Answers
Answer:
B; 1
Step-by-step explanation:
Firstly, we need to find the inverse of the given function
Let us have f(x) as y
To find the inverse, we set out to make x the formula subject
Thus;
y = √(3x + 6)
square both sides
y^2 = 3x + 6
3x = y^2 - 6
x = (y^2 - 6)/3
To write the inverse, replace y by x
So we have the inverse of the function as ;
(x^2 - 6)/3
So what we have to do here is to substitute 3 for x in the inverse
We have this as;
(3^2 -6)/3
(9-6)/3
= 3/3 = 1
Answer:
1 ( option B )
Step-by-step explanation:
The given equation is ,
[tex]\implies f(x) =\sqrt{ 3x + 6 }[/tex]
Now substituting y = f(x) , we have ,
[tex]\implies y=\sqrt{ 3x + 6 }[/tex]
For finding the inverse , Interchange x and y , we have ,
[tex]\implies x =\sqrt{ 3y + 6 }[/tex]
Now solve for y , we have ,
[tex]\implies x ^2=3y + 6 \\\\\implies 3y = x^2-6 \\\\\implies y =\dfrac{x^2-6}{3} [/tex]
Now replace y with f-¹(x) , we have ,
[tex]\implies f^{-1}(x) =\dfrac{x^2-6}{3} [/tex]
Now put x = 3 , we have ,
[tex]\implies f^{-1}(3) =\dfrac{3^2-6}{3}\\\\\implies f^{-1}(3) = \dfrac{9-6}{3}\\\\\implies \underline{\underline{ f^{-1}(3) = 1 }} [/tex]
Related Questions
In a 60 sheet package of construction paper there are 15 yellow sheets what is the probability that a randomly selected sheet will be yellow
Answers
Answer:
15/60 or 1/4, which is 25%
Step-by-step explanation:
Which equations are true? Choose all that apply.
A. 15^0=15
B. (8^3) (8^6)= 8^9
C. 5^2 = 1/5-3
D. (6^5)^3 = 6^15
E. 3^7/3^9 = 3^-2
Answers
Answer:
B, D, E
Step-by-step explanation:
A) anything to the zero power equals one
B) when bases are the same and being multiplied, add their exponents
C) 5² = 25
D) when parentheses separate exponents, they should be multiplied
E) when bases are the same being divided, subtract their exponents
30 points for right answer +brainliest plz plz plz helpp!
due in 10 mins where i live plz help!!!!!!!!!!!!!!!!!!hurryy
Answers
Answer:
Number one is 48 ft and number two is 92 in.
5 b = - 25 for algebra
Answers
Answer:
b= -5
Step-by-step explanation:
because 5x-5=-25
-25 divided by 5 = -5
b= -5
What is the solution of log(2f+4)=log(14-3f)
A)-18
B)-2
C)2
D)10
Answers
Answer:
f = 2
Step-by-step explanation:
equate the log
therefore,
2f + 4 = 14 - 3f
collect like terms
2f + 3f = 14 - 4
5f = 10
divide through by 5
f = 10/5
f = 2
A stack of 500 pieces of paper is 2 inches tall. How tall is a stack of 250 pieces? 100 pieces? 10 pieces?
Answers
100 is 0.4 inch
10 is 0.04 inch
(4rxt – 8r2x + x²) – (6rx² + 5rxt – 2x)
Find the sum or difference
Please help! I’m stuck and can’t figure it out
Answers
Answer:
[tex]sum = (4 - 5)rxt - (8 + 6) {rx}^{2} + (1 + 2)x \\ = - rxt - 14 {rx}^{2} + 3x \\ \\ difference = (4 + 5)rxt + (6 - 8) {rx}^{2} + ( - 2 + 1)x \\ = 9rxt - 2 {rx}^{2} - x[/tex]
[tex] \small{ \underline{{ \blue{becker}}}}[/tex]
How many times larger is 3 x 10^8 than 3 x 10^2
A: 1 x 10^-6
B: 1 x 10^4
C: 1 x 10^6
D: 1 x 10^10
Answers
Answer:
Your answer is C
Step-by-step explanation:
You should look at the exponent. Once you figure out the difference between the two exponents then you get your answer.
List the kinds of measurements have you worked with so far. Describe what area is. Describe what volume is.
How could you find the combined area of all faces of a three-dimensional shape? Give an example of why that would be a good measurement to know.
Answers
2. area is how much space is within a 2D shape.
3. Volume is the amount of mass that a 3D shape takes up.
4. You find the combined area of a 3D shape by finding the individual area of each shapes on the outside of the 3D shape and then add them up.
5. i’m not sure what you mean by “give an example of why that would be a good measurement to know”
Answer:
In the passed I've used measurement cups, rulers, addition, subtration, and multiplication too.
Step-by-step explanation:
Stay Safe <3 =3 Can I maybe Get Brainliest?
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the
second equation is substituted into the first equation
3x + 2y = -21
x - 3y = 4
3(3y + 4) + 2y = -21
3(-3y + 4) + 2y = -21
3x + 2(3y + 4) = -21
3x + 2(-3y + 4) = -21
Answers
Answer:
answer is
3(3y+4) + 2y = -21 .
The box-and-whisker plot below represents some data set. What percenta data values are less than 66?
Answers
Given:
The a box-and-whisker plot if a data set.
To find:
The percentage of data values that are less than 66.
Solution:
From the given box-and-whisker plot, it is clear that the number 66 is the highest value of the data set.
It means all the values of the data set are less than 66 and no value can be more than 66.
All value means 100%.
Therefore, 100% of data values are less than 66.
Consider triangle ABC.
What is the value of y in the triangle?
С
809
Angle y =
B В
Answers
Answer:
50
Step-by-step explanation:
Factor using the x method
( please do not answer without showing work )
Answers
Answer:
[tex]5(x + 10)(10x - 3)[/tex]
Step-by-step explanation:
We are factoring
[tex]50x^{2} + 485x - 150[/tex]
So:
((2•5^2x^2) + 485x) - 150
Pull like factors :
50x^2 + 485x - 150 = 5 • (10x^2 + 97x - 30)
Factor
10x^2 + 97x - 30
Step-1: Multiply the coefficient of the first term by the constant 10 • -30 = -300
Step-2: Find two factors of -300 whose sum equals the coefficient of the middle term, which is 97.
-300 + 1 = -299
-150 + 2 = -148
-100 + 3 = -97
-75 + 4 = -71
-60 + 5 = -55
-50 + 6 = -44
-30 + 10 = -20
-25 + 12 = -13
-20 + 15 = -5
-15 + 20 = 5
-12 + 25 = 13
-10 + 30 = 20
-6 + 50 = 44
-5 + 60 = 55
-4 + 75 = 71
-3 + 100 = 97
Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 100
10x^2 - 3x + 100x - 30
Step-4: Add up the first 2 terms, pulling out like factors:
x • (10x-3)
Add up the last 2 terms, pulling out common factors:
10 • (10x-3)
Step-5: Add up the four terms of step 4:
(x+10) • (10x-3)
Which is the desired factorization
Thus your answer is
[tex]5(x + 10)(10x - 3)[/tex]
Answer:
[tex] \displaystyle \rm 5({x}^{} + 10)( 10x - 3)[/tex]
Step-by-step explanation:
we would like to factor out the following expression:
[tex] \displaystyle {50x}^{2} + 485x - 150[/tex]
notice that, in every term there's a common factor of 5 thus factor it out:
[tex] \displaystyle 5( {10x}^{2} + 97x - 30)[/tex]
now we have to rewrite the middle term as sum or substraction of two different terms in that case 100x-3x can be considered:
[tex] \displaystyle 5( {10x}^{2} + 100 - 3x - 30)[/tex]
factor out 10x:
[tex] \displaystyle 5( 10({x}^{2} + 10)- 3x - 30)[/tex]
factor out -3:
[tex] \displaystyle \rm 5( 10x({x}^{} + 10)- 3(x + 10))[/tex]
group:
[tex] \displaystyle \rm 5({x}^{} + 10)( 10x - 3)[/tex]
and we are done!
hence,
our answer is B)
The perimeter of a square garden is 54 feet. What is the length of one side of the garden?
Answers
Answer: 13.5
Step-by-step explanation:
54/4 = 13.5
13.5 x 4 = 54
The graphs of linear functions fand g are shown on the grid.
which function best represented by the graph of g
Answers
Answer:
g(x) = 3f(x)
Step-by-step explanation:
We can see that for function g;
When x = 1, y = 3
When x = 2, y = 6
When x = -1, y = -3
When x = -2, y = -6
For function f;
When x = 1, y = 1
When x = 2, y = 2
When x = -1, y = -1
When x = -, y = -2
We can see that the output of g(x) is always 3 times that of f(x) for same values of x.
Thus;
g(x) = 3f(x)
Find the circumference of each of the circles described below.
a. Radius of 3 inches
b. Diameter of 27 cm
Answers
Answer:
a) 18.85 or 19
b) 84.82 or 85
How do I graph these points on a graph?
(-1/2, -3/2)
Answers
Answer:
Start at origin (0,0)
Move 1/2 units left
Move 1 and 1/2 units down
Place your point
Step-by-step explanation:
Start at the origin (0,0)
Move 1/2 units to the left
Then move 1 1/2 units down, and place your point.
The first coordinate is locating the position horizontally, or on the x axis
The second coordinate is locating the position vertically, or on the y axis.
If there is a negative number on the x coordinate, the first one, you move left.
If positive, you move right.
If there is a negative number on the y coordinate, the second one, you move down.
If positive, you move up.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
move toward left of the horizontal x axis then plot the point in between o and -1.For next point then move down the vertical y axis and plot the point in between -1 and -2 .
Step-by-step explanation:
Hope this helps u!!
Look at the parallelogram pictured in Figure 1. What is the area of the
parallelogram?
Answers
Answer:
45m²
Step-by-step explanation:
=> Area = base × height
=> A = 5m × 9m
=> A = 45m²
4.
Find the x- and y-intercept of the line.
2x + 3y = -18
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
X - Intercept: (-9, 0)
Y - Intercept: (0, -6)
»»————- ★ ————-««
Here’s why:
The x and y-intercepts of a line is where a given function intercepts the x or y axes.
I have graphed the equation given on a program. The graph shows that the line passes through the points (0, -6) and (-9, 0).
Therefore:
[tex]\rightarrow\text{The x-intercept of the given equation is }\boxed{\text{(-9,0)}}.\\\\\rightarrow\text{The y-intercept of the given equation is }\boxed{\text{(0,-6)}}.[/tex]
See the graph attached below!
»»————- ★ ————-««
Another way to solve this problem is to do this algebraically.
[tex]\text{X-Intercept: Substitute the 'y' variable for zero and solve for 'x'.}\\\\2x + 3y = -18\\-------\\\rightarrow2x+3(0)=-18\\\\\rightarrow2x=-18\\\\\rightarrow\frac{2x=-18}{2}\\\\\rightarrow\boxed{x=-9}\\-------\\\boxed{\text{X-Intercept: (-9,0)}}[/tex]
----------------------------
[tex]\text{Y-Intercept: Substitute the 'x' variable for zero and solve for 'y'.}\\\\2x+3y=-18\\\-------\\\rightarrow2(0)+3y=-18\\\\\rightarrow3y=-18\\\\\rightarrow\frac{3y=-18}{3} \\\\\rightarrow\boxed{y=-6}\\\-----\\\\\boxed{\text{Y-Intercept: (0,-6)}}[/tex]
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Please help with these high school geometry circle questions.
Answers
Answer:
I don't know I'm really sorry please don't be angry
and if you want my social media cause your angry I'll give
The mass of a carbon atom is 1.994 × 10-23 grams. The mass of a hydrogen atom is 1.67 × 10-24 grams. What is the difference of their masses?
Answers
Answer:
carbon is heavier
Step-by-step explanation:
That's the difference right?
Oh and if you want an exact number, you can take the mass of carbon arom and subtract the mass of hydrogen atom
1.994×10^-23 - 1.67×10^-24= 19.94×10^-24 - 1.67×10^-24= 18.27x10^-24
Which line on the graph represents the equation y + 4 = -2x/3
Answers
Answer:
The answer is line D
Step-by-step explanation:
Someone please help will mark brainliest!!!
Answers
Answer: 50°
Step-by-step explanation: ur smart, u don’t need one, but if u really want one just comment on it and I’ll give u one :)
Dana Wright operates an airport limousine service. He owns the limo and does his own driving. He values his driving time at $25 per hour. He pays a commission fee of $10 to the person who brings him the business. A trip to the airport takes three hours and uses $25 worth of gasoline. If Dana charges each customer $200, what is his contribution margin per unit of sale? How much does Dana make on each trip as a driver? As the owner of the business?
Answers
The Fergusons want to install a new tile floor in their kitchen. The kitchen is in the shape of a rectangle and is 9 feet by 12 feet. They have chosen large square tiles that are 2 feet by 2 feet. how many tiles will they need to buy to cover their kitchen floor?
Answers
Answer:
27 tiles
Step-by-step explanation:
First, find the total area of the kitchen.
Use the area formula, A = lw
A = lw
A = (9)(12)
A = 108
So, the area of the kitchen is 108 sq ft
Find the area of the square tiles, using the same formula:
A = lw
A = (2)(2)
A = 4
So, the area of one square tile is 4 sq ft
Find how many tiles they will need to buy by dividing the total area by the area of one tile:
108/4
= 27
So, they will need to buy 27 tiles
Answer:
27 tilesTo find the total area of the kitchen.
We know,area formula, A = lw
A = lw
A = (9)(12)
A = 108
So, the area of the kitchen is 108 sqft
NowTo find the area of the square tiles
A = lw
A = (2)(2)
A = 4
So, the area of one square tile is 4 sqft
AtlastFind how many tiles they will need to buy by dividing the total area by the area of one tile:
108/4
= 27
So, Tiles Needed= 27
Hope This Helps You ❤️a) Make t the subject of the formula
[tex]( \sqrt{t + 2) \div u = 1} [/tex]
Answers
t = u - 2
Square both sides to eliminate the square root.
t + 2 / u = 1
Multiply both sides by u to remove it from the left side of the equation that has t
t + 2 = u
(When the coefficient is 1, you don’t write it)
Subtract 2 from both sides to make t by itself
t = u - 2
I hope that this is what you were asking for, I’m sorry if it wasn’t
When using the quadratic formula to solve 7x2 – 3x + 2 = 0, which number will be squared as part of the formula?
Answers
Answer:
The value of b will be squared
Step-by-step explanation:
Recall that the quadratic formula is [tex]x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
You will see that the only squared coefficient is b.
Can someone help solve this?
Answers
Answer:
C
Step-by-step explanation:
What association does the scatter plot show
A positive nonlinear association
B positive linear association
C no
D negative nonlinear
E negative linear
Answers
This is because there is no definitive line in the graph or upwards or downwards trend
Answer:
The answer would be no association
Step-by-step explanation:
Find the value of x.
Answers
Answer:
46degrees
Step-by-step explanation:
Find the value of x.
Using the circle theorem which states that
The angle at the vertex is half the difference that at the intercepted arcccs
x = 1/2(152 - 60)
x = 1/2 (92)
x = 92/2
x = 46degrees
Hence the value of x is 46degrees