Answers
Answer: They are inverses of each other
==========================================================
Explanation:
We'll need to compute h(f(x)) and f(h(x)) to see if we get x each time.
[tex]h(x) = 9x-4\\\\h(f(x)) = 9(f(x))-4\\\\h(f(x)) = 9\left(\frac{x+4}{9}\right)-4\\\\h(f(x)) = x+4-4\\\\h(f(x)) = x\\\\[/tex]
and,
[tex]f(x) = \frac{x+4}{9}\\\\f(h(x)) = \frac{h(x)+4}{9}\\\\f(h(x)) = \frac{9x-4+4}{9}\\\\f(h(x)) = \frac{9x}{9}\\\\f(h(x)) = x\\\\[/tex]
Both composite functions lead to x each time.
The equations h(f(x)) = x and f(h(x)) = x being true means each function is the inverse of the other.
Related Questions
Find the solution of the system of equations.
3x – 3y = 18
3x – 8y = -2
Answers
Answer:
x=10, y=4
Step-by-step explanation:
3x-3y=18
(-)3x-(-)8y=-(-)2 -3x+8y=2 add to first equation to eliminate x
5y=20
y=4
substitute y with 4
3x-3(4)=18
3x=30
x=10
x=10,y=4
Solve the system of equations.
y= -6x +9
y= -3x +3
a (3,-2)
b. (-2,3)
C. (2,3)
d. No solution
Answers
Answer:
The answer is supposed to be (2,-3), but for some reason I don't see it as one of the choices.
(Please don't get mad or report this answer, the work is below, so you may see for yourself.)
Step-by-step explanation:
Since y equals both -6x + 9 and -3x + 3, we will simply write them into one equation:
-6x + 9 = -3x + 3
Next we will solve for x by isolating it:
So, first subtract 3 on both sides to get -6x + 6 = -3x. Next add 6x on both sides to get 6 = 3x. Then finally divide by 3 on both sides to get 2 = x or you can flip it to be x = 2.
Now that we know what x is, we can plug it back into one of the original equations. In this case we'll plug it into y = -3x + 3:
y = -3(2) + 3
-3 × 2 = -6 and -6 + 3 = -3
So: y = -3
Now we can plug each into an ordered pair (x,y), and your answer is (2,-3).
As always, don't forget to check your work (It's correct btw, I already checked) and I hope this helps you :)
Answer:
x=2, y=-3. (2, -3).
Step-by-step explanation:
y=-6x+9
y=-3x+3
-----------
-6x+9=-3x+3
-6x-(-3x)+9=3
-6x+3x=3-9
-3x=-6
3x=6
x=6/3
x=2
y=-6(2)+9
y=-12+9=-3
Which expression is equal to “seven more than a number multiplied by 9"?
a. 9(x + 7)
b. 7 + 9x
c. 9x - 7
d. 9 + 7x
Answers
Answer:
b
Step-by-step explanation:
a: is not because in the distribution property, the answer would be for a, 9x+63.
b: yes.
c: it's subtracting, not adding. The question states adding
d: 7 is not the one being multiplied in the question, 9 is. Therefore b is right
The explaining is not good but im pretty sure it's b..
Write 762.238 correct to 2 decimal places
Answers
Answer:
762.24
Step-by-step explanation:
Rounded to the hundredth place
Y<-3 which is the solution:
A) 5
B) 0
C)-2
D)-5
Answers
Y needs to be less than -3 the larger the negative number the further from 0 it is so -5 would be less than -3
Answer: -5
please help meeeeeeee due in 5 minutessssssssssssss
Answers
Answer:
I think it would be 6. But im not 100% sure
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Mean x¯¯¯ 12.875
Median x˜ 11.5
Mode 15
Range 34
Minimum 6
Maximum 40
Count n 16
Sum 206
Quartiles Quartiles:
Q1 --> 8.5
Q2 --> 11.5
Q3 --> 14.5
Interquartile
Range IQR 6
Outliers 40
Pls help I’ll brainlest for correct answer you gotta graph it on the graph too
Answers
Answer:
Slope: -2/3
Y Intercept: 0,-3
Step-by-step explanation:
To find the slope, use the formula (y1-y2)/(x1-x2)
(1-(-1))/(-6-(-3))
-2/3
So the slope is: -2/3
If the slope is 3/2, then the using the formula of y=mx+b, we can find the y intercept (b)
y = -2/3x + b
insert any point of x and y
-1 = -2/3(-3)+b
-1=-2+b
so b = -3
thus, the Y intercept is 0,-3
See graph attached for graph
3n + 6n -4 = 2n + 2 + 5n
Answers
Answer:
3n +6n-4=2n+2+5n
9n-4=7n+2
9n-7n=2+4
2n=6
n=6÷2
n=3
How would the expression x3 -3 sqrt 3 be rewritten using difference of cubes?
O A. (x- 13 )(x2-3x - 3)
O B. (x+ 3)(x + 13 x + 3)
C. (x - 13 )(x2 + 3x + 3)
O D. (x- vb)(x2 + v3 x+3)
Answers
Answer:
x^3 - (√3)^3
I'm not so sure since it's not even an option
Step-by-step explanation:
x^3 - 3√3 = x^3 - 3^1 × 3^(1/2)from the laws of indices: 3^1 × 3^(1/2) = 3^(1 + 1/2)= 3^(3/2) which is the same as (√3)^3so it could be written as x^3 - (√3)^3[tex]\sqrt{\frac{-140}{\sqrt{28} }[/tex]
Answers
This is the answer
At the movie theatre, child admission is $5.50 and adult admission is $8.90. On Friday four times as many adults tickets as child tickets were sold, for a total sales of $986.40. How many child tickets were sold that day?
Answers
Answer:
You can use grouping, quantity and value to solve this question.
Child admission = $5.50
Adult admission = $8.90
Friday sales (Quantity):
Child = x
Adult = 4x
Total sales = 5x
Friday sales (Value):
Child = $5.50
Adult = 4 × $8.90
= $35.60
Total sales = $986.40
1 group = $5.50 + $35.60
= $41.10
Number of groups = $986.40 ÷ $41.10
= 24
The number of child tickets sold is 24.
Hilary walked 654 feet in 3 minutes. She says she walked 218 feet per minute. Is Hilary’s
answer reasonable? Explain.
Answers
Because if she is walking 218 feet per minute then if you multiply 218 by 3 we get 654 feet
Which means she must have travelled 654 feet in 3 minutes in order for it to be true which it is! Hope this helps!
help i want to graduate by january :,)
Answers
1. We see that it is 1.04. This means it will increase by 4 percent. 4% growth
2. 0.6 is less than 1. We need to subtract 1 by 0.6. This gives us 0.4. It will decay by 40 percent. 40% decay
3. We need to subtract 0.86 from 1. This gives us 0.14. The decay is 14 percent. 14% decay
4. 1 - 0.96 is 0.04. The decay is 4 percent. 4% decay
5. We see that it is 1.14. So, the growth is 14 percent. 14% growth
6. It is 1.4. The growth is 40 percent. 40% growth
How do you know where to place a decimal in a quotient?
Answers
Match the verbal phrase on the left with the corresponding equation on the right. Write the letter of the answer on the space provided1.c increased by 5 is 5 2.4 more than a number is 12 3. The product of 4 and n is 12 4. The difference of 27 and k is 15 5.8 less than 3 times x is 10 6. 3 times x increased by 8 is 20 7. a number minus 8 is 3 8. three times a number is 9 9. twice a number plus 1 is 11 10.6 less than a number is 5a. 27-k=15 b. n + 4 = 12 d. 3x+8 = 20 e. k-8=3 f. 3x-8=10 g. 2x + 1 = 11 h. c + 5 = 15 i. 4n = 12 c. c-6=15 j. 3n = 9
Answers
Answer:
See belowStep-by-step explanation:
1. c increased by 5 is 5 ⇒ h. c + 5 = 5 2. 4 more than a number is 12 ⇒ b. n + 4 = 12 3. The product of 4 and n is 12 ⇒ i. 4n = 12 4. The difference of 27 and k is 15 ⇒ a. 27 - k = 155. 8 less than 3 times x is 10 ⇒ f. 3x - 8 = 10 6. 3 times x increased by 8 is 20 ⇒ d. 3x + 8 = 20 7. A number minus 8 is 3 ⇒ e. k - 8 = 3 8. Three times a number is 9 ⇒ j. 3n = 99. Twice a number plus 1 is 11 ⇒ g. 2x + 1 = 11 10. 6 less than a number is 5 ⇒ c. c - 6 = 15What is the slope of the line that passes through the points (6-8) and (10,-8)?
Answers
Answer:
The slope of the line that passes through the points would be 0
Step-by-step explanation:
Lets use the formula : y2-y1/x2-x1
In this case lets let y2 be -8 and y1 be -8
And lets let x2 be 6 and x1 be 10, that would look like..
-8-(-8)/6-10
which equals...
0/-4 = 0
We know that the slope of the line is 0
Write and expression for the senqence of operations described below.
raise 6 to the 2nd power, then subtract r from the result
Do not simplify any part of the expression.
Answers
Raise [tex]6[/tex] to the second power, [tex]6^{2}[/tex], the subtract r from the result, that should be [tex]6^{2} - r[/tex], since we are not to simplify the expression, that's the answer.
what is the answer to the following?
9+(60x8)-120?
80(50-24)+20?
Answers
Answer:9+(60x8)-120= 369
80(50-24)+20= 126
Step-by-step explanation:
Jada buys 5 notebooks and 6 pens. Each notebook costs $4. Jada pays the cashier $40 and gets $8 change.
What is the cost, in dollars, of one pen? Show or explain how you got your answer.
Answers
Answer:$2
Step-by-step explanation:
5 notebooks cost $4 each
5*$4=$20
Jada pays the cashier $40 and gets $8 back
So in order to figure out how much was paid you take
$40-$8=$32
Then to figure out how much each pen cost I take
$32-$20=$12
So there was 6 pens that were bought and to get the total per each pen
$12/6=$2 each per pen
A car is traveling at a speed of 70 miles per hour. What is the car's speed in miles per hour? How many miles will the car travel in 5 hours?
Answers
This section is worth 8 points of 31 total.
Drag the item from the item bank to its corresponding match.
ITEM BANK Move to Top
1.2 x 103
drag and drop answet here
0.00056
1.2 x 10-3
drag and drop answer there
0.0012
0.0056
5.6 x 104
drag and drop answerhero
0.012
5.6 x 10-4
dindianswerte
1,200
1.2x 10²
drag and drop answers
120
56,000
1.2 x 102
clog and drop
560
5.6 x 102. Do
5.6 x 103
Answers
Answer:
1200
0.0012
56000
0.00056
120
0.012
560
0.0056
Step-by-step explanation:
which statement correctly compares two value?
The value of the 5 in 50.89 is 1/10 the value of the 5 in 261.58.
The value of the 5 in 50.89 is 10 times the value of the 5 in 261.58.
The value of the 5 in 50.89 is 1/100 the value of the 6 261.58.
The value of the 5 in 50.89 is 100 times the value of the 5 in 261.58
Answers
Answer:
The value of the 5 in 50.89 is 100 times the value of the 5 in 261.58
Step-by-step explanation:
The 5 in 50.89 is in the 10's place
The 5 in 261.58 is in the 1/10's place
1/10(100) = 10
Which of the following expressions is equivalent to 7 - 2 (y - 1)
Answers
Since nothing is shown, you can infer.
First to solve the expression:
1) Expand by distributing terms.
[tex]7-(2y-2)[/tex]
2) 2 Remove parentheses.
[tex]7 - 2y + 2[/tex]
3) Collect like terms.
[tex]-2y+(7+2)\\[/tex]
4) Simplify.
[tex]-2y + 9[/tex]
The expression that is equivalent to [tex]7-2(y-1)[/tex] is [tex]-2y + 9[/tex].
Hope this helps,
- Recordofraganrok
A rectangle has a length of 25 meters less than 6 times it’s width. If the are of the rectangle is 261 square meters, find the length of the triangle
Answers
Which equation has a maximum at y = 5 for 0 < x < 27?
Answers
Answer:
To determine which equation has a maximum at y =5, you will need to compare their graphs looking only at the x-values between 0 and 27.
Step-by-step explanation:
Harry bought two-thirds pound of candy. He ate four-fifths of the candy. What was the weight of the candy he ate?
Answers
Answer:
8/15
Step-by-step explanation:
not sure but I think you just multiply them
c-3=6
x+8=18
y-5=4
Please Show your Work For each problem.
Answers
Answer:
1. 9
2. 10
3. 9
Step-by-step explanation:
c-3=6
+3 +3
-----------
c = 9
x+8=18
-8 -8
------------
x = 10
y-5=4
+5 +5
------------
y = 9
hope this helps! :D brainliest would be very, very much appreciated!! <3
a tube has a radius of 4 inches and a height of 4 inches. what's its approximate volume?
Answers
Step-by-step explanation:
that is the same as the volume of a cylinder :
pi×r²×height = pi×4²×4 = pi×64 = 201.0619298... in³
≈ 201 in³
Volume is a three-dimensional scalar quantity. The volume of the tube is 201.0619 inches³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a cylinder is given by the formula as shown below,
Volume of a cylinder = πr²h
where r is the radius of the cylinder while h is the height of the cylinder.
Given that a tube has a radius of 4 inches and a height of 4 inches. Therefore, the volume of the tube will be,
The volume of the tube = π × R² × h
= π × (4 inches)² × (4 inches)
= 64π inches³
= 201.0619 inches³
Hence, the volume of the tube is 201.0619 inches³.
Learn more about Volume:
https://brainly.com/question/13338592
#SPJ5
The ratio of the sides of two similar regular octagons is 5:7. If the measure of each side of the larger octagon is 21 cm, then the measure of each side of the smaller octagon is ________cm.
Answers
Answer:
15 centimeters.
Step-by-step explanation:
If the ratio of two sides of similar octagons is 5:7, then the larger octagon has a side length that is 7/5 times the smaller one. If the measure of the side of the larger octagon is 21, then the measure of the smaller one is 5/7 times that, which is 5/7 * 21 = 15 centimeters.
Air is being pumped into a spherical balloon at the rate of 7 cm3/sec. What
is the rate of change of the radius at the in stant the volume equals 36π cm3
? The volume of
the sphere of radius r is (4 over PI )r power of 3
Answers
Answer:
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^3\\\frac{dV}{dt} =\frac{4}{3} ~\pi \times ~3r^2\frac{dr}{dt} \\\frac{dV}{dt} =4\pi r^2\frac{dr}{dt} \\7=4\pi r^2\frac{dr}{dt} \\\frac{dr}{dt} =\frac{7}{4\pi r^2} \\when~V=36 \pi cm^3\\36\pi =\frac{4}{3} \pi r^3\\r^3=\frac{36\pi \times 3}{4\pi } =27=3^3\\r=3~cm\\\frac{dr}{dt} =\frac{7}{4\pi \tmes 3^2} \\\frac{dr}{dt} =\frac{7}{36 \pi } cm/sec[/tex]