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
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 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:
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
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
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
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
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
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.
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
How do you know where to place a decimal in a quotient?
Answers
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
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
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..
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]
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
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 = 15which 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
[tex]\sqrt{\frac{-140}{\sqrt{28} }[/tex]
Answers
This is 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:
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:
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.
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
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
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 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
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!
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)^3Which 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
Write 762.238 correct to 2 decimal places
Answers
Answer:
762.24
Step-by-step explanation:
Rounded to the hundredth place
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