Complete the steps in order to write the inverse of f(x) = x + 5 1. = x + 5 2. = y + 5 3. = y 4. = x – 5

Answers

Answer 1

Hi there!

f(x) = x + 5

1. y = x + 5
Switch places from x and y.

2. x = y + 5
Subtract 5.

3. x - 5 = y
Switch sides.

4. y = x – 5
Now we've found our answer.

~ Hope this helps you!

Answer 2

The inverse of the given function y =x+5 is y =x-5.

The given function is:

y =x+5

What is an invertible function?

A function is invertible only if each input has a unique output and each element of the codomain should be mapped.

Step1: check function is invertible i.e. bijective i.e. one-one and onto or not

f(x₁)=x₁+5

f(x₂) = x₂+5

f(x₁) = f(x₂)

x₁+5 =x₁+5

x₁=x₂

So, the function is one-one or injective.

For onto range and codomain should be same.

Step 2: interchange x and y

x=y+5

Step3: bring 5 to the left side of the equation.

x-5 = y

Step4: write in y=f(x) form

y = x-5

Therefore, the inverse of the given function y =x+5 is y =x-5.

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Related Questions

HELPPPPPPPPPPPPP and explain

Answers

Remark
There are a number of ways you could do this. The most straight forward might be to simply multiply the second equation to get the answer.

Step One
Multiply the second equation by 2
2(2x^2 + 1/y^2 = 12) Remove the brackets.
4/x^2 + 2/y^2 = 12 * 2
4/x^2 + 2/y^2 = 24

Step Two
Add the new equation and the first original equation
1/x^2 - 2/y^2 = 1
4/x^2 + 2/y^2 = 24

5 / x^2 = 1 + 24
5/x ^2 = 25 Divide both sides by 5
1/x^2 = 5 Reciprocate the x^2 and the 5 (That means turn them upside down.

x^2 = 1/5
Take the square root of both sides.
x = +/- 1/sqrt(5) Rationalize the denominator.
[tex]{x = } \frac{1}{ \sqrt{5} } * \frac{ \sqrt{5} }{ \sqrt{5} }\\ \\{x = } \frac{ \sqrt{5} }{5} [/tex]

Step 3
Place this answer in for x^2 to get y^2. and then y

1/(1/5) - 2/y^2 = 1

Interlude
You can use your calculator to see what 1/(1/5) is. Change the 1/5 to 0.2
1/0.2 = 5 Just put it in as
1
÷
0.2
=
You should get 5

Continued
5 - 2 / y^2 = 1 Subtract 5 from both sides.
- 2/y^2 = 1 - 5
-2 / y^2 = - 4 Divide both sides by - 2
1 / y^2 = -4/-2
1 / y^2 = 2 Now reciprocate both sides.
y^2 = 1/2 Take the square root.
y = +/- 1/sqrt(2) And rationalize the denominator
y = +/- sqrt(2) / 2 Done the same way as for the x.

There's only 1 there. I'll let you find it.

Please help!!! Mark is learning to snowboard. The club charges $10 per hour for snowboard lessons and $40 for the lift ticket and a snowboard rental. Which value represents the rate of change for this scenario?

Answers

h represents the number of hours:
10h + 40
(40 represents, well $40)

the answer is 40 + 10h

What is the sum os the interior angles of the polygon?

Answers

to find the suum the formula is (n - 2) x 180 degrees

The mass of a grain of sand is about 10^-3 gram. About how many grains of sand are in a 10kg bag of sand?

Answers

10000000

Divide the mass of the bag by the mass of sand. First you need to convert kg to g

The mass of a grain of sand is about 10 to the -3 power gram.
About how many grains of sand are in the bag of sand

Answer

10 kg* (1000 g/ 1 kg)* (1 grain of sand/ 10^(-3) g)= 10^7 grains of sand.
(Note that the units cancel out so you get the answer)
The final answer is 10^7 grains of sand.
Hope this helps~

A distribution of numbers has the following five-number summary:
20.2, 22.4, 30.0, 37.6, 39.8
True or False? These numbers can be used to calculate the standard deviation of the distribution.
Please Answer quickly! I need this done ASAP! Please.

Answers

The answer is False; I put True and it was wrong

The correct answer is:

False.

Explanation:

Using the five number summary, we can estimate the standard deviation.

The quartiles are about 0.67 standard deviations from the mean; this could be used to estimate the standard deviation.

However, we cannot accurately calculate the standard deviation using only the fie number summary.

Multiply the binomial and find the coefficients
(X+y)^1=__×+__y

(×+y)^2=__x^2+__xy+__y^2

(X+y)^3=__×^3+__×^2y+__y^3

(×+y)^4=__×^4+__x^3y+__x^2y^2+__xy^3+__y4

Answers

We can use the pascal triangle to solve this problem.

For this case, rewriting each binomial we have:
(x + y) ^ 1 = 1x + 1y

(x + y) ^ 2 = 1x ^ 2 + 2xy + 1y ^ 2

(x + y) ^ 3 = 1x ^ 3 + 3x ^ 2y + 3xy ^ 2 + 1y ^ 3

(x + y) ^ 4 = 1x ^ 4 + 4x ^ 3y + 6x ^ 2y ^ 2 + 4xy ^ 3 + 1y4

92.4 is 150% of what number?

Answers

1. We assume, that the number 92.4 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 92.4 is 100%, so we can write it down as 92.4=100%.
4. We know, that x is 150% of the output value, so we can write it down as x=150%.
5. Now we have two simple equations:
1) 92.4=100%
2) x=150%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
92.4/x=100%/150%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 150% of 92.4

92.4/x=100/150
(92.4/x)*x=(100/150)*x - we multiply both sides of the equation by x
92.4=0.666666666667*x - we divide both sides of the equation by (0.666666666667) to get x
92.4/0.666666666667=x
138.6=x
x=138.6

now we have:
150% of 92.4=138.6

Answer:

Number is 61.6

Step-by-step explanation:

Given : 92.4 is 150%.

To find : what number.

Solution : We have given 92.4 is 150%.

Let the number = x

According to question :

150% of x = 92.4

[tex]\frac{150}{100} *x[/tex] = 92.4

On multiplying both sides by 100

150 x = 92.4 * 100.

150 x = 9240

On dividing both sides by 150 .

x = [tex]\frac{9240}{150}[/tex].

x = 61. 6

Therefore, Number is 61.6

A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for soccer or volleyball. Out of the total 80 people who liked soccer, 30 also liked volleyball. There were 45 people who liked volleyball.

Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)

Like soccer
Do not like soccer
Total
Like volleyball
A
D
G
Do not like volleyball
B
E
H
Total
C
F
I

Part B: What percentage of the survey respondents did not like either soccer or volleyball? (3 points)

Part C: Do the survey results reveal a greater dislike for soccer or volleyball? Justify your answer. (2 points)

Answers

Asked and answered elsewhere.
https://brainly.com/question/9914822

_____
A picture of your table would be most helpful.

A wood board is one of a 6 different parts in a shelf kit. the width, depth, and height dimensions of the board are 42 inches x 8 inches x .75 inches, respectively. the board is made from southern yellow pine, which has an air dry weight density of .021 lbs/in.3. (watch the units of measure)

Answers

the complete question is
A wood board is one of a 6 different parts in a shelf kit. the width, depth, and height dimensions of the board are 42 inches x 8 inches x .75 inches, respectively. the board is made from southern yellow pine, which has an air dry weight density of .021 lbs/in.3. (watch the units of measure)
1) What is the volume of the wood board? Precision = 0.00
2) What is the surface area of the wood board? Precision = 0.00
3)What is the weight of the wood board? Precision = 0.00
4) If one gallon of paint will cover 35,000 square inches, how many gallons would be needed to give two coats of paint to 15,000 boards? Round your answer to the nearest gallon

Part 1) What is the volume of the wood board? Precision = 0.00
we know that
volume=L*W*H-----> 42*8*0.75----> 252 in³

the answer Part 1) is 252 in³

Part 2) What is the surface area of the wood board? Precision = 0.00

surface area=2*area of the base+perimeter of the base*height

area of the base=42*8----> 336 in²
perimeter of the base=2*[42+8]----> 100 in
height=0.75 in

surface area=2*336+100*0.75----> 672+75----> 747 in²

the answer Part 2) is 747 in²

Part 3)What is the weight of the wood board? Precision = 0.00

we know that
density=mass/volume-----> mass=density*volume
density=0.021 lbs/in³
volume=252 in³
mass=0.021*252----> 5.292 lbs

the answer Part 3) is 5.29 lbs

Part 4) If one gallon of paint will cover 35,000 square inches, how many gallons would be needed to give two coats of paint to 15,000 boards? Round your answer to the nearest gallon

if 1 gallons cover------------> 35000 in²
x -----------------------> 747 in² (one board)
x=747/35000-----> x=0.021 gallons per 1 board
so
15000*0.021------> 320.14 gallons
but remember ------> two coats of paint
so
320.14*2-----> 640.28 gallons------> 640 gallons

the answer Part 4) is 640 gallons

Which number supports the given conjecture?

If a number is divisible by both 3 and 4, then the number is also divisible by 6.

A.
18

B.
42

C.
48

D.
64

Answers

The answer is C.

48/3 = 16
48/4 = 12
48/6 = 8

In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 40 cm tall and 90 cm wide. Find an equation of the parabola with its vertex at the origin.

Answers

Equation of a parabola that opens up with vertex at it's origin: x^2=4py
point on the parabola:(45,40)
equation:
45^2=4p(40)
4p=45^2/40=40.625
thus
x^2=(50.625)y

Answer: x^2=(50.625)y

The average age of the children at a campout is shown in the box plot below. Which statement is true about the box plot? The youngest age is 7. It is skewed right. More of the children were close to 12 years old than 6 years old. Half of the children were between 6 and 9 years old.

Answers

The answer is c. More of the children were close to 12 years old than 6 years old.

The statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.

What is a Box Plot?

A box plot shows how a data is distributed, as it displays the five-number summary.

here, we have,

The five-number summary of the box plot representing the average age of children is:

Min = 6 (youngest age)

Lower quartile (Q1) = 9 (25% of the children are below 9)

Median = 10

Upper quartile = 11 (50%, which is half of the children are between 9 years and 11 years old)

Max = 12 (oldest)

Therefore, the statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.

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Please help with geometry

Answers

[tex]\pi . {12}^{2} . \dfrac{300}{360} + {12}^{2} \dfrac{ \sqrt{3} }{4} \\ {12}^{2} ( \dfrac{5.\pi}{6} + \dfrac{ \sqrt{3} }{4} ) \\( 120\pi + 36 \sqrt{3} ) {cm}^{2} [/tex]

It's a equilateral triangle. The area of the white region is the area of a sector minus the area of a triangle.
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex]
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle: [tex]A_O=\pi r^2[/tex]
The area of the sector:
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
[tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]

The area of the segment: [tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]
The area of the shaded region:
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]

Ellen needs to buy 180 inches of ribbon to wrap a present. The store sells ribbon only in whole yards. How many yards does Ellen need to buy to have enough ribbion

Answers

If very 36 inches is a yard and you divide 180 inches by 36 you would be left with 5 so see would need 5 yards of ribbon

Calculate the length of AC to one decimal?

Answers

We first need to divide the trapezium into a triangle(lets call it A) and a rectangle(lets call it B). We do this by marking a line colored red in the diagram given below from point B to E.
As one side of the rectangle is given length of 4cm, the parallel other must also be equal to 4cm. Hence, Length of A to E is equal to 11cm-4cm=7cm.
Now, we use this length of 7 cm as this is opposite to our desired angle(a colored green) and by making 16cm our hypotenuse we find angle a to be 25.9°. [tex]sin x^{-1}(7/16)=25.9^{o} [/tex]
Next we find angle b by adding angle a with 90. hence getting 115.9°.
Finally we consider our triangle ABC to find the length of AC. We know one angle and length of two sides and can easily use cosine rule to find the remaining length AC. The equation and working is shown in diagram.
Answer= 18.1

There is a ratio of 5 girls to 3 boys in the class in the chorus.there are 24 boys in the chorus how many girls are in the chorus

Answers

40 because 40 girls to 24 boy is equivalent to 5 girls to 3 boys if you divide them by 8

An earthquake strikes and an isolated area is without food or water. three crews arrive. one can dispense needed supplies in 4545 hours, a second in 9090 hours, and a third in 6060 hours. how long will it take all three crews working together to dispense food and water?

Answers

It'll take 10 hours for the crew to finish the work.

1 person takes 20h, the second would hake 30h, third 60h.
1/20+1/30+1/60=1/10

For an angle Θ with the point (12, −5) on its terminating side, what is the value of cosine?

−5
12
negative 5 over 13
12 over 13

Answers

Given that the point (12,-5) which takes the form (x,y), This implies that:
opposite=-5
adjacent=12
thus using using Pythagorean theorem, the hypotenuse will be:
c^2=a^2+b^2
plugging the values we obtain:
c^2=(12)^2+(-5)^2
c^2=144+15
c^2=169
thus
c=13
but
cos θ=adjacent/ hypotenuse
therefore:
cos θ=12/13

Answer is option . D

the perimeter of this figure is 42.5 cm. Find the area of this figure.

Answers

the picture in the attached figure

let
AB=x

we know that
perimeter of the figure=10*x
perimeter=42.5 cm
so
42.5=10*x
x=42.5/10
x=4.25 cm

area of the figure=area of rectangle +area of square
area of rectangle=4.25*(4.25*3)----> 54.1875 cm²
area of square=4.25²----> 18.0625 cm²

area of the figure=54.1875+18.0625-----> 72.25 cm²

the answer is
72.25 cm²

Answer:

72.25

Step-by-step explanation:

I just took the test and got it correct

A boy flies a kite with a 100-foot-long string. The angle of elevation of the string is 48°. Find the vertical distance between the kite and the point at which the boy is holding the string.

Answers

The vertical distance will be given by:
sinθ=opposite/hypotenuse
where:
θ=48°
opposite=h
hypotenuse=100 ft
thus
sin 48=h/100
hence
h=100 sin48
h=74.315 ft

Answer: 74.315 ft

Using the sine function of trigonometry, the vertical distance between the kite and the point where the boy is holding the string is calculated to be approximately 74.31 feet when the string's angle of elevation is 48 degrees.

To find the vertical distance between the kite and the point at which the boy is holding the string, we can use trigonometric functions, specifically the sine function which is defined as the ratio of the opposite side to the hypotenuse in a right triangle. Since we know the length of the string, which acts as the hypotenuse of the triangle, and the angle of elevation, we can set up our equation as follows:s

sin(48°) = opposite/hypotenuse

sin(48°) = vertical distance/100 feet

W then multiply both sides by the hypotenuse (100 feet) to solve for the vertical distance:

vertical distance = 100 feet \sin(48°)

To get the numerical value, we use a calculator to find:

vertical distance ≈ 100 feet * 0.7431

vertical distance ≈ 74.31 feet

Therefore, the vertical distance between the kite and the point where the boy is holding the string is approximately 74.31 feet.

Can somone help me with this 1 problem? QRST is a parallelogram. Determine the measure of ∠Q
Q (4x+10) bottom left
R (9x+1) top left
S (5x-3) top right
T bottom left

Answers

(In the picture, QRST looks like a rhombus, so I will assume that it is a rhombus.)

In a rhombus, opposite angles are congruent based on the alternate interior angle theorem. In other words, R and T along with Q and S are both alternate interior angle pairs.
(You can actually test this by printing out a rhombus, cutting out the angles, and matching up the opposite ones.)

We know that Q is equal to 4x + 10, but we need to solve for x. Since Q and S are congruent, we can set them equal to each other:
1) 4x + 10 = 5x - 3
2) 4x + 13 = 5x
3) 5x = 4x + 13
4) x = 13
Now let's plug 13 in for Q:
5) 4(13) + 10 = 52+10 = 62

I got m<Q = 62 degrees. Hope this helps!

In the parallelogram QRST then measure of ∠Q is 62 degrees.

What is Quadrilateral?

A quadrilateral is a four-sided polygon, having four edges and four corners.

Given that QRST is a parallelogram.

We have to find the measure of ∠Q.

Both pairs of opposite sides are parallel, quadrilateral QRST is a parallelogram.

∠Q= ∠S

4x+10=5x-3

We have to find the value of to find ∠Q measure.

10+3=5x-4x

13=x

Now let us plug in the value of x in ∠Q measure.

∠Q = 4x+10

Now plug in x value in ∠Q

∠Q = 4(13)+10

=52+10

=62 degrees

Hence, in the parallelogram QRST then measure of ∠Q is 62 degrees.

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A teacher asked her students to divide a large number by 50.
• Aslan divided the number by 50.
• Lucy divided the number by 5 and then divided the answer she got by 10.
• Jack divided the number by 10 and then divided the answer he got by 40.
Who among these got the correct answer assuming they did NOT make mistakes in division?

Answers

Answer:

Step-by-step explanation:

Final answer:

Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.

Explanation:

To find out who got the correct answer, we need to evaluate the division calculations of each student. Let's assume the large number is 'x'.

Aslan divided the number by 50, so his answer is x/50.

Lucy divided the number by 5 and then divided the answer by 10, so her answer is (x/5)/10 = x/50.

Jack divided the number by 10 and then divided the answer by 40, so his answer is (x/10)/40 = x/400.

Therefore, both Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.

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PLEASE HELP!!!!!!!!!!!!!!!!! What is the simplified form of the expression k^3(k^7/5)^-5

A. k^4
B. 1/k^1/4
C. k^1/4
D. 1/k^4

Answers

(k^3)(k^(7/5))^-5
= (k^3)(k^(7/5*-5))
= (k^3)(k^-7)
= k^(-7+3)
= k^-4
= 1/k^4
Which is choice D.

40 points!!!!!!!!!!!!!! *If one of the legs of a right triangle is 4 in and the hypotenuse is 8 in, find the length of the other leg (use a calculator if necessary). Can you guess the measures of the acute angles?

Answers

Using pythagoras length of the other leg = sqrt ( 8^2 - 4^2) = sqrt 48 = 4 sqrt3

the ratio of the sides of the triangle = 8 : 4 :4 sqrt3 = 2:1:sqrt3 so this is a
30-60-90 degree triangle

What is the equivalent decimal? Drag the answer into the box to match the fraction. 5/45

Answers

the decimal for is .1 the one is repeating
what you do is divide 5 into 45 to make it a decimal

What's the probability a number is odd given that it's an integer between 0 and 11?

Answers

A odd number lie between 0 and 11(0 and 11 not included), it means that total of ten numbers, starting from {1,2,3........,10} form our sample space.

sample space=s={1,2,3....,10}=total 10 numbers
So,
m=total no. of odd numbers{1,3,5,7,9} in our sample space=5 numbers

probability that number is odd=p=m/s
p=5/10=0.5

Find the number if the square root of another number that is 6 greater than this number is equal to the number itself.

Answers

Answer:

The number is 3 and the another number is 9

Step-by-step explanation:

Let

x-------> the number

y-----> another number

we know that

[tex]y=x+6[/tex] ----> equation A

[tex]\sqrt{y}=x[/tex] ----> equation B

Substitute equation A in equation B

[tex]\sqrt{x+6}=x[/tex]

squared both sides

[tex]x+6=x^{2} \\x^{2}-x-6=0[/tex]

Using a graphing tool

solve the quadratic equation

see the attached figure

The solution is x=3

Find the value of y

[tex]y=x+6[/tex] -------> [tex]y=3+6=9[/tex]

The members of a chorus agree to buy at least 250 tickets for and outside concert. They buy 20 fewer ow tickets that balcony tickets. What is the lowest number of balcony tickets bought

Answers

135 tickets on the balcony and 115 ow tickets.

This is because you can set balcony equal to x and ow equal to x - 20. Then you can add them together and set equal to 250. Simplify and solve for x.

Jamal is 167 cm tall. Which expression finds Jamal’s height in dekameters? Use the metric table to help answer the question.

Answers

we know that
1 cm is equal to -----------> 0.001 dekameters
so
167 cm------------------> X
x=167*0.001------> x=0.167 dekameters

Expression to finds Jamal’s height in dekameters
[Jamal’s height in cm]*0.001 or [Jamal’s height in cm]/1000

Answer:

It is D

Step-by-step explanation:

If the surface area of a sphere is 256π cm2, what is the radius?
4 cm
8 cm
12 cm
16 cm

Answers

8.

If you rearrange the equation for surface area to solve for r then you can plug the 256pi into the equation and get 8.

The formula for surface area of the sphere is -

Surface area of sphere = 4πr²

Now, the surface area of sphere is given to us as = 256π cm²

Thus,

4πr² = 256π cm²

While equating the equations, we will get

4r² = 256 cm²

r² = 64 cm²

64 is the square of 8, thus the radius of sphere will be = 8 cm.

The correct answer will be = 8 cm radius

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