70 POINTS!
{Questions 54 & 58}
The function f is one to one. Find to inverse. State the domain & the range of f & f^-1. Graph f & f^-1, & y=x on the same coordinate axes.
Show work please.
Answers
The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.
InversesA function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.
A function f -1 is the inverse of f if
for every x in the domain of f, f -1[f(x)] = x, andfor every x in the domain of f -1, f[f -1(x)] = xThe domain of f is the range of f -1 and the range of f is the domain of f -1.
Graph of the Inverse FunctionThe inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.
Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.
The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.
Related Questions
On a coordinate grid, point M is at (−8, 2) and point S is at (10, 2). The distance (in units) between points M and S is ______. (Input only whole numbers, such as 2.)
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d=√(x2-x1)² + (y2-y1)²
d=√(-8-10)² + (2-2)²
d=√(-18)² + 0
d=18
And issue of a magazine contain the following statement dropping less than 2 inches per mile after emerging from the mountains a river drains into the ocean 1 days discharge at its mouth for trillion gallons could supply all of country as household for 5 months based on this statement determine how much water and average household uses each month assume that there are 200 million household in country a country a used approximately how many gallons per household per month
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(4*10^12 gallons)/(2*10^8 households·5 months)
.. = 4000 gallons/household/month
Two numbers add to 336 and the first is 124 bigger than the second. What are the two numbers?
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Final answer:
To solve the problem, a system of equations is set up with the second number as 'x' and the first as 'x + 124.' The equations are simplified to find 'x = 106,' which makes the first number '230.' The two numbers are 106 and 230.
Explanation:
To find the two numbers that add to 336 and where the first number is 124 larger than the second, we need to set up a system of equations based on the information given:
Let the second number be x.
Then the first number will be x + 124 since it is 124 bigger than the second.
The sum of the two numbers is 336, so we can write the equation x + (x + 124) = 336.
Simplifying this equation, we get 2x + 124 = 336.
Subtract 124 from both sides to isolate the term with x, yielding 2x = 212.
Divide both sides by 2 to find x, which gives x = 106.
Since the first number is 124 larger, we add 124 to 106, resulting in the first number being 230.
Therefore, the two numbers are 106 and 230.
There are 24 different tables to set up for field day.The principal wants the tables set up in equal rows.should she use 3 rows or 5 rows?Explain
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Miguel has an aquarium in the shape of a rectangular prism. The base is 30.25 inches long and 12.5 inches wide. The aquarium is 12.75 inches high. What is the volume of the aquarium to the nearest cubic inches?
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30.25 × 12.5 × 12.75 = 4821.09375 in^3
Hope this helps!
The result of 4,816.40625 cubic inches is rounded to 4,816 cubic inches to the nearest cubic inch.
To find the volume of Miguel's aquarium, which is in the shape of a rectangular prism, we use the formula for the volume of a rectangular prism:
Volume = length * width * height
In this case, the length is 30.25 inches, the width is 12.5 inches, and the height is 12.75 inches.
So, the calculation for the volume would be:
Volume = 30.25 inches * 12.5 inches * 12.75 inches
= 4,816.40625 cubic inches.
Rounding to the nearest cubic inch, the volume of the aquarium is 4,816 cubic inches.
Let P be the point (1,1,-2). Suppose that the point P0(2, -5, 2) is 1/5 of the way from P to Q. Find the point Q.
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Q = 4P0 -4P +P0
Q = 5P0 -4P
Q = 5(2, -5, 2) -4(1, 1, -2)
Q = (6, -29, 18)
round 149,640 to the nearest thousand.
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a rectangular swimming pool is 3 meter wide. The surface area is 30 sq meters...what is the length of the pool?
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If w is inversely proportional to the square of v, and w=3 when v=6, fund w when v=3
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where k is the constant of proportionality, given by:
k=w√v
w=3 when v=6
thus
k=3√6
hence:
w=(3√6)/√v
hence the value of w when v=3 will be:
w=(3√6)/√3
w~4.24264
The population of city A is 26% less than the population of city B, so city A's population is _____% of city B's.
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Answer:
The population of city A is [tex]74\%[/tex] of the population of city B
Step-by-step explanation:
Let
y------> population of the city A
x-----> population of city B
we know that
[tex](100\%-26\%)=74\%=\frac{74}{100}=0.74[/tex]
so
[tex]y=0.74x[/tex]
therefore
The population of city A is [tex]74\%[/tex] of the population of city B
The sum of two numbers is 52. If twice the smaller number is subtracted from the larger number, the result is 13. Find the two numbers.
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Larger number = y Twice the smaller number subtracted from the larger
Smaller number = x is equal to 13:
y - 2x = 13 Solve for y: y = 2x + 13 Then substitute your value for y into the equation they gave you at the beginning:
(2x + 13) + x = 52 Solve the equation by simplifying:
3x = 52 - 13 3x = 39 x = 13 Then substitute your value for x (13) into the equation we made to solve for y:
y - 2(13) = 13 y - 26 = 13 y = 39
So your answer is, "The two numbers are 13 and 39."
You estimate the distance from your house to your school to be 1.6 miles. The actual distance is 1.9 miles. Find the percent error. Round your answer to the nearest tenth of a percent.
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[tex]% Error = \frac{final value - given value}{given value} [/tex]
% error = (1.6 - 1.9)/1.9 * 100% = 15.79%
Final answer:
The percent error of the estimated distance from your house to school is 15.8% when rounded to the nearest tenth.
Explanation:
To find the percent error of your estimate, you use the formula:
Error = (|Estimated value - Actual value| / Actual value) × 100
Plugging the values from your question:
Error = (|1.6 miles - 1.9 miles| / 1.9 miles) × 100
Error = (|-0.3 miles| / 1.9 miles) × 100
Error = (0.3 miles / 1.9 miles) × 100
Error = 0.15789473684 × 100
Error = 15.789473684%
When rounded to the nearest tenth of a percent, the percent error is 15.8%.
Cpm/pert graphically displays the scheduling of tasks required to complete a project.
a. True
b. False
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The measure of DF is 108. What is the measure of DEF, the tangent-chord angle?
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Answer:
The measure of DE is 108°. What is the measure of ZDEF, the tangent-chord angle?
54
Step-by-step explanation:
Help pleaseeeeeeeeeeeeeeeeee
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a = 12
k = 0.2
v(x) = 0 at the maximum after differentiation
V(x) = kx(a - x)
The easiest way to do this is to remove the brackets.
V(x) = akx - kx^2 Substitute the constants
V(x) = 12*0.2*x - 0.2x^2
V(x)/dx = 2.4 - 0.4x = 0 at the maximum
2.4 - 0.4x = 0
0.4x = 2.4
x = 2.4/0.4
x = 6
If you don't know any calculus yet, you can do this by completing the square.
A piece of solid, spherical glass has a circumference of 18.84 centimeters. The sphere is cut in half, creating two identical hemispheres. Using 3.14 for π, Tran computes the amount of paint needed to cover the sphere. Which statement about the amount of paint found by Tran is true?
Tran found the minimum amount of paint needed to cover the curved surface of a hemisphere
Tran found the minimum amount of paint needed to cover the entire surface of one of the hemispheres.
Tran found the minimum amount of paint needed to cover both hemispheres.
Tran found the minimum amount of paint needed to cover the bases of both hemispheres.
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Final answer:
Tran must calculate the surface area of the hemisphere, including the base, to determine the amount of paint needed, which is the sum of half the surface area of the sphere and the area of the base.
Explanation:
The question is asking what Tran would compute when using π to determine the amount of paint required for a hemisphere. First, Tran needs to calculate the surface area of the sphere to determine the paint needed. Given the circumference C = 18.84 cm, the radius r can be found using C = 2πr, which gives us a radius of r = C / (2π). Once we have the radius, we can find the surface area A of the sphere using A = 4πr², which is necessary to determine the paint needed for the outer surface.
However, when the sphere is cut into two hemispheres, the flat face of each hemisphere (base) also needs paint. The area of the base is a circle with an area of πr². Thus, the total surface area that Tran would need to paint for one hemisphere, including the base, is πr² + 2πr² (half of the sphere's surface area).
Final answer:
Option D.) Tran found the minimum amount of paint needed to cover both hemispheres.
Explanation:
Tran found the minimum amount of paint needed to cover both hemispheres. To calculate the amount of paint needed to cover a hemisphere, we need to find the surface area of the hemisphere. The formula for the surface area of a sphere is 4πr², where r is the radius.
Given that the circumference of the sphere is 18.84 centimeters, we can use the formula C = 2πr to solve for the radius. Plugging in the value for C, we get 18.84 = 2πr.
Simplifying the equation, we find that the radius of the sphere is approximately 3 centimeters.
The surface area of a hemisphere is half the surface area of a sphere, so the surface area of one hemisphere is 2πr²/2 = πr².
Substituting the value of r, we find that the surface area of one hemisphere is approximately 9π square centimeters.
Since Tran cut the sphere in half and created two identical hemispheres, the minimum amount of paint needed to cover both hemispheres would be twice the surface area of one hemisphere, which is approximately 18π square centimeters.
A rectangle is dilated by a scale factor of 4.
a) The original rectangle is 8 cm by 3 cm. What are the dimensions of the new rectangle?
b) Is the new image a reduction or enlargement? Explain.
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To find the new dimensions of the rectangle, what you must do is multiply each of the dimensions by the scale factor.
We have then:
(4) * (8) = 32 cm
(4) * (3) = 12 cm
Answer:
The dimensions of the new rectangle are:
32 cm by 12 cm
b) Is the new image a reduction or enlargement? Explain
As k> 1 (4> 1) then the new image is an enlargement of the original figure.
Answer:
the new image is a enlargement
what is −1.6+(−2.4)?
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Which values of x will make the absolute value equation true? |x – 3| = 40
A. {–43, –37}
B. {43, –37}
C. {40, –40}
D. {43, 37}
Answers
The values of x that satisfy the absolute value equation |x – 3| = 40 are 43 and -37. These are derived from solving the two possible scenarios for absolute value equations, resulting in a positive and a negative solution.
Explanation:To find which values of x will make the absolute value equation |x – 3| = 40 true, we need to consider both the positive and negative scenarios that can result from the absolute value. The absolute value of a number equals the number itself if it is positive or zero, and it equals the negative of the number if it is negative.
So, we set up two equations:
x - 3 = 40 (when x – 3 is non-negative)x - 3 = -40 (when x – 3 is negative)Solving the first equation for x, we add 3 to both sides:
x = 40 + 3
x = 43
Solving the second equation for x, we add 3 to both sides:
x = -40 + 3
x = -37
Therefore, the values of x that will satisfy the equation are 43 and -37. Option D is the correct answer.
Final answer:
The values of x that make the absolute value equation true are 43 and -37.
Explanation:
To solve the equation |x-3| = 40, we need to consider two cases:
1. x-3 = 40: In this case, we add 3 to both sides to isolate x and get x = 43.
2. -(x-3) = 40: In this case, we distribute the negative sign and add 3 to both sides to isolate x, which gives x = -37.
Therefore, the values of x that make the absolute value equation true are {43, -37}.
For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 7 3 π meters?
Answers
Answer : The measurement of a central angle is, [tex]140^o[/tex]
Step-by-step explanation :
Formula used for angle subtended by an arc is:
[tex]s=\frac{\pi r\theta}{180}[/tex]
where,
s = arc length = [tex]\frac{7}{3}\pi m[/tex]
r = radius = [tex]\frac{diameter}{2}=\frac{6m}{2}=3m[/tex]
Now put all the given values in the above formula, we get:
[tex]s=\frac{\pi r\theta}{180}[/tex]
[tex]\frac{7}{3}\pi=\frac{\pi \times (3)\times \theta}{180}[/tex]
[tex]\theta =140^o[/tex]
Thus, the measurement of a central angle is, [tex]140^o[/tex]
In the Venn diagram, consider U = {students in 10th grade at Lee High School}.
The diagram shows the electives chosen by the students in the 10th grade.
How many students chose to participate in the painting class?
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We have been given a Venn diagram in which U = {students in 10th grade at Lee High School}. We are asked to find how many students have chosen to participate in the painting class.
We can see from our Venn diagram that 3 students are participating in chorus and painting. 2 students are participating in chorus, theater and painting. 4 students are participating in painting and theater.
To find total students who have chosen to participate in the painting class we will add all the students who are participating in other activities with painting.
[tex]\text{Students participating in painting class}=8+3+2+4[/tex]
[tex]\text{Students participating in painting class}=17[/tex]
Therefore, 17 students have chosen to participate in painting class.
Answer:
17
Step-by-step explanation:
When p2 – 4p is subtracted from p2 + p – 6, the result is 5p-6 To get p – 9, subtract
Answers
Subtract p² - 4p from p² + p - 6 to get 5p - 6. To obtain p - 9, subtract 15 from 5p - 6.
Let's break it down step by step:
1. Subtracting p² - 4p from p² + p - 6:
Start by writing down the expression p² + p - 6.
Now, subtract p² - 4p from it term by term.
(p² + p - 6) - (p² - 4p)
2. Expand and Simplify:
Distribute the subtraction across each term inside the parentheses:
p² + p - 6 - p² + 4p
This simplifies to: (p² - p²) + (p + 4p) - 6
= 0 + 5p - 6
= 5p - 6
3. Now, to get p - 9:
We want to manipulate 5p - 6 to p - 9.
Subtracting 15 from 5p - 6 gives:
5p - 6 - 15
= 5p - 21
Therefore, subtracting 5p - 21 from 5p - 6 results in p - 9.
silvio earns 10% for each car sale he makes while working at a used car dealership. If he sells a used car for $2,000 what is his commission
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If the car was sold for $2000
commission = 10% of $2000
commission = 0.1 x $2000
commission = $200
If silvio earns 10% for each car sale he makes while working at a used car dealership then he earns $200 as commission for selling car for $2,000.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that silvio earns 10% for each car sale he makes while working at a used car dealership.
silvio sells a used car for $2,000.
We have to find the commission earned by Silvio.
We have to calculate 10% of $2000 to find the commission.
Convert 10% to decimal value by dividing with 100.
commission = 10% of $2000
commission = 0.1 x $2000
commission = $200
Hence, if silvio earns 10% for each car sale he makes while working at a used car dealership then he earns $200 as commission for selling car for $2,000.
To learn more on Percentage click:
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Given: ABCD is a parallelogram m∠A = 60º ; BK ⊥ AD AK = KD; Perimeter of ABCD = 24 Find: BD.
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Then BD = AB. Denote AB by x and AK by y.
Then,
2x+4y=24 (the perimeter)
cos 60=y/x.
From the second equation we get [tex]y=0.5x[/tex]
Plug in the first equation we get:
[tex]2x+4(0.5x)=24\\2x+2x=24\\4x=24\\x=6[/tex]
We deduce that [tex]BD=6.[/tex]
Final answer:
To find BD, we can use the fact that the opposite sides of a parallelogram are equal in length. The length of BD is 4.8 units.
Explanation:
In the given problem, we have a parallelogram ABCD with m∠A = 60º. BK is perpendicular to AD and AK = KD. The perimeter of ABCD is 24. To find BD, we can use the fact that the opposite sides of a parallelogram are equal in length. Since AK = KD, the length of AD is twice the length of AK.
Let AK = x. Then AD = 2x. The perimeter of ABCD is given by P = AB + BC + CD + AD. Substituting the given values, we have 24 = AB + BC + CD + 2x. We know that AB = CD, so the equation becomes 24 = 2AB + 2BC + 2x. Rearranging the terms, we get AB + BC + x = 12.
Using the fact that opposite sides of a parallelogram are equal in length, we can deduce that BC = AB. Substituting this into the equation, we have 2AB + AB + x = 12. Simplifying, we get 3AB + x = 12. Since AK = KD, we have x = KD. Substituting this into the equation, we have 3AB + KD = 12. Since AK = KD, we have 3AB + AK = 12. Since AK = KD, we have 3AB + 2AK = 12. Simplifying, we get 3AB + 2AB = 12. Combining like terms, we get 5AB = 12. Dividing both sides by 5, we get AB = 12/5. Since AB = CD, we have CD = 12/5. Since opposite sides of a parallelogram are equal in length, we have BD = AD = 2x = 2(12/5) = 24/5 = 4.8.
A landscape designer has a drawing of a flower bed that measures 6inches by 9 inches. The owner wants the actual flower bed to be 5 feet by 7.5 feet. What is the scale factor the designer must use to install the new flower bed
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2/5 of the Jazz is by musicians from New Orleans. How much of New Orleans music does Ivan have
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Ivan has 24 minutes of New Orleans jazz on his MP3 player.
To find out how much of an hour of New Orleans jazz Ivan has, we use the following steps:
1. We know that Ivan has an hour of jazz music on his MP3 player.
2. We are given that 2/5 of this jazz music is by musicians from New Orleans.
3. To find out how much of New Orleans jazz music that is, we calculate 2/5 of 1 hour.
Here's the calculation:
[tex]\( \frac{2}{5} \times 1 \text{ hour} = \frac{2}{5} \times 60 \text{ minutes} \)[/tex]
[tex]\( \frac{2}{5} \times 60 = \frac{120}{5} \text{ minutes} \)[/tex]
[tex]\( \frac{120}{5} = 24 \text{ minutes} \)[/tex]
Therefore, Ivan has 24 minutes of New Orleans jazz on his MP3 player.
complete question given below:
PLEASE HELP WILL MARK BRAINLIEST
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.. rectangle + trapezoid = (4 ft)*(24 ft) +(4 ft +8 ft)*(16 ft)/2 = 192 ft^2
.. rectangle + triangle = (4 ft)*(40 ft) +(1/2)*(4 ft)*(16 ft) = 192 ft^2
The side area is multiplied by the width to find the volume.
.. V = (192 ft^2)*(20 ft) = 3840 ft^3 . . . . . . maximum water volume
_____
That's a pint or so more than 28,725 gallons.
A person's website specializes in the sale of rare or unusual vegetable seeds. he sells packets of sweet-pepper seeds for $2.32 each and packets of hot-pepper seeds for $4.40 each. he also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $2.58 per packet. how many packets of each type of seed are in the assortment?
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We have then:
x = packets of sweet-pepper seeds
16-x = packets of hot-pepper seeds
We now write the equation to solve the problem:
2.32x + 4.40 (16-x) = 2.58 (16)
2.32x + 70.40-4.40x = 41.28
-2.08x = -29.12
x = (- 29.12) / (- 2.08)
x = 14
Answer:
there are in the assortment:
14 packets of sweet-pepper seeds
16-14 = 2 packets of hot-pepper seeds
what is the volume of a box that can fit exactly 128 1/8 inch cubes with 1/2 inch sides?
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a 5 inch tall bamboo shoot doubles in height every 3 days. if the equation, y=ab^x where x is the number of doubling periods, represents the height of the bamboo shot, what are the values of a and b?
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Y-height of bamboo
Y=ab^x
1) make a table of values
X Y
1 5
2 10
3 20
2) write equations and substitute
5=ab^1 —> a=5/b^1 —> a=5/b
10=ab^2
Substitute into second equation
10=(5/b)*b^2
10=5b^2/b
10=5b
b=2
Substitute back in
b=2
10=a*2^2
10=4a
a=5/2
End equation:
Y=5/2*2^x