Given f(x) = the quantity of 4x plus 1, divided by 3, solve for f−1(3).
2
4
6
8
Answers
Answer:
2
Step-by-step explanation:
Here, the given function is,
f(x) = The quantity of 4x plus 1, divided by 3
[tex]\implies f(x)=\frac{4x+1}{3}[/tex]
The steps that involve in finding the inverse of f(x) are as follows,
Step 1 : Replace f(x) by y,
[tex]y=\frac{4x+1}{3}[/tex]
Step 2 : Switch x and y,
[tex]x=\frac{4y+1}{3}[/tex]
Step 3 : Isolate y in the left side of the equation,
[tex]3x=4y+1[/tex]
[tex]-4y=1-3x[/tex]
[tex]y=\frac{1-3x}{-4}[/tex]
[tex]y=\frac{3x-1}{4}[/tex]
Step 4 : Replace y by [tex]f^{-1}(x)[/tex],
[tex]f^{-1}(x)=\frac{3x-1}{4}[/tex]
For x = 3,
[tex]f^{-1}(3)=\frac{3\times 3-1}{4}=\frac{9-1}{4}=\frac{8}{4}=2[/tex]
Hence, First option is correct.
Related Questions
Fill in the blank:
To find the values of p, q, r and s, you should start by finding all factor ___ of the leading coefficiant and constant term. Then try them to determine which ones give you the correct product ...?
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for questions 1-2, find the x- and y-intercept of the line.
1. -10x+5y+40
a) x-intercept is 5; y- intercept is -10
b) x-intercept is 8; y-intercept is -4
c) x-intercept is -10; y-intercept is 5
d) x-intercept is -4; y-intercept is 8
2. 5x+4y=80
a) x-intercept is 4; y-intercept is 5
b) x-intercept is 20; y-intercept is 16
c) x-intercept is 5; y-intercept is 4
d) x-intercept is 16; y-intercept is 20
Answers
1 is c and 2. is d
What is the value of x in 5(2x - 7)=15x-10?
Answers
3.1 Pull out like factors :
-5x - 25 = -5 • (x + 5)
4.1 Solve : -5 = 0
This equation has no solution.
A a non-zero constant never equals zero.
4.2 Solve : x+5 = 0
Subtract 5 from both sides of the equation :
x = -5
The value of x in 5(2x - 7)=15x-10 is 5
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Here, the Algebraic expressions with variable in x is given :
5(2x - 7)=15x-10
which is solved using properties of multiplication and solving for value x by arranging variables and constant separately aside:
5(2x - 7)=15x-10
20x - 35 = 15x -10
20x -15x = 35-10
5x = 25
x= 5
Therefore, the value of x in 5(2x - 7)=15x-10 is 5
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round 2.36 to 1 significant figure
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Rounding 2.36 to 1 significant figure results in 2, as the first non-zero digit remains unchanged when the subsequent digit is less than 5.
Explanation:To round 2.36 to 1 significant figure, you look at the first non-zero digit, which is 2. Since the digit following it (3) is less than 5, the number 2 remains unchanged, and any digits after the 3 are dropped. Therefore, the number 2.36 rounded to 1 significant figure is simply 2.
To round 2.36 to 1 significant figure, we look at the digit after the first significant figure. If this digit is less than 5, we round down. If it is 5 or greater, we round up. In this case, the digit after the first significant figure is 6, which is greater than 5, so we round up. The rounded number to 1 significant figure is 2.4.
A fast food restaurant sells between 164 and 328 hamburgers per day. If the company profits $82.00 per 82 hamburgers sold, approximately how much does the company profit in one year from hamburgers?
PLZZZZZZ HELPPPP !!!!!!!!!!
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Approximate profit in one year from hamburgers will be $59860 to $119720.
What is unitary method?The unitary method is used to find the value of a single unit from a given multiple
How much does the company profit in one year from hamburgers?A fast food restaurant sells between[tex]164[/tex]and [tex]328[/tex] hamburgers per day. If the company profits [tex]$82.00[/tex] per [tex]82[/tex] hamburgers sold which mean they make [tex]$1[/tex] profit for one unit of burger sold.
Thus a year being of [tex]365[/tex] days the profit the company will make after selling [tex]164[/tex] to [tex]324[/tex] units of burger will be $59860 to $119720.
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Find The Distance Between (6,1) and (-2,-4)
Answers
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
Answers
multiply first equation by 3 and subtract it from second.
it will become
3x + 3y = 72
after subtracting from second we get:
2y = 28
y = 14
x = 24 - 14 = 10
We can conclude that there are more 5 points question. there are 10 three point questions and 14 five point questions.
For you to see in a mirror, light must be
refracted
reflected
concaved
conducted
Answers
Probably shouldn't put this as a math question
So, option B is your answer.
Hope this helps!
WILL UPVOTE PLEASE HELP
Question 4:
Ellen wants to purchase a book that is regularly priced at $18. The book is discounted 15%. She also needs to pay a 6% sales tax on the discounted price.
What is the total amount Ellen will pay for the book?
Enter your answer in the box.
Answers
3 times the sum of 1/3 of a number and 8 is 11
Answers
11=(3x+25)
3x=-14
x = -14
3
What is the sum?
7/2+(-3/5)
Answers
The lengths of the sides of a triangle are 3x, 5x – 12, and x + 20. Find the value of x so that the triangle is isosceles. ...?
Answers
Any two side are equal in isoscles triangle
5x-12=x+20
4x=32
x=8
5x-12=28
x+20=28
5x=40
28,28,40
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Final answer:
To find the value of x for the triangle to be isosceles, we set the lengths of any two sides equal to each other and solve for x. After testing different cases, we find that x equals 10 satisfies the condition for the triangle to be isosceles.
Explanation:
For a triangle to be isosceles, at least two sides must have equal length. We're given the side lengths as 3x, 5x - 12, and x + 20. We have two cases to consider to find the value of x for the triangle to be isosceles:
Case 1: 3x = 5x - 12
Case 2: 3x = x + 20 or 5x - 12 = x + 20
To solve for x in case 1, we equate the two expressions and solve as follows:
3x = 5x - 12
2x = 12
x = 6
However, if we substitute x = 6 into the third side (x + 20), we get a length of 26, which does not equal either of the first two sides. Therefore, x = 6 does not satisfy the condition for an isosceles triangle.
For case 2, we consider 3x = x + 20:
3x = x + 20
2x = 20
x = 10
By substituting x = 10 into 5x - 12, we get 50 - 12 = 38. We can see that two sides of the triangle are 30 and 30 (since 3x equals 3(10)), confirming that the triangle is isosceles with x equal to 10.
When the nth root of a is written, it is the positive value that is shown
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two numbers that multiply to 120 and add to 29
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the price of an item has been reduced by 65% . the original price was $41 .
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41 ÷ 2 = 20.5. = 50%
41 ÷ 10 = 4.1 = 10%
4.1 ÷ 2 = 2.05 = 5%.
20.5 + 4.1 + 2.05 = 26.65 = 65%
41 - 26.65 = $14.35 (the answer)
3x-1 divided by 2=10 Determine the solution
Answers
(3x-1)/2 = 10
3x-1 = 10*2
3x = 20 + 1
x = 21 / 3
x = 7
So, your final answer is 7
Hope this helps!
A conical paper cup has dimensions as shown in the diagram. How much water can the cup hold when full?
Answers
94.2 cm divided by pi which is 3.14 equals to 30 evenly hoped this helped yall out
The volume of the conical cup is approximately 94.25 cm³. This is the amount of water it can hold when full.
To find the volume of the conical paper cup, we'll use the formula for the volume of a cone:
[tex]\[ V = \frac{1}{3} \times \pi \times r^2 \times h \][/tex]
Where:
- ( V ) is the volume of the cone
- ( pi ) is a constant (approximately 3.14159)
- ( r ) is the radius of the circular base of the cone
- ( h ) is the height of the cone
Given:
- ( r = 3 ) cm (half the diameter)
- ( h = 10 ) cm
Substituting the given values into the formula:
[tex]\[ V = \frac{1}{3} \times \pi \times (3^2) \times 10 \][/tex]
[tex]\[ V = \frac{1}{3} \times \pi \times 9 \times 10 \][/tex]
[tex]\[ V = \frac{1}{3} \times 90\pi \][/tex]
[tex]\[ V = 30\pi \][/tex]
Now, let's calculate the approximate value of [tex]\( \pi \)[/tex] which is 3.14159:
[tex]\[ V \approx 30 \times 3.14159 \][/tex]
V≈94.2477
So, the volume of the conical paper cup is approximately [tex]\( 94.2477 \, \text{cm}^3 \) or \( 94.25 \, \text{cm}^3 \)[/tex] rounded to two decimal places. This is the amount of water the cup can hold when full.
"In ABC, mBAC = 5x + 8, mABC = 6x + 22, and mBCA = 3x 25.
A.Find the value of x.
B.Find the measure of 3. Show your work."
Answers
Actually, the answer is 12.5
5x+8+6x+22+3x+25= 180
(5x+6x+3x)+(8+22-25)= 180
14x+5=180
14x+(5-5)=180-5
14x=175
14x/14=175/14
X=12.5
Double check:
(5*12.5)+8=70.5
(6*12.5)+22= 97
(3*12.5)-25=12.5
70.5+97+12.5=180 degrees.
So, x=12.5
jacob has exactly 84 cents in his pocket.he only has dimes and quartere. how many pennies does he have if he has 3 dimes
Answers
3 times 10=30
30 cents are dimes
84=dimes+quarters
84=30+quarters
minus 30
54=quartesr
that can't be right
quartesr go like this
1 quarter=25
2 quarter=50
3 quarters=75
maybe there are pennies even though a penny is neither a dime nor a quarter
2 quarters make 50
4 pennies make the last 4
I guess 4 pennies
What is the relative maximum and minimum of the function?
f(x)=x^3+6x^2-36
The relative maximum is at (–6, 216) and the relative minimum is at (2, –40).
The relative maximum is at (–6, 40) and the relative minimum is at (2, –216).
The relative maximum is at (6, 216) and the relative minimum is at (–2, –40).
The relative maximum is at (6, 40) and the relative minimum is at (–2, –216).
Answers
f'(x)=3x^2+12x
find where it equals zero
it equal zero at x=0 and x=-4
find the y values
f(0)=-36
f(-4)=-4
the critical points are (0,-36) and (-4,-4)
make sign chart
evalutat f'(x) at x=-5 and x=-1 and x=1, and see their signs
f'(-5)=(+)
f'(-1)=(-)
f'(1)=(+)
see below attachment
max is where sign changes from (+) to (-)
min is where sign changes from (-) to (+)
so
max at (-4,-4)
min at (0,-36)
none of the options are correct, do you have te right problem?
Which is not a property of all similar triangles
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0.63 =1.00 0.634 plus what equals a dollar
Answers
0.63 + 0.37 = 1.00
I hope I was somewhat helpful~
Best Regards~ Sans
or round it to 0.37
A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation 2x3 + 8x2 = 450 can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.
4 inches
5 inches
9 inches
10 inches
Answers
The length of the side of the original cube in the given scenario is 5 inches.
A cube is a three-dimensional figure with equal sides.
Given that
The length of the edge of a cube = x
Also, one of the sides is increased by 4 inches, and another side is doubled,
so, now the new dimensions are x, x+4, 2x, and the shape is a rectangular prism.
The area of the rectangular prism = 450 sq. inches
base × height × length = 450 sq. inches
x × (x + 4) × 2x = 450
2x³ + 8x² = 450
2x³ + 8x² - 450 = 0
x³ + 4x² - 225 = 0
Substitute x=5 to see that it is a root of the equation,
5³ + 4(5)² - 225 = 125 + 100 - 225 = 0
So, x - 5 is a factor of the equation,
Now,
x³ + 4x² - 225 = (x−5)(x² + 9x + 45) = 0
The roots of the quadratic equation are imaginary as
D = 9² - 4 × 1 × 45 = 81 - 180 = -99
The discriminant is negative, therefore, the roots are not real.
So, the length of the side of the original cube is 5 inches.
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Which relation is a direct variation that contains the ordered pair (2, 7)?
Y=4x-1
y=2/7x
y=7/2x
y=7/x
Answers
y = kx + n
Direct variation in simple is equation of a line which has n=0 or in other words which y to x ratio is k.
First option gets 7=7 but it isnt direct variation because n is not equal to 0
third option is indeed correct. once we implement coordinates (2,7) we get 7=7
Answer is
y = 7/2x
Answer: The guy up above, is correct. The answer is D
Step-by-step explanation: Edge 2021
Reduce this algebraic fraction 27c^4d^5/9c^7d^4 ...?
Answers
The fraction is: [tex] \frac{27 c^{4} d^{5}}{9 c^{7} d^{4} } [/tex]
Let's rewrite it: [tex]\frac{27 c^{4} d^{5}}{9 c^{7} d^{4} }= \frac{27}{9}*\frac{c^{4}}{c^{7}}*\frac{d^{5}}{d^{4} }[/tex]
Now, let's use the rule [tex] \frac{ x^{a} }{ x^{b}} = x^{a-b} = \frac{1}{ x^{b-a} } [/tex]:
[tex]\frac{27}{9}*\frac{c^{4}}{c^{7}}*\frac{d^{5}}{d^{4} }=3* \frac{1}{c^{7-4}} * d^{5-4} =3* \frac{1}{ c^{3} } *d^{1}= \frac{3d}{ c^{3} } [/tex]
a radius is a segment that connects any point on the circle to any point inside of that circle
true or false?
Answers
The radius is a line that connects any point on the circle to center. Radius is a constant size line and not line that changes its size therefore it cannot connect any point on circle to any point inside of that circle.
Answer:
If the question is to the center of that circle instead of "any point inside of that circle" then the answer is true.
Step-by-step explanation:
I got it wrong because I didn't read it all but it is true if it is to any point inside of that circle.
Which of the following correctly expresses the number below in scientific notation? 0.00000765
A. 7.65 • 10-6
B. 7.65 • 10-7
C. 7.65 • 10-5
D. 76.5 • 10-7
E. 765 • 10-8
F. 765 • 10-6
Answers
Should be 7.65 * 10^-6
In scientific notation, 0.00000765 is written as 7.65 • 10-6. This represents the number of places to the right of the decimal point to the first non-zero digit.
Explanation:The task is to express the number 0.00000765 in scientific notation. Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in standard decimal form. It is commonly used in science and mathematics.
We have to determine which of the given options correctly represents this number in scientific notation.
The number 0.00000765 can be written as 7.65 times ten to the negative sixth power. This is because there are six places to the right of the decimal point before we encounter the first non-zero digit. Therefore, the correct answer is 7.65 • 10-6.
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simplify this expression 1x/18x
Answers
Answer: 1/18
Step-by-step explanation: The x's basically cancel each other out so all that is left is the 1 and the 18
which even number is not a composite number2, 8, 4, 6
Answers
Janet’s car insurance payment decreases by $30 each year. which expressions represent the total change in her payment, in dollars, after 44 years?
Answers
The total change in Janet's car insurance payment after 44 years is $1320.
Explanation:To find the total change in Janet's car insurance payment after 44 years, we can use the formula:
Total change = decrease per year × number of years
In this case, the decrease per year is $30 and the number of years is 44. So the expression representing the total change in her payment would be:
Total change = $30 × 44 = $1320
Therefore, Janet's car insurance payment will decrease by $1320 after 44 years.