Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x -4
h(x) = 3
h(x) =
77 X
Answers
This is the same as h(x) = x/4
In decimal form, it would be h(x) = 0.25x
=============================================
Explanation:
Inverses undo the original function. The original function tells us to take any input (x) and multiply by 4 to get the output y = f(x) = 4x
To get the inverse, we reverse the operation applied here. The opposite of multiplication is division. So we'll divide by 4 instead of multiply by 4. This is why the answer is x/4 or (1/4)x
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Another approach is to do the following: Replace f(x) with y. Swap x and y. Solve for y
f(x) = 4x
y = 4x
x = 4y
4y = x
y = x/4
h(x) = x/4
We end up with the same result as before.
-----------
Extra info:
For any real number x, the following two equations are true
h( f(x) ) = x
f( h(x) ) = x
Related Questions
The surface area of a cube is 302.46 m2. The length of each side of the cube = ______ m. A. 6.7 B. 7.1 C. 50.4 D. not enough information given to solve
Answers
Answer:
B. 7.1 m
Step-by-step explanation:
The surface area of a cube is given by ...
SA = 6s^2
where s represents the side length.
Filling in the given information and solving for s, we have ...
302.46 = 6s^2
s = √(302.46/6) = 7.1 . . . . meters
The length of each side is 7.1 meters.
Answer:
B. 7.1
Step-by-step explanation:
write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind only 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step
Answers
Answer:
Plane speed = 40 m/s.
Wind speed = 300 m/s.
Step-by-step explanation:
Let the speed of the plane = Y
And the speed of the wind = X
If the plane then travel 340 miles per hour with the wind, that means the plane and the wind are moving in the same direction. Therefore,
X + Y = 340 ..... ( 1 )
Also, 260 miles per hour against the wind. That is, the plane is moving opposite to the direction of the wind. Therefore,
X - Y = 260 ..... ( 2 )
Solve the two equations simultaneously by addition. That will eliminate Y
X + Y = 340
X - Y = 260
2X = 600
X = 600/2
X = 300 m/s
Substitutes X in equation (1)
300 + Y = 340
Make Y the subject of formula by collecting the like terms
Y = 340 - 300
Y = 40 m/s
Therefore, the speed of the plane is 40 m/s. While the speed of the wind is 300 m/s.
In the figure below, PR and PQ are tangent to the circle with center O. Given that OQ = 10 and OP = 26, find PR.
Answers
Explanation:
OQ = 10 is the radius, and so is segment RO. Both are the same length as they are the radii of the same circle. Triangle ORP has a leg of RO = 10 and a hypotenuse of PO = 26. The unknown side is PR = x.
Use the pythagorean theorem. We can use this theorem because the tangent formed (at point R) creates a 90 degree angle.
a^2 + b^2 = c^2
(PR)^2 + (RO)^2 = (PO)^2
x^2 + 10^2 = 26^2
x^2 + 100 = 676
x^2 = 676 - 100
x^2 = 576
x = sqrt(576) ... apply square root
x = 24
If y varies jointly with x and y=5 when x=15 and z=24 find y when x=6 and z=14
Answers
Answer:
if they vary together then y would be 2
Step-by-step explanation:
since they vary together 5 multiplied by 3 is 15 so you would divide 6 by 3 to get 2 the z is irrelevant because it has no relation to x or y
A line passes through the point (6,1)and has a slope of 3/2. write an equation in slope intercept form
Answers
Answer:
Step-by-step explanation:
Slope intercept form : y - y1 = m(x -x1)
m = 3/2
(x1, y1) = (6, 1)
[tex]y - 1 = \frac{3}{2}(x - 6)\\\\y -1 = \frac{3}{2}*x -\frac{3}{2}*6\\\\y-1=\frac{3}{2}x-3*3\\\\y-1=\frac{3}{2}x-9\\\\y=\frac{3}{2}x-9+1\\\\y=\frac{3}{2}x -8[/tex]
Answer:
y=3/2 x -8
Step-by-step explanation:
The slope should be in front of the x and the y intercept should be right after the x to create the slope intercept form. I used a graphing calculator which continued the line of 6,1 with a slope of 3/2 and then got
y=3/2x-8
What is the sum of the series *picture attached*
Answers
Answer:
[tex]\sum_{n=4}^{18}(n+1)^2=2440[/tex]
Step-by-step explanation:
Series: [tex]\sum_{n=4}^{18} (n+1)^2[/tex]
Formula :[tex]\sum_{k=m}^n=\sum_{k=1}^n-\sum_{k=1}^{m-1}[/tex]
[tex]\Rightarrow \sum_{n=4}^{18}(n+1)^2=\sum_{n=1}^{18}(n+1)^2-\sum_{n=1}^{3}(n+1)^2[/tex]
[tex]\sum_{n=1}^{18}(n+1)^2=2469[/tex]
[tex]\sum_{n=1}^{3}(n+1)^2=29[/tex]
[tex]\Rightarrow \sum_{n=4}^{18}(n+1)^2=2469-29[/tex]
[tex]\Rightarrow \sum_{n=4}^{18}(n+1)^2=2440[/tex]
So, Option C is true
Luis and Darcy are required to write essays for their English class. The table shows the number of words they wrote for 10 randomly chosen essays. Complete the steps below to compare the number of words in Luis’s and Darcy's essays using the mean and the median. Luis Darcy 178 231 213 210 198 245 245 259 236 286 198 245 221 231 253 244 189 236 177 228 Part A What is the mean number of words in Luis’s essays?
Answers
Answer:
210.8 (mean for Luis), 241.5 (mean for Darcy)
Step-by-step explanation:
Luis 178 + 213 + 198 + 245 + 236 + 198 + 221 + 253 + 189 + 177 = 2108
2108/10 = 210.8 (mean for Luis)
Darcy 231 + 210 + 245 + 259 + 286 + 245 + 231 + 244 + 236 + 228 = 2415
2415/10 = 241.5 (mean for Darcy)
Answer:
it is 210.8
Step-by-step explanation:
ALGEBRA 1
Find the number of terms in the sequence given below:
1.5, 9, 13, ........, 201
a. 51
b. 42
c. 59
d. 45
Answers
Answer:
a. 51
Step-by-step explanation:
[tex]t_{n} =a+(n-1)d[/tex]
201 = 1 + (n - 1)4
200 = (n - 1)4
50 = n - 1
51 = n
I just took the test
The fourth and fifth graders at Jackson Elementary had a competition to see who could
recycle the most newspaper in a 3-day period. Use the chart to answer the question,
The students at Lee Elementary collected 3 times as much as the students at Jackson. How
many pounds did the students at Lee recycle?
Answers
Answer: the elementary 45
Step-by-step explanation: if you need anything else let me know
Find the variation constant and an equation of variation where y varies directly as x and y=16 when x=2
Answers
Answer:
variation constant = k = 8
equation of variation : y = 8x
Step-by-step explanation:
Any relationship of variation can be written as y = kx
where k is the variation constant.
_______________________________________
Let the equationof relation between y and x be y =kx here as well
given
y = 16 when x = 2
substituting this value in the equation y = kx
16 = k*2
=> k = 16/2 = 8
Thus,
variation constant = k = 8
equation of variation : y = 8x
PLEASE HELP Draw the reflection of the figure over the line shown.
Answers
The answer is in the picture
Describe the transformation of ƒ(x) = log5 x which is given by g(x) = 3 log5 (x−7). Question 16 options: A) g(x) is shrunk vertically by a factor of 1∕3 and translated to the right 7 units compared to ƒ(x). B) g(x) is stretched vertically by a factor of 2 and translated to the left 7 units compared to ƒ(x). C) g(x) is stretched vertically by a factor of 3 and translated to the right 7 units compared to ƒ(x). D) g(x) is shrunk vertically by a factor of 1∕3 and translated to the left 7 units compared to ƒ(x)
Answers
Answer:
C) g(x) is stretched vertically by a factor of 3 and translated to the right 7 units compared to ƒ(x).
Step-by-step explanation:
Notice that by transforming [tex]f(x)=log_5\,(x)[/tex] into [tex]g(x)=3\,log_5\,(x-7)[/tex] we have performed the following transformations:
a) a horizontal shift to the right 7 units by subtracting 7 from the x-variable, and
b) stretching the full function vertically by a factor of 3, by multiplying the full function by 3.
Therefore, our answer matches answer C in the list of possible options
a. Find the measure of angle A. b. Find the measure of angle CBD. c. Find the measure of AD. d. Find the measure of BC. e. Find the measure of CD. f. Find the measure of BD. Round all answers to two decimal places. please type/ explain work !
Answers
Answer:
a. m<A = 35°
b. m<CBD = 61°
c. m AD is sin55 = AD/40 AD = 32.77
d. m BC is sin 29 = 22.94/BC BC = 47.32
e. m CD is tan 29 = 22.94/CD CD = 41.38
f. m BD is cos 55 = BD/40 BD = 22.94
Step-by-step explanation:
The solution is,
a. m<A = 35°
b. m<CBD = 61°
c. m AD is sin55 = AD/40 AD = 32.77
d. m BC is sin 29 = 22.94/BC BC = 47.32
e. m CD is tan 29 = 22.94/CD CD = 41.38
f. m BD is cos 55 = BD/40 BD = 22.94
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
from the given figure, we get,
a) ∠D = 90
i.e. ∠A= 90 - 55 = 35
b) similarly,
∠CBD = 90-29
=61
c) m AD is sin55 = AD/40
i.e. AD = 32.77
d) m BC is sin 29 = 22.94/BC
i.e. BC = 47.32
e) m CD is tan 29 = 22.94/CD
i.e. CD = 41.38
f) m BD is cos 55 = BD/40
i.e. BD = 22.94
To learn more on angle click:
brainly.com/question/28451077
#SPJ2
if the ratio of a to b is 10 to 3 then a is
1) 3/10 of b
2) 3 1/3 times b
3)10 times b
4)3 times b
Answers
Answer:
3 1/3 times b
Step-by-step explanation:
10+3 = 13 (total of a and b)a = 10/13 and b = 3/13a/b = (10/13)÷(3/13)= 3 1/3
Rosa’s work finding the median of a set of test scores is shown below.
Which statement best describes Rosa’s first error?
She should have reordered the elements from least to greatest.
She should have added the elements and divided by 9.
She should have counted repeated elements only once.
She should have found the difference between the first and last elements.
Answers
Answer:
She should have reordered the elements from least to greatest.
Step-by-step explanation:
when finding median you need to line up the number from least to greatest or it will not be right
Answer:
It’s A bro
Step-by-step explanation:
Took the quiz on EDG
someone please help me on this question
Answers
Answer:
3.5 m
Step-by-step explanation:
Use sine.
1. Set up the equation using sin = opposite / hypotenuse
sin 59 = 3/x
2. Solve
x = 3.5
Find the algebraic representation of the reflection below.
Answers
Answer:
(x,y) -> (x, -y)
Step-by-step explanation:
This is a reflection about the x-axis.
Algebraically, it can be represented by:
(x,y) -> (x, -y)
since the position along the x-axis does not change, and the y-coordinates are flipped about the x-axis, therefore flipped in sign.
Answer:
Step-by-step explanation:
Search Results
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Find the algebraic representation of the reflection below. a. (-x ...brainly.com › Mathematics › Middle School
Apr 15, 2020 - Find an answer to your question Find the algebraic representation of the reflection below. a. (-x ,y) b. ( x,-y) c. (-x ,-y) d. ( y,x )
Hurry!!
State the domain of the glven relation.
Answers
Answer:
x ≤ -1
Step-by-step explanation:
Translate into an algebraic expression and simplify if possible. I have a total of 10 gigabytes of data on my computer, xgigabytes are movies, pictures take up half the amount of space that movies do and the rest is music. How many gigabytes of music is stored on my computer?
Answers
Answer:
(20-3x)/2 GB
Explanation:
Total amount of data on my computer = 10GB
Total amount of data occupied by movies = x GB
If pictures take up half the amount of space that movies do, then;
Total amount of data occupied by pictures = 1/2 of space occupied by movies = 1/2 x
If the remaining are music, the amount of space occupied by music will be expressed as shown;
Total space -(space occupied by movies + space occupied by pictures)
= 10 - (x+1/2 x)
Total amount of data occupied by music = 10 - (x+1/2 x) GB
On simplification;
= 10 - (x+1/2 x)
= 10-{(2x+x)/2}
= 10 - {3x/2}
= (20-3x)/2 GB
Hence, amount of gigabytes of music stored on my computer is expressed as (20-3x)/2 GB.
The temperature of a mixture is decreasing by 5∘C every hour. When it was first mixed, its temperature was recorded at −20∘C.
Which answer correctly represents the temperature of the mixture over time?
f(x)=−20x−5
That is incorrect.
f(x)=−5x−20
f(x)=−20x+5
f(x)=5x+20
f(x)=−15x
Answers
Answer:
f(x)=−5x−20
Step-by-step explanation:
It's decreasing 5 degrees every hour, which is represented by -5x
You also have to take away the 20 (-20) from where it started.
So, f(x)=−5x−20
Answer:
f(x) = -5x - 20
Step-by-step explanation:
f(x) = starting temperature + decreasing temperature * number of hours
= -20 + (-5) * x
= -20 - 5x
I NEED HELP ASAP! What is the interquartile range (IQR) of the data set below? Will give one lucky person the title as the brainliest (if they are correct).
Answers
Hey there! I'm happy to help!
First, we arrange the numbers from least to greatest.
26,29,31,31,32,37,43
The median here is 31 because it is the middle number. The three numbers before it is one half of it and the last 3 numbers are their own half, because you cannot split the 31 between the two halves.
Now, we want to find the first quartile. This is basically the media of the first half of numbers. So, our first half consists of 26,29, and 31.
The middle number of this first half is 29.
So, our Q1 (first quartile) is 29.
Now, for the third quartile. We do the exact same thing here but with the second half.
32,37,43
Looking at this, our Q3 is 37
The interquartile range is how far apart Q1 and Q3 are, so to find it, we subtract our Q1 from the Q3.
37-29=48
Therefore, our IQR is 8.
Congratulations! Now you can find the IQR of a data set! Have a wonderful day! :D
Answer:
8
Step-by-step explanation:
You first put the numbers in order. Then you find the median(in this case, 31) and after that you find the Q1 and Q3(think of Q1 as the median of the lower half and Q3 as the mdian of the upper half.) Subtract Q1 from Q3, in this case, 37-29=8. 8 is the IQR or the interquratile range.
What solid is represented by this net? A. cylinder B. triangular pyramid C. rectangular prism D. triangular prism E. cone F. rectangular pyramid
Answers
i guess it is hexagonal pyramid
as it has 7 verticies
Select the fraction that is a recurring decimal. A 28/35 B 16/18 C 19/76 D 133/190 E30/48
Answers
Answer:
Step-by-step explanation:
B because 16 over 18 in decimal is .8 repeating
Hi dude....
Pls mark my ans as brainliest :)
Answer:
B. 16/18
Step-by-step explanation:
A 28/35 = 0.8
B 16/18 = 0.88888888888.....
C 19/76 = 0.25
D 133/190 = 0.7
E 30/48 = 0.625
Hope it helps.....
Pls mark my ans as brainliest
While making oatmeal cookies, Angela needs to add cup of milk to her dough. However, she has only a -cup measuring cup. How many times does she need to fill the measuring cup to pour cup of milk?
Answers
Answer:
Once
Step-by-step explanation:
She needs 1 cup of milk.
She has a cup measuring cup.
Therefore she will only to fill the measuring cup to pour cup of milk.
Answer:
1
Step-by-step explanation:
hurry up plz!! Harry performed an experiment with a standard number cube. He rolled the cube and recorded the results in a frequency table. The frequency table is given below. Find the experimental probability of the cube landing on an even number.
Answers
First find the total frequency
6+7+4+7+6+10=40
Now count up the frequency of ALL EVEN NUMBERS
7+7+10=24
Your answer should then be 24/40
In probability you don’t have to simplify but just in case I’ll leave the simplified answer
3/5
Hope this helped!
The number of members of an online community increases each month. The
function M(t) = N(1 + ) represents the number of members at month t, where
Nis the initial number of members and ris the rate of increase. Select the
correct statement.
O A. Nincreases each month.
B. The initial value is (1 + r).
C. The function is linear.
D. The value of Mis a product of Nand a factor that does not depend
on N.
Answers
Plot 1 1/3 and 2 7/9
Answers
Answer:
I plotted them for you!
The first dot (closest to the left) is 1 1/3 and the one closest to the right is 2 7/9 :)
Step-by-step explanation:
Hope this helped :) good luck!
I need help with this question, i am not exactly sure how to do it, help is veryy much appreciated
Answers
Please help! Will mark as brainliest!
Answers
Answer:
x=10 and y=15
Step-by-step explanation:
1: Plug y into the equation
y=2x-5
5x-4(2x-5)=-10
2: Solve for x
-3x=-30
x=10
3: Plug x into the other equation
x=10
y=2(10)-5
4: Solve for y
y=15
Hope this helped! Brainliest would be really appreciated :)
PLEASE HELP DUE NOW!!!!
Answers
Answer:
4. x=120
5. x=65
9. x=150
10. x=45
Step-by-step explanation:
4. Half=180
There is already a 60, so you do 180-60=120. x=120.
5. This is a parallel line, so you determine the opposite angle of 115, which is 65. That just becomes the x. x=65
9. It is similar to #5, You look at the opposite side of 30 (15+15) which is 150. That just comes to the other side which is x=150.
10. A triangle has 180 degrees in total. 45 degrees is already given, and line j is 90 degrees which means a full line is 180. 180-90=90.
90+45=135
180-135=45
x=45
Hope this helped!
Answer:
4. x=120
5. x=65
9. x=150
10. x=45
Step-by-step explanation:
4. Half=180
There is already a 60, so you do 180-60=120. x=120.
5. This is a parallel line, so you determine the opposite angle of 115, which is 65. That just becomes the x. x=65
9. It is similar to #5, You look at the opposite side of 30 (15+15) which is 150. That just comes to the other side which is x=150.
10. A triangle has 180 degrees in total. 45 degrees is already given, and line j is 90 degrees which means a full line is 180. 180-90=90.
90+45=135
180-135=45
x=45