The inverse function of f(x) = x^2 - 81 is found by swapping x and y in the original equation and solving for y, resulting in f^-1(x) = ±√(x + 81).
Explanation:To find the inverse function f-1(x) of the function f(x) = x2 - 81, we need to swap the roles of x and y in the original function and solve for y, which represents f-1(x). Here are the steps:
Start with the original function: y = x2 - 81.Rearrange to solve for x: x = y2 - 81.Swap x and y: y = x2 - 81 becomes x = y2 - 81.Add 81 to both sides: x + 81 = y2.Take the square root of both sides: y = ±√(x + 81).The correct answer is option 1, ±√(x + 81).
Rebekahs baby brother weighs 7.71 ponds. her newborn kitten weighs 0.24 pound. how much more does rebekahs baby brother weigh then her kitten
Find f(-7) if f(x) = 2x 8. -6 2 3 22
Answer:I hope this helps you
f (-7)=2. (-7)+8
f (-7)= -14+8
f (-7)= -6
Step-by-step explanation:
An online music service that customers download an unlimited number of songs for $0.25 each after paying a monthly membership fee of $5 the total amount of money a customer spends on the music in dollars in a single month can be found using the function y equals 0.25 x +5 what does the variable X represent in this function
Which number(s) below belong to the solution set of the inequality? 11x < 132
(Check all that apply)
A) 6
B) 12
C) 3
D) 10
E) 11
F) 26
Answer:
6, 3, 10 and 11
A, C, D and E are correct options.
Step-by-step explanation:
The given inequality is 11x < 132
Now, divide both sides by 11.
x < 12
Now, from the given options we check, the numbers that are less than 12. All those number should lie in the given solution set.
The numbers 6, 3, 10 and 11 are less than 12.
Hence, the numbers 6, 3, 10 and 11 belongs to the solution set of the given inequality.
A, C, D and E are correct options.
Convert the follow statement into a conditional statement. All squares are rectangles
If an object is a square, then it is a rectangle
If an object is a rectangle, then it is a square.
An object is a square so it is a rectangle.
An object is a rectangle so it is a square.
A transversal must intersect two or more parallel lines
true or false
The answer is false.
Which of the following is equivalent to log base 9 27 ?
Which of the following is equivalent to log base 9 27 ?
The equivalent of log base 27 of 9 is 2/3, as 27^(2/3) equals 9.
Thus, the correct answer is b. 2/3 among the provided choices.
To find an equivalent expression for log base 27 of 9, we need to determine the exponent to which 27 must be raised to obtain 9. In other words, we want to find x in the equation 27^x = 9.
Recognizing that 27 is 3^3 (as 3 times 3 times 3 equals 27), we can rewrite the equation as (3^3)^x = 9. Applying the exponent rule (a^b)^c = a^(bc), this simplifies to 3^(3x) = 9.
Now, equating the exponents, 3x = 2 since 3^2 equals 9. Solving for x, we find x = 2/3. Therefore, log base 27 of 9 is 2/3.
Among the provided choices:
a. 1/3
b. 2/3
c. 3/2
d. 0.798
The correct equivalent is b. 2/3, as it matches the determined value of log base 27 of 9.
The question probable may be:
Which of the following is equivalent to log27 9?
answer choices:
a 1/3
b 2/3
c 3/2
d 0.798
The equivalent of log base 27 of 9 is 2/3, as 27^(2/3) equals 9.
Thus, the correct answer is b. 2/3 among the provided choices.
We must ascertain the exponent to which 27 must be raised in order to
achieve 9 in order to discover an analogous formula for log base 27 of 9.
Put otherwise, we wish to determine x in the formula 27^x = 9.
Since 3 times 3 times 3 is 27, we may express the equation as (3^3)^x = 9 since we know that 27 is 3^3.
Applying the exponent rule (a^b)^c = a^(bc), this simplifies to 3^(3x) = 9.
Now, equating the exponents, 3x = 2 since 3^2 equals 9.
Solving for x, we find x = 2/3. Therefore, log base 27 of 9 is 2/3.
Among the provided choices:
a. 1/3
b. 2/3
c. 3/2
d. 0.798
The correct equivalent is b. 2/3, as it matches the determined value of log base 27 of 9.
Question
Which of the following is equivalent to log27 9?
answer choices:
a 1/3
b 2/3
c 3/2
d 0.798
Given the problem below, which set of equations translates the information using variables a, b, and c?
Old MacDonald grew some apples, bananas, and coconuts. He decided to package his fruit and price it as follows:
1 apple, 5 bananas, 1 coconut for $14
3 apples, 3 bananas, 3 coconuts for $18
1 apple, 2 bananas, 3 coconuts for $14
A.a + 5b + c = 14
3a + 3b - 3c = 18
a + 2b + 3c = 14
B.a + 5b + c = 14
3a + 3b + 3c = 18
a + 2b + 3c = 14
C.2a + 5b + c = 14
3a + 3b + 3c = 18
a + 2b + 3c = 14
D.a + 5b + 3c = 14
3a + 3b + 3c = 18
a + 2b + 3c = 14 ...?
The correct set of equations based on the information given about the pricing of apples, bananas, and coconuts by Old MacDonald is: a + 5b + c = 14, 3a + 3b + 3c = 18, and a + 2b + 3c = 14.
Explanation:The student is asking which set of equations corresponds to the problem given, involving prices for apples, bananas, and coconuts. In the context of this problem, variables a, b, and c represent the price of an apple, a banana, and a coconut, respectively. By analyzing the problem's given information, we can deduce the following equations:
a + 5b + c = 143a + 3b + 3c = 18a + 2b + 3c = 14These equations reflect the costs of different combinations of fruit based on the prices provided by Old MacDonald. To solve for the variables a, b, and c, we could use a system of linear equations.
What is larger: The height of a standard can of tennis balls, or the circumference of its lid?
(Assume the can fits three tennis balls perfectly). Explain your reasoning. ...?
Final answer:
The height of a can holding three tennis balls is 20.1 cm, while the circumference of the lid is approximately 21.02 cm. Hence, the circumference of the can's lid is slightly larger than its height.
Explanation:
The question is comparing two different measurements of a can that holds tennis balls. One measurement is the height of the can, and the other is the circumference of the can's lid. In a standard can of tennis balls, three tennis balls are stacked on top of each other perfectly. Knowing that the diameter of a standard tennis ball is approximately 6.7 cm, we can calculate the height of the can by multiplying the diameter of one tennis ball by three (since the diameter is the same as the height for a ball stacked in such a can).
Height of can = Diameter of tennis ball × number of balls
= 6.7 cm × 3
= 20.1 cm.
To determine the circumference of the can's lid, we first need to find the radius of the lid which would be half the diameter of a tennis ball:
Radius of lid = Diameter of tennis ball / 2
= 6.7 cm / 2
= 3.35 cm.
Then, we use the formula for the circumference of a circle, which is C = 2πr:
Circumference of lid = 2π × Radius of lid
= 2π × 3.35 cm
≈ 21.02 cm.
The circumference of the lid is slightly larger than the height of the can. Therefore, the circumference of the can's lid is larger than the height of the can of tennis balls.
1) A comet that passes through the solar system just once has a path that is modeled by a conic section. Astronomers discover a comet whose path is modeled by the following equation, with the Sun at one focus. What type of conic section is the comet's path?
x^2/2,500-y^2/37,500=1
2) What are the vertices of the comet's path? (Hint: Examine the general formula for the path and identify the numbers that determine the vertices.)
3) At its closest point to the Sun, this comet is ____ million miles from the Sun. (Enter only the number.)
Hint: Subtract the vertex from the focus
how do you do prime factorization on a negative number?
ex:
-48, 108
How would i find the rule for this pattern:1280,640,320,160?
The rule for this pattern is to divide each number by 2 to get the next number.
Explanation:To find the rule for this pattern, we need to identify the relationship between the numbers. In this case, each number is half of the previous number. So, to find the next number, we divide the previous number by 2.
For example, 640 is half of 1280, 320 is half of 640, and so on. This means that to find the next number, we divide 320 by 2 to get 160.
Therefore, the rule for this pattern is to divide each number by 2 to get the next number.
four times daphne's age plus five times isaac's age adds up to 57. also, isaac's age is 11 less than twice daphne's age. how old is isaac?
120% of what number is 36?
Answer:
The answer is 30.
Step-by-step explanation:
A farmer wants to build a pen for his sheep. One side of the pen will be a river. The sheep need about 2000 m2 of area to graze. About what length (x) and width (y) should the organization use to use the LEAST amount of fencing possible?
A) length = 43 m, width = 46 m
B) length = 50 m, width = 40 m
C) length = 63 m, width = 32 m
D) length = 100 m, width = 20 m
The option closest to [tex]\( x = 10\sqrt{10} \) and \( y = 200\sqrt{10} \)[/tex] is option D) length = 100 m, width = 20 m. So, the answer is option D.
To minimize the amount of fencing needed, we want to maximize the area of the pen while fulfilling the requirement of 2000 m².
Let's denote the length of the pen as x and the width as y. Since one side of the pen is a river, we only need to fence three sides: two sides of length x and one side of length y. So, the total fencing required is 2x + y.
We're given that the area of the pen should be 2000 m², so we have the equation:
xy = 2000
We want to minimize 2x + y. We can solve the area equation for one variable and substitute it into the expression for the fencing:
[tex]\[ y = \frac{2000}{x} \][/tex]
Substitute this expression for y into the expression for the fencing:
[tex]\[ \text{Fencing} = 2x + \frac{2000}{x} \][/tex]
To minimize this expression, we can take its derivative with respect to x, set it equal to zero, and solve for x.
[tex]\[ \frac{d}{dx}(2x + \frac{2000}{x}) = 2 - \frac{2000}{x^2} = 0 \][/tex]
[tex]\[ 2 = \frac{2000}{x^2} \][/tex]
[tex]\[ x^2 = \frac{2000}{2} = 1000 \][/tex]
[tex]\[ x = \sqrt{1000} = 10\sqrt{10} \][/tex]
Once we find x, we can find y using the area equation:
[tex]\[ y = \frac{2000}{x} = \frac{2000}{10\sqrt{10}} = 200\sqrt{10} \][/tex]
Now, we need to choose the option closest to x and y.
Checking the options:
A) length = 43 m, width = 46 m
B) length = 50 m, width = 40 m
C) length = 63 m, width = 32 m
D) length = 100 m, width = 20 m
The option closest to [tex]\( x = 10\sqrt{10} \) and \( y = 200\sqrt{10} \)[/tex] is option D) length = 100 m, width = 20 m.
So, the answer is option D.
Using the graph below, calculate the average rate of change for f(x) from x = 0 to x = 2.
x = −4
x = −2
x = 2
x = 4
$45.00 for 9 pounds what is the unit rate?
need help which of the following appear in the diagram
Will subscribes to a monthly auto magazine. his one year subscription costs $29.97. if he pays for the subscription in 3 equal installments, how much is each payment?
1. What is the sum of the polynomials?
(m + n + 3) + (m + n + 4)
2. Find the difference of the polynomials
(10m – 6) – (7m – 4)
3. Find the difference of the polynomials
(4m – 5) – (6m – 7 + 2n)
Answer:
1. 2m+2n+7
2. 3m-2
3.-2m+2-2n
Explanation:
To find the sum of given polynomials (m+n+3) +(m+n+4)
Firstly, open the parenthesis we will get m+n+3+m+n+4
After simplification we will get 2m+2n+7
To find the difference of given polynomials (10m-6)-(7m-4)
Firstly, open the parenthesis we will get 10m-6-7m+4
After simplification we will get 3m-2
Again to find the difference of the polynomials (4m-5)-(6m-7+2n)
Firstly, open the parenthesis we will get 4m-5-6m+7-2n
After simplification we will get -2m+2-2n
The sum of the polynomials (m + n + 3) and (m + n + 4) is 2m + 2n + 7. The difference of the polynomials (10m – 6) and (7m – 4) is 3m - 2. The difference of the polynomials (4m – 5) and (6m – 7 + 2n) is -2m - 2n - 2.
Explanation:To find the sum of the polynomials (m + n + 3) and (m + n + 4), we simply combine like terms:
(m + n + 3) + (m + n + 4)
= m + m + n + n + 3 + 4
= 2m + 2n + 7.
To find the difference of the polynomials (10m – 6) and (7m – 4), we subtract the second polynomial from the first:
(10m – 6) – (7m – 4)
= 10m - 7m - 6 + 4
= 3m - 2.
Lastly, to find the difference of the polynomials (4m – 5) and (6m – 7 + 2n), we again subtract the second polynomial from the first:
(4m – 5) – (6m – 7 + 2n)
= 4m - 6m + 5 - 7 - 2n
= -2m - 2n - 2.
If the addends are 170 and 130, then what is the sum?
The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.89 per gallon. Write a direct variation to model the total cost c for g gallons of gas.
Answer:c=1.89g
Step-by-step explanation: gradpoint
HELLO! who can help me?
Name one segment that is tangent to Circle Q
A) Line BC
B) Line DE
C) Line GH
D) Line QE
Answer:
GH
Step-by-step explanation:
If 8 = x + y and y > 0, then x is ___ 8.
Choose the relationship symbol that makes the statement true.
A. <
B. =
C. >
Answer: The correct option is,
A. <
Step-by-step explanation:
Given,
[tex]8=x+y-----(1)[/tex]
Also,
[tex]y > 0[/tex]
Adding x on both sides ( additive property of inequality )
[tex]x+y>x+0[/tex]
[tex]x+y>x[/tex]
From equation (1),
[tex]8>x[/tex]
Hence, x is less than 8,
We use < sign for less than,
⇒ x is '<' 8
Option A is correct.
Translate the percent word problem in a equation: If 5 is increased to 8, the increase is what percent of the original number?
Answer:
The equation that describes the problem "If 5 is increased to 8, the increase is what percent of the original number?" would be
[tex]x=\frac{8-5}{5}*100%[/tex] where x is the percent of increasing of 5 to 8.
Step-by-step explanation:
First it is required to define which is the question, or unknown value. In this case is the percentage of increasing. The x letter is assigned to this unknown.The rest of the provided information is used to setup the function that solves the unknown value. In this case, the original value (5) and the new value (8) are known.Then, it is needed to select the operations that allow the known information to solve the unknown. The subtraction allows to found the absolute increasing in the original value. And a division allows to compare this absolute increasing how much of the original value is, in other words the fraction of increasing.Finally, it is required to multiply by 100%, in order to convert the fraction of increasing into a percentage form.How does 0.42 divide by 0.35 equal 1.2?
The sum of three consecutive odd integers is -27. What are the numbers?
The three consecutive odd integers are [tex]-11, -9,[/tex] and [tex]-7[/tex].
To find three consecutive odd integers whose sum is -27, let's define the three integers as follows:
Let the first consecutive odd integer be [tex]x[/tex].The second consecutive odd integer will be [tex]x + 2[/tex].The third consecutive odd integer will be [tex]x + 4[/tex].According to the problem, the sum of these integers is -27. We can write this as an equation:
[tex]x + (x + 2) + (x + 4) = -27[/tex]
Now, let's simplify and solve the equation step-by-step:
Combine like terms on the left-hand side of the equation:
[tex]x + x + 2 + x + 4 = -27[/tex]
[tex]3x + 6 = -27[/tex]
Subtract 6 from both sides to isolate the term with [tex]x[/tex]:
[tex]3x + 6 - 6 = -27 - 6[/tex]
[tex]3x = -33[/tex]
Divide both sides by 3 to solve for [tex]x[/tex]:
[tex]x = \frac{-33}{3}[/tex]
[tex]x = -11[/tex]
So, the first consecutive odd integer is [tex]-11[/tex].
Find the second consecutive odd integer:
[tex]-11 + 2 = -9[/tex]
Find the third consecutive odd integer:
[tex]-11 + 4 = -7[/tex]
Which one of the following shows the diameter of a circle
The figure which is drawn in option D shows a circle with a diameter.
What is the diameter of the circle?
The diameter of a circle is the distance from one point on the surface of a circle to the other point on the circle's surface, which passes through the center.
What is radius of circle?Radius of a circle is the distance from the center of the circle to any point on it's circumference.
According to the given question
We have, some figures of a circle.
In option A there is no any diameter and radius is drawn for the given circle.
In option B, the given line which is drawn in the circle is the radius of the circle not a diameter. Because " radius of a circle is the distance from the center of the circle to any point on it's circumference.
In option C, there is no any diameter and radius is drawn is the given figure or circle.
In option D, the given line which is drawn in the circle is the diameter of the circle because the distance from one point on the surface of a circle to the other point on the circle's surface, which passes through the center is called diameter.
Learn more about the diameter of a circle here:
https://brainly.com/question/266951
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The graph shows the temperature of ice cream in an ice chest during an overnight trip. What is the domain of this function?
The domain is negative 10 through 30.
The domain is all integers from negative 10 through 30.
The domain is all real numbers 0 through 30.
The domain is all integers from 0 through 30.
Let
x-------> the number of hours
y------> the temperature in degrees Fahrenheit
we know that
For [tex]x=0\ hours[/tex]
[tex]y=-10\°\ F[/tex]
For [tex]x=30\ hours[/tex]
[tex]y=30\°\ F[/tex]
The domain of the function is the interval----------> [tex][0,30][/tex]
[tex]0\ hours \leq x\leq 30\ hours[/tex]
The range of the function is the interval----------> [tex][-10,30][/tex]
[tex]-10\°\ F \leq y\leq 30\°\ F[/tex]
therefore
the answer is
The domain is all real numbers 0 through 30
Name the property illustrated by each question.
5x · (4y + 3x) = 5x · (3x + 4y)
Answer:
The property used here is:
Commutative property of addition
Step-by-step explanation:
Commutative property of addition states that if a and b are any two elements
then, a + b = b + a
We are given a equality we have to determine the property used here
5x · (4y + 3x) = 5x · (3x + 4y)
In the above equation, 4y + 3x = 3x + 4y
a= 4y and b= 3x
Then, a+b=b+a
Hence, the property used above is:
Commutative property of addition