Exchanging x and y and isolating y, it is found that the inverse function is:
[tex]g^{-1}(x) = \frac{1 + x}{x}[/tex]
The function given is:
[tex]g(x) = y = \frac{1}{x - 1}[/tex]
To find the inverse function, we exchange x and y and isolate y, hence:
[tex]x = \frac{1}{y - 1}[/tex]
[tex]x(y - 1) = 1[/tex]
[tex]xy - x = 1[/tex]
[tex]xy = 1 + x[/tex]
[tex]y = \frac{1 + x}{x}[/tex]
Hence, the inverse function is:
[tex]g^{-1}(x) = \frac{1 + x}{x}[/tex]
You can learn more about inverse functions at https://brainly.com/question/16485117
For what value of k are the lines 2x + 3y = 4k and x - 2ky = 7 parallel?
Answer:
k = -3/4
Step-by-step explanation:
The lines will be parallel if their slopes are equal. To find the slope of each line, write its equation in slope-intercept form (y = mx + b). In other words, solve each equation for y and look at the coefficient of x.
2x + 3y = 4k
3y = -2x + 4k
y = (-2/3)x + 4k/3
The slope of the first line is -2/3.
x - 2ky = 7
-2ky = -x + 7
y = [1/(2k)]x - 7/(2k)
The slope of the second line is 1/(2k).
If the slopes are equal, then
1/(2k) = -2/3
Multiply by 2k.
1 = (-2/3)(2k) = (-4/3)k
1 = (-4/3)k
k = -3/4
What is a÷3+11=-5 and how to doit with steps?
[tex]a\div 3 +11 = -5\\\\\implies a\div 3 = -5 -11\\\\\implies a \cdot \dfrac 13 =-16\\\\\implies a = -16 \cdot 3\\\\\implies a = -48[/tex]
Answer:-5 it's already given you the answer its only asking how you got it it's simply asking for the work
Step-by-step explanation: First off you're solving for A, (-5 x 14) which is -70 so now all you need is to do the work for (-70 by 14) and there you have it (probably)
PLEASE I NEED HELP RN
use the elimination method to solve. -7x+y=-19 -2x+3y=-19
Answer:
(x, y) = (2, -5)
Step-by-step explanation:
The coefficient of y in the second equation is an integer multiple of the coefficient in the first equation, so it is convenient to eliminate y. Subtracting 3 times the first equation from the second, we have ...
(-2x +3y) -3(-7x +y) = (-19) -3(-19)
-2x +3y +21x -3y = -19 +57 . . . . . . . eliminate parentheses
19x = 38 . . . . . . . . . simplify
x = 2 . . . . . . . divide by 19
-7(2) +y = -19 . . . . . substitute for x in the first equation
y = -5 . . . . . . add 14
The solution is (x, y) = (2, -5).
PLS ANSWER AS SOON AS POSSIBLE
Help pretty please it’s 4:30 rn and I’m trying to get this done
Answer:
8b is 1.5*10^4=1.5*10000=15000
9. is 100*1.1=110meters to 100 yards
Hope This Helps!!!
Answer:
91
Step-by-step explanation:
PLZ HELP ME!! IF YOUR A GENUIS
The equation 4.05p+14.40=4.50(p+3) represents the number of p of pounds of penuts you need to make a trail mix. How many pounds of peanuts do you need for the trail mix?
Since "p" represents the number of pounds of peanuts and:
4.05p + 14.40 = 4.50(p + 3) [then by distributing we have:
4.05p + 14.40 = 4.50p + 13.5 [then by subtracting 13.5 from both sides we have:
4.05p + 0.9 = 4.50p [then by subtracting 4.05p from both sides we have:
0.9 = 0.45p [then by dividing both sides by 0.45 we have:
2 = p
So there are 2 pounds of peanuts needed for the trail mix.
3 3/8 divided by 1 1/4
Answer:
Step-by-step explanation:
3 3/8 changes to 27/8 because we multiply 3*8=24 and then add 24 to 3 = 27
same thing for 1 1/4
and then while dividing we flip the left hand side meanig 5/4 becomes 4/5 and division changes to multiplication
Solve the inequality
4x - 19 ≥ -27
The answer is X>-2. I uploaded a picture of the steps below. Hope this helps. :)
Isa is building a picture frame. The perimeter of the frame is 114 cm. If the frame is 30 cm tall, how wide is it? And how much cloth Isa will need to cover the frame?
Answer:
810 cm squared
Step-by-step explanation:
30 = height
multiply 30 by 2 = 60
subtract 60 from 114 = 54
divide 54 by 2 = 27 = width
multiply 27 x 30 to get 810 cm squared
find the value of x from the following figure
Answer: 70°
Oki so...
The corresponding angle in a transversal line cut by a parallel line is equal. So in this case, angle QSP is 110°
Line PSR is a straight line and a straight line angle is 180°
So, 180-110=70° (angle QSR)
Now that you know the two angle of the triangle is 40° and 70° and that a triangle is 180°
Simply, 180-(40+70)
This comes 70. So x is 70°
pls help me im stuck and i need to pass this lesson
What is the value of y?
Answer : i believe 100 X is 13 Z is 12
Step-by-step explanation:
sorry if im wrong
If y varies directly as x, find y:
{(8, -12). (20, y)}
[tex]\\ \sf\longmapsto x_1y_2=x_2y_1[/tex]
[tex]\\ \sf\longmapsto 8y=-12(20)[/tex]
[tex]\\ \sf\longmapsto 8y=-240[/tex]
[tex]\\ \sf\longmapsto y=-240/8[/tex]
[tex]\\ \sf\longmapsto y=-60[/tex]
can someone help with this
Answer:
y=-2/3
x=-20/3
Which expression is equal to the expression below ( 6.9)5
Answer:
270 or 34.5
Step-by-step explanation:
1. (6.9)= 54
54x5= 270
2. 6.9x5= 24.5
Hopes This Helps :)
Write the slope-intercept form of the equation of the line.
Answer:
y = x + 2
Step-by-step explanation:
By doing the rise over run, the slope is 1
The y - intercept is 2
You plug the numbers in the equation y = mx + b
y = x + 2
3
3
3
3
3
I pentagon
2 pentagons
3 pentagons
Represent the relationship using a table. Complete the table below.
Number of Perimeter,
Pentagons, X
1
Ordered
Pair (x,y)
2
3
(Simplify your answers.
The relationship between the number of pentagons and the perimeter will be
[tex]x=1,y=15,(x,y)=(1,15)\\x=2,y=29,(x,y)=(2,29)\\x=3,y=43,(x,y)=(3,43)[/tex]
From the diagram in the question, each side of a pentagon has length [tex]3units[/tex].
Also, each time another pentagon is attached, a side is removed.
Using these observations, we can create a relationship between the number of pentagons, [tex]x[/tex], and the perimeter, [tex]y[/tex], as follows
For [tex]x=\text{number of sides}=1[/tex]
[tex]y=\text{perimeter}=3\times 5=15units[/tex]
For [tex]x=2[/tex]
[tex]y=3\times5+3\times5-1\\=15+15-1\\=29units[/tex]
For [tex]x=3[/tex]
[tex]y=3\times5+3\times5-1+3\times5-1\\=3\times5+3\times5+3\times5-1-1\\=15+15+15-2=43units[/tex]
The relationship will be
[tex]x=1,y=15,(x,y)=(1,15)\\x=2,y=29,(x,y)=(2,29)\\x=3,y=43,(x,y)=(3,43)[/tex]
Learn more about perimeter here: https://brainly.com/question/17756657
if f(x) = 2x-1 what is f(4)
GIVING BRAINLIEST. please help!
E Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select three options. 6 feet by 2 feet by 3 feet 6 feet by 5 feet by 4 feet 7 feet by 6 feet by 4 feet 8 feet by 3 feet by 7 feet 8 feet by 4 feet by 3 feet
Answer:
6feet by 5feet by 4feet
7feet by 6feet by 4feet
8feet by 3feet by 7feet
=
Let f(x) = 3x + 8, g(x) = 2x -12
and h(x) = -4x
=
1a) f + g =
1b) f-g=
2b) g*f=
2b) g-f=
Answer:
it's the 2nd one
Step-by-step explanation:
yeah it's the 2one
Korena is paid $40 it weed the garden 5 times. At this rate, how many times must she weed the garden to earn $100?
What we know:
Korena is paid $40 every five times she does the job
What we need to figure out:
How many times does she have to do it to earn $100
Math:
First I'm going to figure out how much she makes each time she weeds
Money earned ÷ Amount of times
40 ÷ 5
= 8
In order to determine the rest of the time we are going to multiply everything we know by 2
Korena is paid $80 if she does it 10 times
We clearly aren't going to do that again because that will surpass the amount so now we are going to use the unit rate we figured out;
($8 per time)
Korena is paid $88 if she does it 11 times
Korena is paid $96 if she does it 12 times
Korena is paid $104 if she does it 13 times
Statement
Therefore if Korena weeds the garden 13 times she will make $104 surpassing the $100 needed.
3 eggs weigh 120grams total. Assume each egg weighs the same, what is the Constant of Proportionality?
Answer:
let the weight of all the eggs be x g
therefore..
3x = 120
[tex] \\ x = \frac{120}{3} \\ x = 40g[/tex]
hope helpful~
The high school soccer booster club sells tickets to the varsity matches for $4 for students and $8
for adults. The booster club hopes to earn $200 at each match. Let x be the number of student
tickets and y be the number of adult tickets.
List some of the possible combinations of number of tickets they can sell to make $200.
Set up an equation:
4x + 8y = 200
200/4 = 50
200/8 = 25
They callus sell 50 student tickets and 0 adult tickets
They could sell 0 student tickets and 25 adult tickets.
They could sell 10 student tickets and 20 adult tickets
They could sell 10 adult tickets and 30 student tickets
Write an equation for the graph
Answer:
y=3x +4
Step-by-step explanation:
your y intercept is 4, go 3 down 1 across and that is the slope.
There is a string of red and blue lights strung around
a window. The red lights blink every 3 seconds, and
the blue lights blink every 5
seconds. How many
times will they blink at the same time in one
minutes?
Answer:
4 times because they will have the common number of 15 and since there is 60 seconds in a minute you would divide 60 by 15, and that equals 4
Step-by-step explanation:
Please show work!!!!
10. If the area of a parallelogram is 690.84 m2 and the height is 20.2 m, what is the length of the base?
Answer:
The length of the base of this parallelogram is 34.2
Step-by-step explanation:
To calculate the length, we work backward and calculate the base by doing area/height
We have 690.84/20.2 = 34.2
I hope this explained your confusion
scores on a test have a mean of 66 and Q3 is 80. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth.
A) 10.5
B) 20.9
C) 9.4
D) 18.7
You are given three cards. One card has the number 1 on it, another card has. 2, and the last card has the number 3 on it. Use two cards to make a fraction. What is the largest fraction that you can make?
Answer:
2/3
Step-by-step explanation:
I hope it's the answer. if it isn't tell me so that I can try it again bye.
an equivalent expression to x-2y+3
Answer:
[tex]y=\frac{-x-3}{-2}[/tex]
Step-by-step explanation:
1. The first thing you should do is put it equal to 0:
[tex]x-2y+3=0[/tex]
2. You want to get y by itself so the next thing you do is subtract 3 to the other side because it is being added right now. It should look like this:
[tex]x-2y+3=0[/tex]
-3 -3
[tex]x-2y=-3[/tex]
3. Since x is also being added on the left side of the equation you want to get x to the other side so you do the opposite of addition (subtraction) and subract the x to the other side of the equation:
[tex]x-2y=-3[/tex]
-x -x
[tex]-2y=-x-3[/tex]
4. The next thing you want to do is get rid of that -2. Right now it is being multiplied by the y and the opposite of multiplication is division, so you are going to want to divide -2 by both sides of the equation.
[tex]\frac{-2y}{-2} =\frac{-x-3}{-2}[/tex]
5. The -2's cancel out and the right side of the equation cannot be simplified anymore which makes the new or equivalent equation:
[tex]y=\frac{-x-3}{-2}[/tex]