question is attached
Hello!
[tex]\large\boxed{f^{-1} = \frac{5x+2}{4x-2}, f^{-1}(3) = \frac{17}{10} }[/tex]
[tex]f(x) = \frac{2x +2}{4x - 5}[/tex]
Find the inverse by swapping the x and y variables:
[tex]y = \frac{2x +2}{4x - 5}\\\\x = \frac{2y +2}{4y - 5}[/tex]
Begin simplifying. Multiply both sides by 4y - 5:
[tex]x(4y - 5) = 2y + 2[/tex]
Start isolating for y by subtracting 2 from both sides:
[tex]x(4y - 5) -2 = 2y[/tex]
Distribute x:
[tex]4yx - 5x - 2 = 2y[/tex]
Move the term involving y (4yx) over to the other side:
[tex]- 5x - 2 = 2y - 4yx\\\\[/tex]
Factor out y and divide:
[tex]- 5x - 2 = y(2 - 4x)\\\\y = \frac{-5x-2}{-4x+2} \\\\y = \frac{-(5x + 2)}{-(4x - 2)} \\\\y^{-1} = \frac{5x + 2}{4x - 2}[/tex]
Use this equation to evaluate [tex]f^{-1}(3)[/tex]
[tex]f^{-1}(3) = \frac{5(3) + 2}{4(3) - 2} = \frac{17}{10}[/tex]
-3x + 8 = 11
pls help
Answer:
x=-1
Step-by-step explanation:
A band earned $550.00 for playing at a concert. Their manager takes 15% of the money earned for each show and the band is donating 20% of the money earned to charity. How much money is left for the band to split?
Answer:
The amount of the money earned left for the band to split is $357.5
Step-by-step explanation:
The amount the band earned for playing at the concert = $550.00
The percentage of the money earned taken by the manager = 15%
The percentage of the money earned the band is donating to charity = 20%
The amount of the money earned the manager takes = 15/100 × 550 = 82.5
∴ The amount of the money earned the manager takes = $82.5
The amount of the money earned that is donated to charity = 20/100 × 550 = 110
∴ The amount of the money earned that is donated to charity = $110
The amount of the money earned left for the band to split = $550 - $82.5 - $110 = $357.5.
Easy points if u know it
Answer:
True
Step-by-step explanation:
The formula for the area of a circle is πr² where r is the radius. So if 3 is the radius, plug it into the formula:
π(3²)
Simplify it:
π(9)
This can be rewritten as:
9π
So, the answer is true
Hope this helps! :)
What additional information do you need to prove triangle NOP is congruent to triangle QSR?
Answer:
Angle O congruent to Angle S, because this would pass the SAS proof. (Side Angle Side)
PLEASE HELP ASAP!!!
I will mark brainliest if there are multiple answers!!!
Answer:
80%
Step-by-step explanation:
Not so sure about the answer, but hopefully it helps.
I can't figure out it's multiple choice
Answer:1,5
Step-by-step explanation:
gimme brainliest
A set of 6 water bottles are sold for 12. What is the unit cost per water bottle?
$2.00 US Dollars is the answer
I really need some help somebody
Simplify all four questions correctly-
(p - 3) + (p - 7)
(3n - 1) + ( -n + 4)
(-t + 5) + (3t + 2)
(7k + 9) + (4k - 3)
Answer:
1. 2p - 10
2. 2n + 3
3. 2t + 7
4. 11k + 6
Step-by-step explanation:
The temperature was 8 degrees below zero at 5 A.M. By 1 P.M. the temperature had risen 23 degrees. What was the temperature at 1 P.M.?
Answer:
15 degrees
Step-by-step explanation:
Write y= -1(x-4.5)^2 + 15.25 in standered form
Given:
The equation is
[tex]y=-1(x-4.5)^2+15.25[/tex]
To find:
The standard form of the given equation.
Solution:
We have,
[tex]y=-1(x-4.5)^2+15.25[/tex]
It is a quadratic equation.
The standard form of a quadratic equation is [tex]y=ax^2+bx+c[/tex]. So, we need to write the given equation in this form.
[tex]y=-(x-4.5)^2+15.25[/tex]
[tex]y=-[x^2-2(x)(4.5)+(-4.5)^2]+15.25[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]y=-[x^2-9x+20.25]+15.25[/tex]
[tex]y=-x^2+9x-20.25+15.25[/tex]
[tex]y=-x^2+9x-5[/tex]
Therefore, the required equation in standard form is [tex]y=-x^2+9x-5[/tex].
28. (03.05 MC) Martin walked away from his school at a constant velocity for the first 30 seconds. He realized that he had to pick up a book from his friend's house which he had already passed. He turned around and walked to his friend's house at a constant velocity for 10 seconds. He stopped at his friend's house for 40 seconds and then walked away from school again at a constant velocity for the next 20 seconds. Which of the following graphs best represents Martin's motion? (5 points) First straight line joins ordered pairs 0, 0 and 40, 25, second straight line joins 40, 25 and 80, 25, and third straight line joins 80, 25 and 100, 10 First straight line joins ordered pairs 0, 0 and 30, 25, second straight line joins 30, 25 and 40, 20, and third straight line joins 40, 20 and 100, 50 First straight line joins ordered pairs 0, 0 and 30, 25, second straight line joins 30, 25 and 40, 20, third straight line joins 40, 20 and 80, 20, and fourth straight line joins 80, 20 and 100, 10 First straight line joins ordered pairs 0, 0 and 30, 25, second straight line joins 30, 25 and 40, 20, third straight line joins 40, 20 and 80, 20, and fourth straight line joins 80, 20 and 100, 50
Answer:
The answer is A
Step-by-step explanation:
I did it in FLVS
HELP ASAP
What is the slope of the line?
Answer:
-1
Step-by-step explanation:
What is the sum of -1/2 and 8/6 please help
Solve -3n+2≥-4n-3............
Answer:
It is a two step equation
Step-by-step explanation:
First you have to solve the first part then solve the second part :)
Answer:
n ≥ − 5
Step-by-step explanation:
Move all terms containing
n to the left side of the inequality.
n + 2 ≥ − 3
Move all terms not containing
n to the right side of the inequality.
n ≥ − 5
The result can be shown in multiple forms.
Inequality Form: n ≥ − 5
interval Notation: [ − 5 , ∞ )
Write the prime factorization of 42. Use exponents when appropriate and order the factors from least to greatest (for example, 22
Answer:
2 * 3 * 7 = 42
Step-by-step explanation:
2,3 and 7 are prime numbers
Can somebody help outtt ?? pleasee
Answer:
y=71
x=109
Step-by-step explanation:
Nohdjxjxhxhxhdhdjdjfjdjdhfhfjfjfj
Answer:
gfdxkcgftdkrxclfdrkyxcfdretkx
Step-by-step explanation:
please please help me im just gonna spam the questions that i dont know until people start answering
Answer:A
Step-by-step explanation:
When graphed it is the only one to semi-complete the pattern
which postulate or theorem justifies the congruence statement, ABE is congruent to CDE?
- SSS
- SAS
- ASA
- AAS
Answer:
SAS
Step-by-step explanation:
Hope this helps:)
Answer:
SAS
Step-by-step explanation: You can use vertical angles congruence theorem for angles AED and BEC which gives you an angle, using taht info you can detremine that its SAS
can you help plzzz
Answer:
1.1 ithink
Step-by-step explanation:
The lines graphed below are perpendicular. The slope of the red line is 4 what is the slope of the green line
m=
Answer:
m=-1/4
Step-by-step explanation:
Perpendicular lines are negative reciprocals.
So if you have a slope of m= 4x you can break it up into, two parts
m= -4x
this is the negative^
and the reciprocal of m= -4x is m= -1/4x
The slope of the green line if the lines are perpendicular would be -1/4.
How to find if two lines are perpendicular to each other?If two lines are perpendicular to each other, then their slopes are negative reciprocal of each other.
That means, if one line's slope is 'a', then its perpendicular line's slope would be -1/a.
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
For the two lines two be perpendicular, the product of their slope must be -1.
Let the slope of the red and green line be m1 and m2.
Given the following
The Slope of red line = 4
According the definition, we get,
4m2 = -1
m2 = -1/4
Hence, the slope of the green line if the lines are perpendicular is -1/4
Learn more on perpendicular lines here:
brainly.com/question/1202004
#SPJ5
What is the value of x ?
It is already to late to answer this because my final was due yesterday:
What percent is increase if the boy had 12 comic books and bought mores so now he has 15 comic books.
Answer:
increase by 25%
Step-by-step explanation:
15-12=3
12÷3=4
4=25%
Use the triangle to answer the question. What is the value of x?
Answer:
B). 48
Step-by-step explanation:
48•64=3072
3072÷64=48
Answer:
value of X=180-(48+48)
=180-96
=84
Plz solve this as soon as possible it is due today, all it is is yes or no
Answer:
1 Rational, Integer
2 Rational
3 Rational, Whole
4 Rational , Whole
5 Rational
6 Rational
7 Rational
8 Rational
Step-by-step explanation:
Pretty sure this is correct
14 butter cookies 7 oatmeal cookies
Answer:
what?
Step-by-step explanation:
can you give me some more details
write an equation in slope-intercept form for the line. slope=4,y-intercept=3
Answer:
y = 4x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 4 and c = 3, then
y = 4x + 3 ← equation of line
6x-(2x-9)=-31 whats x?
Answer: [tex]x = -10[/tex]
Step-by-step explanation:
Hey there! I hope these steps will help you accomplish this problem :)
Step 1: Remove the parentheses.
[tex]6x - 2x + 9 = -31[/tex]
Step 2: Simplify.
[tex]6x - 2x + 9[/tex] to [tex]4x + 9[/tex].
[tex]4x + 9 = -31[/tex]
Step 3: Subtract 9 from both of the sides.
[tex]4x = -31 - 9[/tex]
Step 4: Simplify.
[tex]-31 - 9[/tex] to [tex]-40[/tex].
[tex]4x = -40[/tex]
Step 5: Divide both of the sides by 4.
[tex]x = -\frac{40}{4}[/tex]
Step 6: Simplify.
[tex]\frac{40}{4}[/tex] to [tex]10[/tex].
[tex]x = -10[/tex]
Answer:
Step-by-step explanation:
Here you go mate
step 1
6x-(2x-9)=-31 equation
step 2
6x-(2x-9)=-31 simplify
6x+-1(2x-9)=-31
step 3
6x+(-1)(2x-9)=-31 distribute
6x+-1(2x)+(-1)(-9)=-31
6x+-2x+9=-31
step 4
(6x+-2x)+(9)=-31 combine the terms that are alike
4x+9=-31
step 5
4x+9(-9)=−31(-9) subtract-9
4x=-40
step 6
4x/4=-40/4 divide by 4 because 4 is a number that can make the division easier
answer
x=-10
