Write a piecewise function for the given graph.

The inverse function of one-to-one function f(x)= 7x - 2 is [tex]f^{-1}=\frac{x}{7}+\frac{2}{7}[/tex].

The graphs of f and [tex]f^{-1}[/tex] are symmetric with respect to the line defined by y = x.

Given that:-

f(x)= 7x - 2

Let f(x) = y

Hence,

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

Hence, we can write,

y = 7x - 2

y + 2 = 7x

x = y/7 + 2/7

[tex]f^{-1}(y) = y/7 + 2/7[/tex]

Replacing y by x, we get,

[tex]f^{-1}(x) = x/7 + 2/7[/tex]

Hence, the inverse function of f(x) is [tex]f^{-1}(x) = x/7 + 2/7[/tex].

The graph of inverse is always the mirror image of the function's graph in the line y = x. It is because they're basically 100% similar but in reverse just like you in a mirror.

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Answer:

37.2 rotations

Step-by-step explanation:

35 / (3.14 x .3) = 37.15499

Rounded = 37.2 rotations

The best estimate of the cost to ship 5 large packs is 94.75 and 3 small packages is 29.25.

What is the best estimate?

Best estimate means an income, expense, or circumstance prediction based on past amounts of income and expenses and known factual information concerning future circumstances which affect eligibility, expenses to be incurred; or income to be received in the benefit month.

Given that

Shipping company charges 18.95 for a large package.

Shipping company charges 9.75 for a small package.

For 5 large packs shipping company charges = 5 × 18.95 = 94.75

For 3 small packs shipping company charges = 3 × 9.75 = 29.25

Therefore,  the best estimate of the cost to ship 5 large packs is 94.75 and 3 small packages is 29.25.

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Answer: 57.14 km/hr

Step-by-step explanation:  if an hour is divided into quarters it will be in increments of 15 minutes, since  one hour is 60 minutes.  60 minutes divided by 5 is 15 minutes.  

So 1 hour and 38 minutes is rounded off to 1 hour and 45 minutes.

this is 1 hour + 3/4 hour = 1 3/4 hour.  This is same as 1.75 hour

3/4 is .75

speed divided by the time will give the average speed.

100km/1.75hours  = 57.14 km/per hour

Answer:

(a)  1 hour 45 min

(b)  57.1 km/h (nearest tenth)

Step-by-step explanation:

Given information:

[tex]\large\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]

[tex]\begin{aligned}\sf \dfrac{1}{4}\;hour &= \sf 1 \; hour \div 4 \\& = \sf 60 \;mins \div 4\\& = \sf 15 \; mins\end{aligned}[/tex]

Therefore, the nearest ¹/₄ hours either side of the given time is:

1 h 38 min 45 sec is 8 min 45 sec more than 1 hour 30 min.

1 h 38 min 45 sec is 6 min 15 sec less than 1 hour 45 min.

Therefore, the nearest ¹/₄ hour to the given time is:  

1 hour 45 min = 1.75 min (in decimal form)

Substitute the given distance and the rounded time (in decimal form) into the formula and solve for speed:

[tex]\begin{aligned} \implies \sf Speed & =\sf \dfrac{Distance}{Time}\\\\& = \sf \dfrac{100}{1.75}\\\\& = \sf 57.1\;km/h\;(nearest\;tenth)\end{aligned}[/tex]

Here, use this to help you: https://www.map.mathshell.org/download.php?fileid=1676

Solving the circumference function, we have that:

The corresponding interval for diameters of the washers is 1.85 ≤ d ≤ 1.97.

The circumference of a circle of diameter d is given by:

C = 3.14d.

As stated in the problem.

The interval of circumference values is:

5.8 ≤ C ≤ 6.2.

Hence the lowest possible value for the diameter is given by:

3.14d = 5.8

d = 5.8/3.14

d = 1.85.

The highest possible value for the diameter is given by:

3.14d = 6.2

d = 6.2/3.14

d = 1.97.

Then the compound inequality that completes the given sentence is:

1.85 ≤ d ≤ 1.97.

The interval for the circumference values is given by:

5.8 ≤ C ≤ 6.2.

We have to complete the following sentence with the compound inequality:

The corresponding interval for diameters of the washers is

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The linear equation 20x + 35(60-x) = 1500 can be solved to find the number of tickets.

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its related terms in various languages may have somewhat different definitions; for example, in French, an equation is described as including one or more elements, but in English, an equation is any well-formed formula that includes two expressions linked by an equals sign.

Let the number of advance tickets sold = x

And then, the number of same-day tickets sold = 60 - x

Then, the equation formed is

20x + 35(60-x) = 1500

=> 20x + 2100 - 35x = 1500

=> -15x = 1500 - 2100

=> x = -600/ -15 = 40

Hence, the number of advance tickets sold = 40

And the number of same-day tickets sold = 60 - 40 = 20

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With regards to the rigid transformations, Yes, it is true to state that ∠ABD is congruent to ∠EFM. This can be justified by translating ∠ABD by superimposing it on ∠EFM.

It is also true to state that ∠ ABD is congruent to ∠GFHG. To justify this, rotate ∠ABD by 180°

A rigid transformation in mathematics is a geometric transformation of a Euclidean space that retains the Euclidean distance between each pair of points. Rotations, translations, reflections, and any combination of these are examples of rigid transformations.

Hence, the above statements are true. Note that rigid transformations do not modify the distance angles, size or shape.

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Line (0, 2), (-5, -3) ---> y = x + 2

Line (0, 5), (-5, -5) ---> y = 2x + 5

Point of intersection ---> we need to equate both equations:

If x = -3 ---> y = -3 + 2 ---> y = -1

The point of intersection in this case is (-3, -1) (the last one, from left to right).

Line (-2, 1), (-3, -1) ---> y = 2x + 5

Line (0, 2), (2, 0) ---> y = -x + 2

Equating both equations to find the intersection point:

If x = -1, then y = -(-1) + 2 ---> y = 1 + 2 ---> y = 3

The point of intersection is (-1, 3) (the second one, from left to right).

Line (4, -2), (1, 1) ---> y = -x +2

Line (4, 2), (0, -2) ---> y = x - 2

Then, we have ---> intersection point:

Using the second equation to find y ---> y = 2 -2 ---> y = 0

The point of intersection is (2, 0) (the first point, from left to right).

Line (2, -2) (0, 2) ---> y = -2x + 2

Line (2, 1), (3, 2) ---> y = x - 1

Then, we have:

Using the second equation to find y ---> y = 1 - 1 ---> y = 0

The point of intesection is (1, 0) ( the third point, from left to right).

Answer:

Step-by-step explanation:

To find the value of x and y, isolate it on one side of the equation.

-3x+2y=4, 4x=13y=5

-3x+2y=4

[tex]\rightarrow \sf{x=-\dfrac{4-2y}{3}}[/tex]

Substitute.

[tex]\sf{4\left(-\dfrac{4-2y}{3}\right)-13y=5}[/tex]

Solve.

Use the distributive property.

A(B+C)=AB+AC

A(B-C)=AB-AC

[tex]\sf{=\dfrac{-16-31y}{3}=5}[/tex]

Isolate the term of y.

Multiply by 3 from both sides.

[tex]\sf{\dfrac{3\left(-16-31y\right)}{3}=5*3}[/tex]

Solve.

Multiply the numbers from left to right.

5*3=15

-16-31y=15

Add by 16 from both sides.

-16-31y+16=15+16

Solve.

15+16=31

-31y=31

Divide by -31 from both sides.

-31y/-31=31/-31

Solve.

y=-1

Substitute of y=-1.

[tex]\sf{x=-\dfrac{4-2\left(-1\right)}{3}}[/tex]

Solve.

Use the order of operations.

PEMDAS stands for:

4-2(-1)

Do parentheses by multiply first.

2(-1)=-2

4-(-2)

4+2=6

-6/3

Divide.

-6/3=-2

x=-2

[tex]\Rightarrow \boxed{\sf{x=-2, \quad y=-1}}[/tex]

Therefore, the correct answer is x=-2, and y=-1.

I hope this helps, let me know if you have any questions.

The distance between the two points is 5.

The formula to find the distance between two points (x1, y1) and (x2, y2)

distance = [tex]\sqrt{(x2-x1)^{2} + (\\ y2-y1)^{2} }[/tex]

Substituting points A(2,9) and B(-2,6), we get

distance = [tex]\sqrt{(-2-2)^{2} + ( 6-9)^{2} }[/tex]

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

              = [tex]\sqrt{16 + 9}[/tex]

              =[tex]\sqrt{25}[/tex]

             = 5

Therefore the distance between the two points is 5.

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Answer:

Step-by-step explanation:

(i) Find the value of y when x = - 2

(ii) See the graph attached

(iii) The axis of symmetry is the vertical line passing through the vertex, which is x + 1 = 0 or x = - 1.

This is also reflected on the attached graph.

(iv) From the graph it is visible that in the given interval the function is decreasing, so the value at x = - 4 is the maximum and the value at x = - 2 is minimum:

These two points too are given on the same graph.

(v) There ate two x-intercepts, the one on the right is the larger one.

It is (0.732, 0), marked on the graph.

(vi) This function is the standard form of the given:

With the positive leading coefficient of 1, it has a minimum value but no maximum. The minimum of this function is at its vertex, which is (- 1, 3) as per graph.

(vii) The function y = x² + 2x is the translation of the given function up by two units.

So its minimum value is 2 units greater:

Answer:

-8, -10i, 10i

Step-by-step explanation:

x^3 + 8x^2 + 11x = -800

I just plugged it into my calculator

m∠2 = m∠7

and

m∠4 = m∠8

Both are correct answers and should be ticked

Here, we want to select which of the statements must be correct based on the diagram given

a) m∠2 = m∠7

This is correct

m∠2 = m∠3 as they are vertically opposite angles

However, m∠3 = m∠7 as they are vertically opposite angles

b) m∠7 = m∠10

We cannot compare the relationship between b and c as the pair are not parallel lines

c) m∠8 = m∠9

This is not correct also as the pair of lines are not parallel

d) m∠4 = m∠8

These two are corresponding angles, so they are congruent and thus equal in value

Given the following question:

Part A:

Your answer is option B, you can find this by checking the values. We are given 107, 128, 163, 212, 275 if you check the values on the graph, you can see that they are exact. So, your answer is option B.

The most appropriate choice for average will be given by-

Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.

What is  average?

In a data set, there are many numbers. Average is the single number which acts as a representative of all the numbers in the data set.

Average is calculated by sum of all observations divided by total number of observations.

Here,

Let the score of Shureka Washburn in her last test be x

Score of Shurek Washburn on first test = 86

Score of Shurek Washburn on second test = 84

Score of Shurek Washburn on third test = 83

Score of Shurek Washburn on fourth test = 49

Total sum of all her scores = 86 +  84 + 83 + 49 + x

                                           =  302 + x

Average = [tex]\frac{302 + x }{5}[/tex]

By the problem,

                          [tex]\frac{302 + x}{5} \geq 76[/tex]

                          [tex]302 + x \geq 76[/tex] [tex]\times 5[/tex]

                          [tex]302 + x \geq 380[/tex]

                          [tex]x \geq 380 - 302[/tex]

                          [tex]x \geq 78[/tex]

Shureka Washburn must get 78 or higher in her final exam to make her average 76 or higher.

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E = 38.33 the margin of error at a 98% confidence level by standard deviation mean.

What does standard deviation mean ?

Given that,

bar x = 36

s = 9

n = 12

Degrees of freedom = df = n - 1 =12 - 1 = 11

At 98% confidence level the t is ,

∝ = 1 - 98% = 1 - 0.98  ⇒ 0.02

∝/2 = 0.02/2 = 0.01

t∝/2 df = t0.01 ,11 = 1.231

Margin of error = E = t∝/2, df * ( s/n/sqrtn)

                             E = 1.231 * ( 9 /0.01/sqrt12)

                              E = 38.33

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The exponent is 81[tex]m^{} 4[/tex] [tex]n^{20}[/tex]

Here we have to determine the sign for exponential or radical expression

(-3m[tex]n^{5}[/tex])^4

Simplify using the exponent rule with the same exponent [tex](ab)^{n}[/tex] = [tex]a^{n}[/tex] . [tex]b^{n}[/tex]

Similarly

(-3m[tex]n^{5}[/tex])^4

= [tex](-3)^{4}[/tex] . [tex]m^{4}[/tex]. [tex](n^{5} )^{4}[/tex]

Now using the exponent  power rule [tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex]. We get

= 81 . [tex]m^{4}[/tex].[tex]n^{20}[/tex]

Therefore the exponent as a product of power is 81[tex]m^{4} n^{20}[/tex].

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The level of ibuprofen in the patients bloodstream increased from 0 hours to 2 hours.

What is ibuprofen?

Ibuprofen is an example of an NSAID that is used to relieve pain, fever, and inflammation. This includes menstruation pain, migraines, and rheumatoid arthritis. Additionally, it can be applied to seal off a premature infant's patent ductus arteriosus. It can be given orally or intravenously. After an hour, it usually begins to function.

In the graph that is attached, the y-axis represents the concentration of ibuprofen in the patient's bloodstream, and the x-axis represents the number of hours since ibuprofen was last consumed.

As we can see from the graph, the curve increases from a time of 0 hours, which corresponds to 0 mg of ibuprofen, to a time of 2 hours, which corresponds to 400 mg of ibuprofen.

The curve starts to descend after that point. We will settle for the first assertion because increase is what we are interested in.

Thus, we may conclude that the increase in ibuprofen level occurred between 0 and 2 hours.

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From the given parameters to determine the cost of the airline ticket, we can interpret that that the maximum amount that each ticket costs is $295 while the maximum amount of bags is 5 bags.

We are given the linear equation that represents the cost of an airline ticket after adding a number of checked bags as;

y = 145 + 30x

where;

y is the cost (in dollars) of an airline ticket after adding a number of checked bags

x is the number of checked bags

Thus, if there is a maximum of 5 bags that can be checked, then we have;

y = 145 + 30(5)

y = $295

This means that the maximum amount that each ticket costs is $295 while the maximum amount of bags is 5 bags.

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y ≤ 16 - x (option A)

let the total number of pieces Luke ate at a time = y

Let the total number of pieces James ate at a time = x

They have never eaten more than 16 pices of pizza

This is written as:

maximum 16 : ≤ 16

number of pieces Luke ate at a time + total number of pieces James ate at a time ≤ 16

y + x ≤ 16

rewritting to make y subject of formula:

y ≤ 16 - x (option A)

Solution

- The formula for finding the area of a triangle is given below:

- We have been given:

- Therefore, we can find the area as follows:

Final Answer

The area is 5.4cm²

Slope

[tex]\frac{-10-(-2)}{1-(-3)}=-2[/tex]

Equation

[tex]y+10=-2(x-1)[/tex]

x-intercept

The x-intercept is when y=0.

[tex]10=-2(x-1)\\\\-5=x-1\\\\x=-4[/tex]

So, the x-intercept is (-4, 0).

The most appropriate choice for linear inequation will be given by-

The range of ages to which the squirrels live is 5 to 8 years

What is Linear Inequation?

Linear Inequation involves comparision between two values with the help of <,   >,   [tex]\leq , \geq[/tex]

   .

Here,

Let the range of ages (in years) to which the squirrels live be [tex]x[/tex] years

The lifespans of the squirrels may vary by as much as 1 year.

By the problem,

                        [tex]|x - 6.5|\leq 1.5\\-1.5 \leq x - 6.5 \leq 1.5\\x - 6.5\geq -1.5[/tex]and    [tex]x-6.5\leq 1.5[/tex]

                        [tex]x \geq 6.5-1.5[/tex] and [tex]x \leq 6.5 + 1.5\\[/tex]

                        [tex]x \geq 5[/tex] and [tex]x \leq 8[/tex]

The range of ages to which the squirrels live is 5 to 8 years

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Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

-xy^2 =

Let x=2 and y = -3

-(2) (-3)^2

-2 (9)

-18

Answer:

18.

Step-by-step explanation:

(2)(-3)^2

Parentheses first. There's nothing to do so, the exponent is next. -3^2 is 9. 9 * 2 = 18.

Hope this helps! :)

THE MIDPOINT FORMULAR IS GIVEN BY

[tex]( \frac{x1 + x2}{2} . \frac{y1 + y2}{2} ) \\ \\ = (\frac{ - 2 + ( - 4)}{2} . \frac{ - 3 + 10}{2} ) \\ = ( \frac{ - 6}{2} . \frac{7}{2} ) \\ = ( - 3. \frac{7}{2} )[/tex]

ATTACHED IS THE SOLUTION

The owner loses the figure and the $70 that gives back, so the total amount he loses is $90.

We know that the owner initially has a figure whose price is $20, and he sells it for $30.

Then, he sells it for a $100 bill, so he gives $70 back.

The problem is that the $100 bill was fake, so at this point the total amount that he loses is:

The value of the action figure (which is $20) plus the $70 that he gives back.

Adding these two we get:

$20 + $70 = $90

The owner loses $90 in total.



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Answer: x= 13/2 or 6 1/2

Step-by-step explanation:

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

Simplify the equation,

2x+8-6x+15 = -3

-4x+23= -3

-4x = -26

Cancel the minus sign, now we get

2x = 13

i.e., x= 13/2

Answer: Less than 470 minutes

Step-by-step explanation:

This equation represents this problem.

0.04x + 44.4 = 0.06x + 35

Solve,

0.02x = 9.4

1 / .02 = 50

x = 470

At 470 minutes they're equal and we are looking for when Plan A is cheaper then Plan B, so x < 470

Use m instead of x in this problem, sorry didn't read the last line.