[tex]f(x)=3x\to y=3x\\\\\text{Interchange the y and the x}\\\\x=3y\\\\\text{Solve for y}\\\\3y=x\qquad|:3\\\\y=\dfrac{x}{3}\\\\Answer:\ C.\ f^{-1}(x)=\dfrac{x}{3}[/tex]
The required inverse function would be f⁻¹(x) = x / 3, which is the correct answer would be option (C).
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
To determine the inverse of a function, all you have to do is switch where x and y are and resolve for y.
We have to find the inverse of the function below :
f(x) = 3x
So after switching x and y,
Now, we solve for y regularly.
f(x) = x = 3y
Solve for y :
⇒ x = 3y
⇒ x / 3 = y
⇒ y = x / 3 = f⁻¹(x)
Therefore, the required inverse function would be f⁻¹(x) = x / 3.
Hence, the correct answer would be an option (C).
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what is the answer to 2 2/7
A little more specific? So i could help out, thanks
What is the expanded form for 4.3
4.3 you can't expand a number, only an equation
The expanded form of a number shows the value of each digit. Meaning you must separate each digit by its placement.
4 is in the ones, therefore it just remains as 4
.3 is in the tenths, and therefore turns into 0.3
Now combine the two terms. The expression would be the answer:
4 + 0.3
Please send out a step by step solution
the picture is blurry
Does anyone know the answer to this question? Or at least a way to solve it?
From the fact that the two horizontal lines are parallel, you can deduce <A=<B
so you can equate the two right-hand sides of the equations:
6x+12=3x+63 and solve for x
3x = 51
x= 17 degrees is the measure <A (and <B as well)
y=5x-6 and -15x+3y=-18
Infinitely many solutions.
what is the equation of the product of three more than a number and eight is fourteen
First, we start with the product
so _________ * _________
Now, the first part of the product is 3+ (a number), n
so (3+n)*___________
And the other side is 8
(3+n)*8
or 8(3+n) =14
Let the number is x
Three more than a number: x + 3
so the product of three more than a number and eight : 8(x + 3)
Now you can write he equation of the product of three more than a number and eight is fourteen
8 (x + 3) = 14
Hope that helps
If one bottle of the national brand of cough medicine costs $12, what is the cost of a bottle of the store brand if its 2/3 of the national brand
The answer is $8, sense 12÷3×2=4×2=8.
To find the cost of the store brand cough medicine, which is 2/3 the cost of the national brand priced at $12, you multiply $12 by 2/3, resulting in the store brand costing $8.
Explanation:The question asks: If one bottle of the national brand of cough medicine costs $12, what is the cost of a bottle of the store brand if it's 2/3 of the national brand? To find the answer, you multiply the cost of the national brand by 2/3, since the store brand costs 2/3 of the national brand's price.
Here's the calculation:
Cost of national brand = $12Cost of store brand = $12 × (2/3) = $8Therefore, the cost of a bottle of the store brand cough medicine is $8.
I need help PLEase (if you have the time)
im just not very smart
a person on a tour has rupees 12000 for his daily expenses. In order to extend his journey for 2 more days he had to cut down his daily expenses by Rs.300 .find the duration of the tour he planned first.
Answer:
Duration of the tour he planned first is 8 days.
Step-by-step explanation:
Given that a person has 12000 rupees for his daily expenses.
Let x be the number of days.
Then daily expenses per day [tex]=\frac{12000}{x}[/tex]
Given that number of day is increased by 2 more days, that is number of days is x+2.
New daily expense per day [tex]\frac{12000}{x+2}[/tex]
Given that this new daily expenses are 300 less than original.
That is [tex]\frac{12000}{x}-\frac{12000}{x+2}=300[/tex]
[tex]\frac{12000(x+2)-12000x}{x(x+2)}=300[/tex]
[tex]\frac{24000}{x(x+2)}=300[/tex]
[tex]x(x+2)=\frac{24000}{300}[/tex]
[tex]x^{2}+2x-80=0[/tex]
(x-8)(x+10)=0
x=8 or -10.
Since number of days cannot be negative, duration of the tour planned=8.
What property of numbers is demonstrated in the equation (10 + 7) × 9 = (10 × 9) + (7 × 9)?
This is the distributive property because you are distributing the 9 into both terms of the parenthesis.
(10 + 7) x 9 = 10(9) + 7(9)
Answer: Distributive Property
i believe its distributive property
Please help don't guess.
The easy way to do this is:
Since the radius of the second circle is exactly 6 times the radius of the first circle, you could just multiply the circumference by 6:
9.42 x 6 = 56.52! But let's double-check.
9 x 2 = 18 So, the diameter is 18.
18 x 3.14 = 56.52! So, 56.52 is the correct answer!
Remark
The formula you should be using is
C = k*r because this is a variation question. There are ways of doing this without solving for k, but it is a good idea to solve for k first.
Givens
C = 9.42
r = 1.5
k = ??
K =
C = k*r
9.42 = k * 1.5
k = 9.42/1.5
k = 6.28 which is what it should be given that pi = 3.14. But you must check.
r = 9
C = k*r
C = 6.28 * 9
C = 56.52 which rounded = 57 to the nearest inch
57 Answer
Find the percent of the number. What is 256% of 75
It is 192.
75 is 100% so we can write it down as 75=100%.
75=100% x=256%
CROSS MULTIPLY, proportions.
75/100 X/256
19200/100 equals 192
What are the closest integers that the square root of 300 is in between?
The square root of 300 is approximately 17.32, placing it between the integers 17 and 18. The square of 17 is 289, and 18 is 324, confirming this placement.
The square root of 300 falls between two consecutive integers. To find the closest integers, we can estimate the square root's value. The square root of 300 is approximately 17.32, as 17 squared is 289 and 18 squared is 324. Therefore, the square root of 300 is greater than 17 but less than 18.
In terms of integers, the square root of 300 is between 17 and 18. These are the closest integers that the square root of 300 falls between.
To further validate this, we can square both 17 and 18. The square of 17 is 289 (less than 300), and the square of 18 is 324 (greater than 300). This confirms that the square root of 300 indeed lies between 17 and 18.
In summary, the closest integers that the square root of 300 falls between are 17 and 18.
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The equation of the graphed line is x + 2y = 5. What is the x-intercept of the graph?
The x-intercept is
If you have to find x-intercept, then you have to equate y to 0. Thus,
when y=0, x+2·0=5 and x=5.
Point (5,0) is x-intercept.
Answer: (5,0)
The x-intercept of the graph is:
5
and the point where it is obtained is (5,0)
Step-by-step explanation:We know that the x-intercept of a graph is the x-value of the point where it's y-value is zero.
Similarly the y-intercept of a graph is the y-value of the point where it's x-value is zero.
We are given a equation of a line as:
[tex]x+2y=5[/tex]
Hence, when y=0 in the equation we get:
[tex]x=5[/tex]
Hence, the point where the x-intercept is obtained is: (5,0)
and the x-intercept of the graph is: 5
How many times greater is the value of 5.3 than the value of 0.53
To find the number of times greater, let us divide 5.3 by 0.53.
Number of times greater = [tex]\frac{5.3}{0.53}[/tex]
[tex]=\frac{5.3}{0.53}(\frac{100}{100} )[/tex]
[tex]=\frac{530}{53}[/tex]
= 10
Hence, 5.3 is 10 times greater than 0.53.
Meredith Pick 4 times as many green peppers as red peppers if she picked a total of 20 peppers how many green peppers does she pick
Help!!! On geometry all help is appreciated
(1)
we are given two points
A=(-3,-4)
B=(2,0)
and point P [tex](-1, -\frac{12}{5} )[/tex] partitions AB
Let's assume it partitions into m:n
so, we get
[tex]\frac{AP}{PB}=\frac{m}{n}[/tex]
so, we can write our point as
[tex](-1,-\frac{12}{5} )=(\frac{2m-3n}{m+n},\frac{0m-4n}{m+n})[/tex]
now, we can set x-value to x-value
and y-value to y-value
and then we can solve for m and n
[tex]-1= \frac{2m-3n}{m+n}[/tex]
[tex]-\frac{12}{5} =\frac{0m-4n}{m+n}[/tex]
now, we can solve for m/n
[tex]-m-n=2m-3n[/tex]
[tex]3m=2n[/tex]
[tex]\frac{m}{n} =\frac{2}{3}[/tex]
so, option-C.........Answer
(2)
we are given points as
J=(10, -2)
N=(-4 ,6)
Let's assume mid-point between J and N as M
so, we get
[tex]M=(\frac{10-4}{2},\frac{-2+6}{2})[/tex]
[tex]M=(3,2)[/tex]............Answer
write an equation involving absolute value for graph
The absolute value inequality which illustrates the information on the number line is 1 ≤ X ≤ 11
The use of thick shaded dots on a number line represents the ≤ or ≥ notation. The value of X could be any value in between the dotted point. This means the value could be any value between 1 and 11 (With 1 and 11 inclusive). Since, the we have a shaded dot, then 1 ≤ X ; similarly X ≤ 11.Combining the two conditions ; we obtain 1 ≤ X ≤ 11.Therefore, the expression depicted by the absolute value graph is 1 ≤ X ≤ 11
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In one weekend,a theatre sells 74,877 tickets to a new movie. Write the values for each of the 7s in 74,877
The values for each of the 7s in 74,877 can be expressed as ;
The first 7 from the left means thousands, which is express in the value of 7,000.The middle 7 means hundreds, with a value of 700.The last 7 from the right means ones, with the value of 7.What is Ones Tens Hundreds Thousands?The rank or position of a digit in a huge number is one tens hundred thousand. It establishes the place value where the digit is located. The value a digit in a number represents based on where it is in the number is known as place value.
For instance, 700 is the place value of 7 in 3,743. Nevertheless, 7,000 or 7,000 is the place value of 7 in 7,432.
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-6x-11x=68 HEEEEEEEEEEELP
Answer:
The correct answer would be 4. Explanation below
Step-by-step explanation:
-6x-11x = 68
-6x-11x = -17x
-17x = 68
68/-17 = 4
Hope this helps!
~Starr
Answer:
Hey there! The correct answer would be x=-4.
Step-by-step explanation:
To start, you would first need to combine your like terms, terms that are not only raised to the same power but also have the same exact variables. In this case, your like terms are -6x and -11x:
-6x-11x=68 --> -17x=68
Now, divide both sides by -17 in order to isolate your variable term:
-17x/-17 = 68/-17
x=-4
Therefore, your answer would be x=-4.
To check to make sure this answer is right, plug -4 in for x and see if the result is 68=68:
-6(-4)-11(-4)=68
24+44=68
68=68
Hope this helps! :)
What is the slope and y-intercept of the equation 3(y − 2) + 6(x + 1) − 2 = 0? A. slope = -2, y-intercept = B. slope = 2, y-intercept = C. slope = -2, y-intercept = D. slope = 2, y-intercept = E. slope = -2, y-intercept =
3(y − 2) + 6(x + 1) − 2 = 0
3y - 6 + 6x + 6 - 2 = 0
3y + 6x - 2 = 0
3y = -6x + 2
y = -2x + 2/3
Slope = - 2
Y intercept = b - 2/3
Answer
A. slope = -2, y-intercept = B
slope = -2
Y-intercept= 2/3
You dont have the Y-intercept numbers so i cant say if its A,B,C, or D.
Jenny's frog made one jump of 2.34 meters. Christina's frog made jumps of 1.22 meters and 0.89 meters.
How much further did Jenny's frog jump in one jump than Christina's frog in two jumps combined?
Lets go through the steps
1) 1.22 + .89 = 2.11
2) 2.34 - 2.11 = .23
Jenny's frog jumped .23 meters further than Christina's frog.
I hope this helped!
Have a fantastic day!
Jenny's: 2.34
Chistina's: 1.22+0.89
The first thing you want to do is add 1.22 and 0.89 which is 2.11
Then too find how much further Jenny's frog jumped you subtract 2.34 and 2.11 which is 0.23.
Therefore your answer would be:0.23
Use the corresponding angles diagram to answer the question. If m angle 5=42 degrees, what is m angle 4?
The measure of angle 4 will be 42 degrees because corresponding angles are equal when two lines are cut by a transversal, and in this case, angle 5 and angle 4 are corresponding angles.
Explanation:The concept involved here is that corresponding angles are equal when two lines are cut by a transversal. In the given problem, angle 5 and angle 4 are corresponding angles because they occupy the same relative position at an intersection of a transversal and two lines. Therefore, if the measure of angle 5 (m angle 5) is 42 degrees, then the measure of angle 4 (m angle 4) will also be 42 degrees.
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-4x - 2y = 14
-10x + 7y = -25
? I don't know how to solve systems of equations
how can graphing help solve a problem involving ratios
To solve a problem involving ratios:
The higher the ratio, the line will seem steeper.
What is ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
To solve a problem that has ratio:
We can solve by graphing.
Ratios can be compared using tables and graphs.
The higher the ratio, the line will seem steeper.
Therefore, the line will seem steeper.
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If two numbers represented 2m+1 and 2m+5 have a sum of 74 find m
mr. Russell owes 1235 shares of XYZ stock. On Monday, the start decreased by $0.67 a share. On Tuesday, decreased by $0.53 a share. What is the change in the value of stock shares for their two days?
loss of $1,482.00 is the answer
The figures below have the same perimeter determine if each statement is true or false
Need help with this can you tell me exactly where I’m supposed to place the dot plz and plz get me this answer fast thank you
The function y=60/x relates y, the time in hours that it takes micheal to travel to his grandparents house,to x , his average speed in miles per hour what does the number 60 the
Remember the formula for time is distance/speed
So 60 would be the distance, or 60m.
Answer:
60 represents the distance
Step-by-step explanation:
Given : y is the time in hours that it takes Micheal to travel to his grandparents house,
x is his average speed in miles per hour.
To Find: What does the number 60 represents
Solution :
Time= y
x = speed
So, To find distance we will use formula :
[tex]Time = \frac{Distance}{Speed}[/tex]
[tex]y = \frac{Distance}{x}[/tex] -- A
Given function: [tex]y = \frac{60}{x}[/tex] --B
On comparing A and B
Distance = 60 miles
So, 60 represents the distance .