2.21 and move the decimal point to the left:

= 0.000021210

To convert 28,000 to scientific notation, write the non-zero digits, placing a decimal after the first non-zero digit: 2.8, then, multiply by 10 elevated to 4 (number of digits after 2):

28,000 = 2.8 x 10

nswer:

Compound interest formula:

A = P (1 + r/n )^nt

Where:

A = future vale

P= Principal investment = 9,000

r = interest rate in decimal form = 9/100 = 0.09

n = number of compounding periods = 4

t = years = 8

Replacing:

A = 9000 ( 1 + 0.09/4)^ (4*8)

A = 9000 (1.0225)^32

A= 18,342.93

The future value is $18,342.93

It is proved that ∠2 and ∠3 are supplementary angles.

So, according to the given image below:

(A) m∠1 = m∠3 ⇒ Alternate angles.

(B) m∠1 + m∠2 = 180°

Reason:

(C) m∠3 + m∠2 = 180° due to: Linear Pair Axiom.

(D) m∠2 and m∠3 are supplementary because: Since a linear pair of angles always results in a straight line, their sum is always 180°.

Therefore, it is proved that ∠2 and ∠3 are supplementary angles.

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Answer:

The money that Wilbert has is -$229 because of the debt.

$0 Represents his current, with no debts.

The sequence 64, 16, 4,. is geometric

Arithmetic Sequence can simply be defined as a sequence in which the difference between successive or consecutive terms is known as a constant.

The sequence is in the form a, a + d, a + 2d, a + 3d, a + 4d

Where;

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + (n – 1)d

Geometric sequence can simply be defined as a sequence where the ratio of every two consecutive or successive terms is a known constant.

Given the sequence;

64, 16, 4, ...

We can see that the common ratio between the terms is 4 and hence a geometric sequence

Hence, it is a geometric sequence

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SOLUTION:

Case: Pythagoras Triple

Method:

The Pythagorean triple:

(8, 15, 17) can be formed with factor integers

8----> 4

15---->3.

Final answer:

x=4, y= 3

Solution

For this case we have the following information given:

A= 1000

r= 0.06

n = 1

A= 2100

So we can set up the following formula:

We can solve for t on this way:

Solving for t we got:

Rounded to the nesrest tenth we got:

12.7 years

The speed of airplane in miles per hour (mph) is 380.2968 .

What is speed?

Speed is the time rate at which an object is moving along a path. The SI unit of speed is meter per second ( m/s ). Miles per hour ( mph ) is a British imperial and United States customary unit of speed expressing the number of miles travelled in one hour.

Given that

Speed of a certain airplane = 170 m/s or m[tex]s^{-1}[/tex]

We know that

In 1 meter = 0.0006214 miles

In 1 sec = [tex]\frac{1}{3600}[/tex] hour

but 1 [tex]sec^{-1}[/tex] = 3600 hour

Speed of this airplane in miles per hour = 170 × 0.0006214 ×  3600 mph

                                                                  = 0.105638 × 3600 mph

                                                                  = 380.2968 mph

Hence, the speed of airplane in miles per hour (mph) is 380.2968 .

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When two or more fractions are provided, the least common denominator is defined as the smallest common multiple of all the common multiples of the denominators.

Let's assume we have to add the fractions: (2/9)+(3/4)

We need to determine a common integer that is a multiple of both denominators, which are 9 and 4.

This common multiple will aid in the solution of the problem. As a result, the least frequent multiple for 9 and 4 is 36. As a result, the expression can be written as follows:

(2/9)+(3/4) = (2/9 × 4/4) + (3/4 × 9/9) = (8/36) + (27/36) = 35/36

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To check if an ordered pair is a solution to an equation, substitute the value for each coordinate into the equation.

Since the substitution has to be performed in alphabetical order, then the coordinates are given in the form:

Substitute r=-6 and s=-2 into the given equation to check if (-6,-2) is a solution:

Since -4 is NOT equal to 4, then the point (-6,-2) is not a solution to the equation r-s=4.

The result of the synthetic division of 2x^4 - 12x³ + 18x² - 13x + 20 by x - 4 is given by:

2x³ - 4x² + 2x - 5.

For this problem, the polynomial is given by:

2x^4 - 12x³ + 18x² - 13x + 20.

Hence the coefficients are:

2, -12, 18, -13, 20.

The divisor is:

x - 4.

Hence the left coefficient is:

4.

From the image at the end of the answer, the resulting coefficients are given as follows:

2, -4, 2, -5, with a remainder of 0.

Hence the result is:

2x³ - 4x² + 2x - 5.

For the procedure, we consider that the coefficient 2, the first of the polynomial, is moved down, then multiplied with 4 and added with the next coefficient(-12), and this procedure happens until the last coefficient.

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Based on the relationship between the number of phone calls that Amy received for the three evenings, the number of phone calls received on each evening was:

The first evening saw Amy receiving 7 more calls than the second evening while the third evening saw Amy receiving 3 times as many calls as the second evening.

Assuming the second evening is x, the relationship can be represented by the equation:

First evening calls + Second evening calls + Third evening calls = Total number of calls

(7 + x) + x + 3x = 112

Solving for the number of phone calls on the second evening gives:

(7 + x) + x + 3x = 112

7 +  x + x + 3x = 112

7 + 5x = 112

5x = 112 - 7

x = 105 /5

= 21 calls

Number of calls on first evening:

= 21 + 7

= 28 calls

Number of calls on third evening:

= 21 x 3

= 63 calls

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The solution to the equation, −112 = 8x, is: x = -14.

To find the value of the variable in an equation, means to solve the equation.

To solve any given equation, we are to apply all necessary properties of equality in other to isolate, as much as possible, the variable of the equation to one side of the equation. Th value of the variable is the solution to the equation.

Given the equation:

-112 = 8x

Divide both sides of the equation by 8:

-112/8 = 8x/8 [division property of equality]

-14 = x

x = -14

Check: Plug in x = -14 into the equation:

-112 = 8(-14)

-112 = -112 [true]

Thus, the solution to -112 = 8x is: x = -14.

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The derivative of the given function [g(r) = -2r + 2] is d/dr (rⁿ) = nrⁿ⁻¹.

So, g(r) = -2r + 2:

Differentiate with respect to r as follows:

Using Power rule:

Therefore, the derivative of the given function is d/dr (rⁿ) = nrⁿ⁻¹.

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Given the information on the problem, we can write the following system of equations:

then, we can write the following augmented matrix:

now, if we multiply by 5 the first row and then substract it from the second row, we get:

notice that from the second equation, we can find the value of y:

now that we have that y = 4, we can use this value on the first equation to find x:

now, we have that the babysitter worked 1 hour before 11pm and 4 hours after 11 pm,then, the Burkes came home at 3 am

The expression which can be used to represent the total owed for 3 months given the cost per month and a one-time equipment fee is 3(c) + 25

The correct answer option is option C

The total owed = Number of months(Price of the cable per month) + One time equipment fee

The total owed = 3(c) + 25

I'm conclusion, the expression for the total owed is represented by 3(c) + 25

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Answer: option c

bc 3<c> is the fee for 25                                                                                                                  

Answer:

3

because 3 divided by one is 3 so then you would have to divide with nine which we know is 3

Step-by-step explanation:

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