The inverse function of f(x) = 6x^4 is f^(-1)(x) = (x/6)^(1/4), and f^(-1)(x) is a function.
To find the inverse function of f(x) = 6x^4, we can follow these steps:
1. Replace f(x) with y:
y = 6x^4
2. Swap x and y:
x = 6y^4
3. Solve for y:
Divide both sides by 6:
x/6 = y^4
4. Take the fourth root of both sides:
(x/6)^(1/4) = y
Now we have found the inverse function:
f^(-1)(x) = (x/6)^(1/4)
To determine if f^(-1)(x) is a function, we need to check if it passes the vertical line test. The vertical line test states that if a vertical line intersects a graph in more than one point, then the graph is not a function.
Let's imagine graphing f^(-1)(x) = (x/6)^(1/4). We see that for every x-value, there is only one corresponding y-value. Hence, each vertical line will intersect the graph at most once, confirming that f^(-1)(x) is indeed a function.
In conclusion, the inverse function of f(x) = 6x^4 is f^(-1)(x) = (x/6)^(1/4), and f^(-1)(x) is a function.
1. Lisa is working with the system of equations x + 2y = 7 and 2x ‒ 5y = 5. She multiplies the first equation by 2 and then subtracts the second equation to find 9y = 9, telling her that y = 1. Lisa then finds that x = 5. Thinking about this procedure, Lisa wonders:
There are lots of ways I could go about solving this problem. I could add 5 times the first equation and twice the second or I could multiply the first equation by ‒2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?
What is the answer to Lisa’s question? Explain.
2. Does the answer to the first question change if we have a system of two equations in two unknowns with no solutions? What if there are infinitely many solutions?
Answer:
1. Yes
2. Yes
Step-by-step explanation:
1. Lets test Lisa's different solution. Lets times 5 to the first equation:
[tex]5\cdot{x}+10\cdot{y}=35[/tex]
and 2 times the second equation:
[tex]4\cdot{x}-10\cdot{y}=10[/tex]
lets add the two equations:
[tex]9\cdot{x}=45[/tex]
[tex]x=5[/tex]
The second method is multiplying the first equation by -2:
[tex]-2\cdot{x}-4\cdot{y}=-14[/tex]
and add the second equation:
[tex]-9\cdot{y}=-9[/tex]
[tex]y=1[tex]
Substitute into equation 1:
[tex]x+2\cdot{1}=7[/tex]
[tex]x=5[/tex]
The answer to Lisa's question is yes she wull get the same solution if she uses a different method.
2. Yes, The answer would change if the same amout of x and y values are the same and therefore we cannot solve for x and y. If there was infinitely many solutions we would have quadratic equations.
How many terms are in the expression shown below?
a2 - ab + 8b + b2 - 1
2
3
4
5
square root of 4x squared times square root of 20x squared
The expression -50 + 100 represents the balance in dollars of a bank account after X months what is the rate of change in dollars per month of the bank account balance
Yup the answer is -50 give the other person brainly they deserve it
If the area of the outer square is 4x2, then the area of the inner square is
Final answer:
The area of the inner square is x squared. This is determined by the rule that the ratio of areas of similar figures is the square of the scale factor, with the larger square having dimensions and area four times that of the smaller square.
Explanation:
Considering a larger square with an area of 4x², and given that the dimensions of this square are twice that of a smaller square, we can derive the area of the smaller square by understanding the relationships between the scale factor and the area of similar figures. If Marta's original square has a side length of 4 inches, doubling the dimensions gives a side length of 8 inches for the larger square.
The scale factor for the sides is 2, but when considering area, the scale factor is squared. Consequently, the area of the larger square, which is 8 inches by 8 inches, will be 64 square inches. This area is four times larger than the area of the smaller square, which is 16 square inches (4 inches x 4 inches). Thus, the rule that the ratio of areas of similar figures is the square of the scale factor applies. The area of the inner square would be equivalent to the area of the outer square divided by 4, which in our case, with an outer square area of 4x², leads to an inner square area of x².
Find the coordinates of the missing endpoint if B is the midpoint of AC. C(-5,4), B(-2,5) I need the steps and answer pls and ty
The coordinates of the missing endpoints (1,6) and can be determined by using the midpoint formula.
Given :
B is the midpoint of AC. Points -- C(-5,4), B(-2,5)The following steps can be used in order to determine the coordinates of the missing endpoint:
Step 1 - According to the given data, points C(-5,4) and B(-2,5).
Step 2 - The mid-point formula is given below:
[tex]\rm x = \dfrac{x_1+x_2}{2}[/tex]
[tex]\rm y = \dfrac{y_1+y_2}{2}[/tex]
Step 3 - Let the endpoint be (x,y).
Step 4 - Now, substitute the values of the points in the above formula.
[tex]\rm -2= \dfrac{-5+x}{2}[/tex]
[tex]\rm 5 = \dfrac{4+y}{2}[/tex]
Step 5 - Simplify the above expression.
x = 1
y = 6
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Julie is selling candy bars to raise money for new band uniforms. Candy bar x sells for $2 and candy bar y sells for $3. The number of y candy bars Julia sells must be greater than or equal to three times the number of x candy bars she sells. She has at most 36 candy bars to sell. What is the maximum revenue she can make? $36 $99 $108 $216
Correct Answer.
$36
$99 <---
$108
$216
The difference of the squares of twenty and thirteen.
put in numerical form
The difference between the squares of twenty and thirteen will be 234.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.
The group's total number of items decreases or becomes lower when we subtract from it.
Square of twenty = 20²
20² = 20 × 20 = 400
Square of thirteen = 13²
13² = 13 × 13 = 169
Difference ⇒ 400 - 169 = 231.
Hence "The difference between the squares of twenty and thirteen will be 234".
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Write an equation for the line, given that m=3 and the y-intercept is (0,2)
Answer:
The equation of required line is y=3x+2.
Step-by-step explanation:
The slope intercept form of a line is
[tex]y=mx+b[/tex] ..... (1)
where, m is slope and b is y-intercept.
We need to find the equation of line whose slope is m=3 and the y-intercept is (0,2).
Substitute m=3 and b=2 in equation (1), to find the equation of required line.
[tex]y=(3)x+(2)[/tex]
[tex]y=3x+2[/tex]
Therefore the equation of required line is y=3x+2.
The equation for the line hose gradient/slope is 3 and a y-intercept of (0, 2) is y = 3x + 2
Further Explanation Equation of a straight line Equation of a straight line is written in the form y=mx+ c, where m and c are numbers. m is the gradient of the line while c is the y-intercept.
Equation of a straight line can be found when given:
A slope of the line and one point where the line is passing through Two points where the line is passing through A slope of the line and the y-intercept Double intercept When an equation of a straight is written in the form of x/a + y/b = 1 Where a is the x-intercept and b is the y-interceptIn this case;
The equation of the straight line with gradient m, passing through a point (x1,y1) is
y-y1 = m(x-x1)
We are given the y-intercept as (0, 2) and the slope is 3
Therefore;
To get the equation, we take another point (x,y)
(y-2)/(x-0) = 3
y-2 = 3x
y= 3x + 2
Keywords: Equation of a straight line, y-intercept,
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Level: High school
Subject: Mathematics
Topic: Equation of a straight line
John runs every day. The number of miles that he runs varies per day. Write a variable expression to show John's total miles for three days."
The Richter scale is used to measure the magnitude of an earthquake. The magnitude, R, is given by the earthquake. Determine the amount of energy released be an earthquake of magnitude of 7.5.
It says simplify so it is written in the form b = log a.
Amount of energy released during Earthquake is [tex]5.23*10^{6} kilowatt[/tex]
The Richter scale is used to measure the magnitude of a earthquake. The magnitude R is,
[tex]R=0.65log(0.39E)+1.45[/tex] E is the energy (measured in kilowatt-hours) released by the earthquake.
Given that, R = 7.5
Substituting the value of R into above equation.
[tex]7.5=0.65log(0.39E)+1.45\\\\7.5-1.45=0.65log(0.39E)\\\\6.05=0.65log(0.39E)\\\\9.31=log(0.39E)\\\\0.39E=10^{9.31}\\\\E=\frac{10^{9.31} }{0.39} \\\\E=5235225499watt\\\\E=5.23*10^{6} kilowatt[/tex]
Thus, Amount of energy released is [tex]5.23*10^{6} kilowatt[/tex]
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one serving of granola provides 4% of the protien you need daily. you must get the remaining 48 grans of protien fron other scources. how many grams of protein do you need daily?
Michelle listed her three children as equal beneficiaries on her life insurance policy. If she has a $400,000 policy, how much will each receive in the event of her death?
The beneficiaries received by each of Michelle children is $133333.3.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Michelle listed her three children as equal beneficiaries on her life insurance policy.
Here, insurance amount received by each is
400000/3
= $133333.3
Therefore, the beneficiaries received by each of Michelle children is $133333.3.
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Final answer:
Each of Michelle's three children would receive $133,333.33 from her $400,000 life insurance policy if they are listed as equal beneficiaries.
Explanation:
Michelle has a $400,000 life insurance policy and has listed her three children as equal beneficiaries. To calculate how much each child will receive in the event of her death, we divide the total policy amount by the number of beneficiaries.
$400,000 ÷ 3 = $133,333.33
Therefore, each child would receive $133,333.33 from the life insurance policy. In this scenario, the division of the life insurance policy ensures an equal distribution among Michelle's three children, with each child entitled to $133,333.33. This approach maintains fairness in the allocation of the financial benefit, aiming to provide an equitable share to each beneficiary.
If the product of two numbers is zero then at least one of the numbers must be zero
what is the property of 7(3+4y)=21+28y
The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool?
The height of the water increases 2 inches per minute.
The height of the water decreases 2 inches per minute.
The height of the water was 2 inches before any water was added.
The height of the water will be 2 inches when the pool is filled.
The correct statement describes how the slope relates to the height of the water in the pool is,
The height of the water increases by 2 inches per minute.
Given that,
The slope of the line through the points is 2.
And, the slope relates to the height of the water in the pool.
Here, a table for the height of the water in a pool is shown.
Since the slope of the line through the points is 2.
Hence, It means that,
if the height of the water is increased by 4 inches for 2 minutes, then for 1 minute is increased,
4/2 = 2 inches.
So, the correct statement is,
The height of the water increases by 2 inches per minute.
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write an expression to model the following phrase an hourly wage of 13.50 plus a 75 bonus
One third of a number is three more than one fourth the same number. What is the number.
One moving company charges $800 plus $16 per hour. another moving company charges $720 plus $21 per hour. at what number of hours will the charge be the same and what is the charge?
If the coefficient of static friction between the coffee cup and the roof of the car is 0.21, what is the maximum acceleration the car can have without causing the cup to slide? ignore the effects of air resistance.
Lori makes $64,000 each year as an accountant. At Christmas she was given a 12% bonus. What was Lori's total income for the year?
12% = 0.12
64000 x 0.12 = 7680
64000 + 7680 = $71,680
in the chorus there is 12 more girls than boys there 32 students in the chorus how many boys are there and how many girls are there
Can you can help me with 6.7 round the decimal the nearest whole number
the number to the right of the deciml point, 7 is greater than 4, so the number would be rounded up
so 6.7 would round to 7.0
Which expression illustrates the associative property of addition?
A. (3 + 19) – 12 = (3 + 12) – 19
B. 3 + (19 – 12) = 3 + (19 + 12) (Not B)
C. (3 + 19) – 12 = 3 + (19 – 12)
D. 3 + (19 –12) = 3 – (19 + 12)
Answer:
C.(3+19)-12=3+(19-12)
Step-by-step explanation:
We have to find an expression which illustrate the associative property.
We know that associative property of addition of three numbers a, b and c
[tex]a+(b+c)=(a+b)+c[/tex]
A.(3+19)-12=(3+12)-19
(3+19)-12=10
(3+12)-19=-4
It is not associative property of addition because both sides are not equal.
B.3+(19-12)=3+(19+12)
3+(19-12)=10
3+(19+12)=34
It is false because both sides are not equal .
C.(3+19)-12=3+(19-12)
(3+19)-12=10
3+(19-12)=10
It is illustrate the associative property of addition.
D.3+(19-12)=3-(19+12)
3+(19-12)=10
3-(19+12)=-28
Both sides are not equal . Hence , it is false.
I've been trying to solve this, but I have no idea how.
-1/2x + 3 = -x + 7
How to do the how long will it take two people to paint a room problem?
Enter the solution to the inequality in the box.
8+4(x−3)+3x≤24
Answer: The required solution is [tex]x\leq4.[/tex]
Step-by-step explanation: We are given to solve the following inequality :
[tex]8+4(x-3)+3x\leq24~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given inequality, we must find the value of the unknown variable x.
From inequality (i), we have
[tex]8+4(x-3)+3x\leq24\\\\\Rightarrow 8+4x-12+3x\leq24\\\\\Rightarrow 7x-4\leq24\\\\\Rightarrow 7x\leq24+4\\\\\Rightarrow 7x\leq28\\\\\Rightarrow x\leq\dfrac{28}{7}\\\\\Rightarrow x\leq4.[/tex]
Thus, the required solution is [tex]x\leq4.[/tex]
Miss violet is buying granola bars for her students. she already has 16 granola bars in her desk and needs a total of 100 bars. they are sold in packs of 12. how many more boxes of granola bars does she need to purchase for her students?
In ABC, C is a right angle, what is the measure of x?
A. 22.4°
B. 67.6°
C. 20.9°
D. 69.1°
B is the right answer
Answer:
Option B. 67.6°
Step-by-step explanation:
In the given triangle ABC angle C is the right angle, side AB = 21 and side AC = 8.
We have to find the measurement of angle A.
Now from cosine rule we can write
[tex]CosA = \frac{Base}{hypotenuse}[/tex]
Here Base in the corresponding side of the angle A that is 8 and hypotenuse is 21.
Now we put the values
Cos x = 8/21 = 0.3809
[tex]x=cos^{-1}0.3809[/tex]
Or x = 67.61°
Therefore measurement of angle A or x = 67.6° is the answer.
28Students were surveyed and the results showed that of 18 of them loved to play video games what percentage of the students loved to play video game.