The inverse of the function f(x) = (3x)^2 is f-1(x) = 1/3√x
How to determine the inverse of the function?The function is given as:
f(x) = (3x)^2
Remove the bracket in the above equation
So, we have:
f(x) = 9x^2
Express f(x) as y
So, we have
y = 9x^2
Swap the positions of x and y
So, we have
x = 9y^2
Make y the subject of the formula
y^2 = x/9
Take the square root of both sides
y = 1/3√x
Express as an inverse function
f-1(x) = 1/3√x
Hence, the inverse of the function f(x) = (3x)^2 is f-1(x) = 1/3√x
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The ratio of stars to circles is 3 to 2. If
there are 28 circles, then how many stars are there?
Answer:
42
Step-by-step explanation:
3 to 2 can be represented as 3/2. Remember the numerator represents stars while the denominator represents circles. Set up a proportion the criss multiply. This ratio would be 3/2 = x/28. First multiply 28 x 3 and set it equal to 2x. This gives you 84=2x. Divide 2 by each side and you will get 42 stars.
HELP
The coordinates of point T are (0,4). The midpoint of ST is (1,−3). Find the coordinates of point S.
The coordinates of S are (-1 , 11)
In the given statement is :
The coordinates of point T are (0,4). The midpoint of ST is (1,−3).
To find the coordinates of point S.
Now, According to the question:
Let the coordinate of point S are (x, y).
T (0, 4) is the mid point of ST
=> [tex]\frac{x+1}{2}=0 , \frac{y+(-3)}{2}=4[/tex]
=> x+1 =0 , y -3 = 8
=> x = -1 , y = 11
So, the coordinates of S are (-1 , 11)
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I don’t understand this question
Answer:
f(-4) = - 64
f(3) = - 15
f(-a) = - 3a² - 4a
-f(a) = 3a² - 4a
f(a + h) = - 3a² - 6ah - 3h² + 4a + 4h
Pay careful attention that you do not miss the negative signs in some of these terms
Step-by-step explanation:
The function is f(x) = -3x² + 4x
To evaluate the function at any value of x, simply substitute for x in the function expression
f(-4)
The first step in determining the solution to the system of equations, y=x²-4x-3 and y= 2x+5, algebraically is to
set the two equations equal
as-x²-4x-3=2x+5. What is the next step?
Set y = 0 in y=-x2²-4x-3.
O Factor each side of the equation.
Use substitution to create a one-variable equation.
O Combine like terms onto one side of the equation
Answer: The first step in determining the solution to the system of equations algebraically is [-4,-2].
Step-by-step explanation:
Determining the solution to the system of equations,
so, y=-x²-4x-3 and y= 2x+5, algebraically is to set the two equations are equal to:
-x²-4x-3 =2x+5
Then the solve in this equation
To put all terms into the lest side of the equation and group the terms:
solve it: -x²-4x-3-2x-5=0
-x²+(-4x-2x)+(-3-5)=0
-x²-6x-8=0
now you can multiply this equation by -1
x²+6x+8=0
and solve it using Quadratic equation
x(1,2)=[-b±√[tex]b^{2}[/tex]-4ac]/2a
replace with a=1,b=6,c=8 values
x(1,2)=[-6±√[tex]6^{2}[/tex]-4.8.1]/2.1
x(1,2) =[-6±√4]/2
x(1,2) =[-6±2]/2
x(1,2) =[-4,-2]
The first step in determining the solution to the system of equations algebraically is [-4,-2].
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The measure of one angle is four times the measure of its supplement. Find the measure of each angle.
The measure of the angle is 36° and its supplement is 144°.
The supplement of an angle is calculated by subtracting the value of the angle from 180°.
A linear pair of angles are supplement of one another.When two straight lines intersect at a point then any 2 adjacent angle of the four angles formed are supplementary angles. In a cyclic quadrilateral ( quadrilateral whose 4 sides touch the same circleat different points ) opposite angles are supplementary.Given that the supplement of the angle is 4 times the angle.
Let us consider the value of the angle be x°.
Therefore the value of the supplement is 4x°
Now the sum of the two supplementary angles is 180°.
∴x° + 4x° = 180°
or, 5x° = 180 °
or, x° = 36°
Therefore the larger angle = 4x° = 4 × 36° = 144° .
Hence the angles are 36° and 144° .
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the sum of 4 times a number and 9 is equal to 6
use the variable y for the unknown number
Answer:
-3/4
Step-by-step explanation:
4y + 9 = 6
4y = 6-9 = -3
y = -3/4
Nick buys a bag of cookies that contains 9 chocolate chip cookies, 6 peanut butter cookies, 7 sugar cookies and 7 oatmeal cookies. What is the probability that Nick randomly selects a sugar cookie from the bag, eats it, then randomly selects a chocolate chip cookie? Express you answer as a reduced fraction.
Answer: 2/29
Step-by-step explanation: because he has 29 cookies in total therefor if he just randomly picks a cookie from the bag this would be 2/29 as he randomly chose 2 cookies out of 29 total cookie. we have no idea what he could have chose and all the cookies are mixed in a bag.
================================================
Explanation:
There are 7 sugar cookies
This is out of 9+6+7+7 = 29 total cookies
The probability of getting a sugar cookie is 7/29
After that cookie is selected, the total drops to 29-1 = 28 cookies. The probability of getting a chocolate chip on the second selection is 9/28
Multiply the fractions mentioned to get the final answer
(7/29)*(9/28) = (7*9)/(29*28) = (7*9)/(29*7*4) = 9/(29*4) = 9/116
Given: f(x)
=
x - 2
x+8
Answer:
f×=×-2×+8=10×f=20xf=30×f
Bre'Aujanaye operates a flower shop in Paris. All employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and
special events. Why type of organization does Bre'Aujanaye have?
The type of market in which all employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and special events is Oligopoly.
What is Oligopoly?An oligopoly is a market characterized by a small number of firms who realize they are interdependent in their pricing and output policies. The number of firms is small enough to give each firm some market power.
Given situation:
All employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and special events.
As, we know that A market structure known as an oligopoly occurs when a few large sellers or manufacturers control a sizable portion of a market or an entire sector.
Oligopolies are frequently the outcome of corporate collaboration as a way to increase profits.
Some examples of oligopolies include the car industry, petrol retail, pharmaceutical industry, coffee shop retail, and airlines.
So, as discussed in the given case employee can take orders, sell flowers, make arrangements, and commit the store to large orders for weddings, banquets, and special events to make some profit.
Hence, type of market is Oligopoly.
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On an inch ruler AC is 3 1/2 AB is 1 7/8 then find BC
Answer: can you give me some more information??
Step-by-step explanation:
PLEASE HELP ME I AM SO CONFUSED!
Answer: The student is wrong because you have to figure out the area of each of the rectangles to find the total area. Add each of the areas to get your answer.
Step-by-step explanation:
Answer:
the total area is 1400
Step-by-step explanation:
The student is wrong. The shape's area can be calculated.
If you divide the shape into 3 separate rectangles horizontally
1st: area = 35 x 10 = 350
2nd area = 10 x 60 = 600
3rd area = (60 - 15) x 10 = 450
the total area is 350 + 600 + 450 = 1400
EASY-ISH How to put 5x-2y=-4 in slope intercept form???
Answer:
Step-by-step explanation:
5x-2y=-4
-2y=-5x-4
y=5/2x+2
Suppose the price of a sweater is $10. Jaylen's marginal benefit for purchasing each additional sweater is given in the table below. He
gets the most benefit from the first sweater and less benefit from each additional sweater. If Jaylen is behaving rationally, how many
sweaters will he purchase?
1st sweater
2nd sweater
3rd sweater
4th sweater
5th sweater
6th sweater
50
35
30
23
12
8
The number of sweaters that Jaylen will purchase, based on his marginal benefit, is 5 sweaters.
What is marginal utility?Marginal utility or benefit is the added satisfaction that a consumer derives from the consumption of an additional unit of a product or service.
Using the concept of marginal utility, we can determine the number of units consumers will be willing to purchase.
The law of marginal utility states that a consumer will continue to purchase more of an item until their marginal benefit or utility is fewer than the cost of the item.
For instance, Jaylen will buy sweaters until his marginal benefit is lower than the price of a sweater ($10).
Jaylen is likely to buy 5 sweaters since his marginal benefit, though progressively reducing, still exceeds the price of the sweaters.
Data:Price per sweater = $10
Marginal Benefits
1st sweater 50
2nd sweater 35
3rd sweater 30
4th sweater 23
5th sweater 12
6th sweater 8
Thus, based on marginal utility, Jaylen will purchase 5 sweaters.
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The probability that Roger wins a tennis tournament (event A) is 0.45, and the probability that Stephan wins the tournament (event 8) is
0.40. The probability of Roger winning the tournament, given that Stephan wins, is O. The probability of Stephan winning the tournament.
given that Roger wins, is 0. Given this information, which statement is true?
O A
Events A and Bare not independent because P(AB) # PA)
The true statement is that C. Events A and B are not independent because P(A|B) ≠ P(A).
How to illustrate the information?The probability that Roger wins a tennis tournament (event A) is 0.45 i.e. P(A)=0.45
The probability that Stephan wins the tournament (event B) is 0.40 i.e. P(B)=0.40
It should be noted that if A and are independent events, then P(B|A) = P(B). This isn't possible in this situation.
Therefore, the true statement is that events A and B are not independent because P(A|B) ≠ P(A).
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The probability that Roger wins a tennis tournament (event A) is 0.45, and the probability that Stephan wins the tournament (event B) is 0.40. The probability of Roger winning the tournament, given that Stephan wins, is 0. The probability of Stephan winning the tournament, given that Roger wins, is 0. Given this information, which statement is true?
1.Events A and B are independent because P(A|B) = P(A).
2.Events A and B are independent because P(A|B) ≠ P(A).
3. Events A and B are not independent because P(A|B) ≠ P(A).
4. Events A and B are not independent because P(A|B) = P(A).
Which statement correctly describes the graph of G(x) = -3f(x)?
A. The graph of g is the graph of f horizontally stretched by a scale factor of 3 and reflected over the x-axis
B. The graph of g is the graph of f horizontally stretched by a scale factor of 3 and replicated over the y-axis
C. The graph of g is the graph of f vertically stretched by a scale factor of 3 and reflected over the x-axis
D. The graph of g is the graph of f vertically stretched by a scale factor of 3 and reflected over the y-axis
Answer:
C is the correct choice.
Step-by-step explanation:
Here are the rules for vertical stretches and reflection
Given a function f(x), a new function [tex]g(x)= a \cdot f(x),[/tex] where a is a constant, is a vertical stretch or vertical compression of the function f(x).
Since the question use a multiplicative of -3, and -3 < 0 we get the correct choice as C: The graph of g is the graph of f vertically stretched by a scale factor of 3 and reflected over the x-axis
A baseball team has home games on Friday and Sunday. The two
games together earn $3546.00 for the team. Friday's game
generates $374.00 less than Sunday's game. How much money
was taken in at each game?
The money earned on friday is $1586 and on sunday is $1960.
What is meant by linear equation in one variable?A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable.
Let us assume the money generated by Friday game is 'F'.
Let us assume the money generated by Sunday game 'S'.
The two games together earn $3546.00 for the team.
Equation will become;
F + S = 3546.00 ........(equation 1)
Friday's game generates $374.00 less than Sunday's game. Thus,
F = S - 374.00
Since, F = S - 456.50 use the substitution method and put this value in equation 1.
(S - 374.00) + S = 3546.00
Simplifying the equation;
2S = 3546.00 + 374.00
2S = 3920
S = 1960.
Put this value in equation 1 and find F.
F + S = 3546.00
F + 1960 = 3546.00
F = 1586.
Thus, the money generated on friday is $1586 and on sunday is $1960.
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Beth makes her own liquid cleaner. the recipe makes ⅔ gallons. Beth prefers to carry smaller bottles, so she puts cleaner in ⅛ gallon bottles. How man bottles can she fill from each batch?
A fraction is a way to describe a part of a whole. Beth will able to fill 5 complete bottles from a single batch of liquid cleaner.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
Given that the recipe makes ⅔ gallons. Also, Beth puts cleaner in ⅛ gallon bottles. Therefore, we can write,
Total batch size = ⅔ gallons
Size of a bottle = ⅛ gallon
Now, the number of bottles that Beth will be able to feel from a single batch of liquid cleaner is,
Number of bottles = Total batch size / Size of a bottle
= ⅔ gallons / ⅛ gallon
= (2×8) / (3×1)
= 16 / 3
= 5.3333 ≈ 5
Therefore, Beth will able to fill 5 complete bottles from a single batch of liquid cleaner.
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Which rational number is positive
Taylor and Alex are looking for a daycare for their child. They want to make sure the daycare is midway between their jobs. Taylor works at the Rogers Middle School located at (4, -5), and Alex works at St. Philip's located at (2, 5). Where should the daycare be located?
The location of the coordinate of the daycare is (3, -1.5)
Midpoint of coordinatesThe formula for calculating the midpoint of coordinate is expressed as;
M(x, y) = {(x₁+x₂/2, y₁+y₂/2)}
Given the coordinate points (4, -5) and (2, 5), on substituting, we will have:
M(x, y) = {(4+2/2, -5+2/2)}
M(x, y) = (6/2, -3/2)
M(x, y) = (3, -1.5)
Hence the location of the coordinate of the daycare is (3, -1.5)
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np bisects MNQ, measurement MNQ, measurement MNP = (6X-12)° and measurement PNQ = (4x+8)°. find measurement MNQ
The Required answer is ∠MNQ is (10x - 4)°
Two unique points on a line define the boundaries of a line segment. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Given NP bisects MNQ as shown in the given figure
A line segment that bisects two lines divides them into two equal parts.
Given ∠MNP =( 6x - 12)°
Given ∠PNQ = (4x + 8)°
We have to determine ∠MNQ as
∠MNQ = ∠MNP + ∠PNQ
= 6x - 12 + 4x + 8
= 10x - 4
Therefore, the answer for the given question is ∠MNQ is (10x - 4)°
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(01.01 LC)
What is the simplified form of
a
b
C
d
45√x
√√4x
√√x.√√x-√√x-√√x?
Answer:
Step-by-step explanation:
Determine the number of solutions of this equation.
2(x-1)=3(x-4)
Infinitely many solutions
One solution
No solutions
Answer:
One solution.
Step-by-step explanation:
2(x-1)=3(x-4)
2x - 2 = 3x - 12
-2 + 12 = 3x - 2x
10 = x.
The empire state building in new york city is about 1,450 feet high (including the antenna at the top) and 400 feet wide. Andre wants to make a scale drawing of the front view of the empire state building on an 8 1/2 inch by 11 inch piece of paper. select a scale that you think is the most appropriate for the scale drawing.
A. 1 inch to 1 foot
B. 1 inch to 100 feet
C. 1 inch to 1 mile
D. 1 centimeter to 1 meter
E. 1 centimeter to 50 meters
F. 1 centimeter to 1 kilometer
The scale factor that is most appropriate for the scale drawing is 1 centimeter to 50 meters. (Correct choice: E)
What scale factor is the most appropriate to make an scale drawing of the Emipre State Building?
Scale factor are useful resources to make representations of huge and diminute representations of entire systems based on the application of length ratios defined below:
d / d' = r (1)
Where:
r - Length ratio, in feet per inchd - Real length, in feetd' - Scale length, in inchesNow we find the minimum reduction scale to fit the building in the paper.
Width
r' = 400 ft / 8.5 in
r' = 47.058 ft / in
Height
r' = 1,450 ft / 11 in
r' = 131.819 ft / in
The minimum reduction scale to fit the building in the paper is 131.819 ft / in (approx. 15.818 m / cm, that is 1 centimeter to 15.818 meters), that is, 1 centimeter to 131.819 feet. Then, the scale factor that is most appropriate for the scale drawing is 1 centimeter to 50 meters.
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Order the following rational and irrational numbers from least to greatest.
square root of 20, -2 3/5, 10/3,3.9, 3 7/5
The order of the number from the least to the greatest is -2 3/5, 10/3,3.9, 3 7/5, 20.
What are the order of the numbers?A rational number is a number that can be expressed as the fraction of two numbers in which the decimal is not zero. A rational number can be positive or negative. An example of a rational number is 3, -1.2.
An irrational number is a number that cannot be expressed as the fraction of two numbers. An example of a irrational number is 1/3, 22/7.
In order to order a number, all the numbers should have the same form. Thus, all the numbers would be converted to decimals where possible.
-2 3/5 = -2.6
10 /3 = 3.33
3 7/5 = 4.5
In order to order the numbers, note that the farther a negative number is from zero the smaller the number is and the farther a positive number is to zero, the greater the number is.
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9n - 50 = 4, what does n equal?
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{9n - 50 = 4}[/tex]
[tex]\large\text{Add 50 to both sides:}[/tex]
[tex]\mathsf{9n - 50 + 50= 4 + 50}[/tex]
[tex]\large\text{Simplify it:}[/tex]
[tex]\mathsf{9n = 4 + 50}[/tex]
[tex]\mathsf{9n = 54}[/tex]
[tex]\large\text{Divide 9 to both sides:}[/tex]
[tex]\mathsf{\dfrac{9n}{9} = \dfrac{54}{9}}[/tex]
[tex]\large\text{Simplify it:}[/tex]
[tex]\mathsf{n = \dfrac{54}{9}}[/tex]
[tex]\mathsf{n = 6}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{n = 6}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
GIVING BRAINIEST IF CORRECT!!!!
Express in simplest radical form.
Your answer is in the screenshot!
745.5×101 i really need help
Answer: 75295.5
Step-by-step explanation:
Answer: 75255.1
Step-by-step explanation: 745.1×101
Multiply 745.1 and 101 to get 75255.1.
FACTOR
[tex]\frac{101.7541}{2.5}[/tex]=75255[tex]\frac{1}{10}[/tex]=75255.1
twicw the sum of a number and 7 is more than 6 or at most -3
Answer:
2(x+7) more than(>) 6
Step-by-step explanation:
Answer:D
Step-by-step explanation:
Thank me later
the total weight of henry peter and david is 123.peterr is 15 kg hevier than david. david is 3kg lighter than henry find henrys weight
The ages will be:
Henry's weight = 38kg
David =35kg
Peter = 50 kg
How to calculate the weight?Let Henry's weight be represented by x
David is 3kg lighter. This will be x-3.
Peter is 15kg heavier. This will be:
= x-3 + 15 = x +12
This will be:
x + x-3 + x + 12 = 123
3x + 9 = 123
3x = 123 - 9
3x =114
Divide
x = 114/3 = 38
Therefore, Henry's weight = 38kg
David =x - 3 = 38 - 3 = 35kg
Peter =35 + 15 50 kg
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A survey of 279 SPC students was taken at registration. Of those surveyed: 51 students had signed up for a Language Arts course 36 students had signed up for a Humanities course 18 students had signed up for both a Math and Language Arts course 8 students had signed up for both a Math and Humanities course 9 students had signed up for both a Language Arts and Humanities course 4 students had signed up for all three courses students did not sign up for any of these classes How many students signed up for only Math (of these three)?
Treating the amounts as Venn sets, we have that 161 students signed up for only Math, considering that 40 did not sign for any.
What are the Venn sets?For this problem, we consider the following sets:
Set A: Students that have signed up for Arts.Set B: Students that have signed up for Humanities.Set C: Students that have signed up for Math.4 students had signed up for all three courses students, hence:
(A ∩ B ∩ C) = 4.
8 students had signed up for both a Math and Humanities, hence:
(B ∩ C) + (A ∩ B ∩ C) = 8
(B ∩ C) = 8.
18 students had signed up for both a Math and Language Arts, hence:
(A ∩ C) + (A ∩ B ∩ C) = 18
(A ∩ C) = 14.
9 students had signed up for both a Language Arts and Humanities, hence:
(A ∩ B) + (A ∩ B ∩ C) = 9
(A ∩ B) = 5.
36 students had signed up for a Humanities course, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 36
B + 5 + 8 + 4 = 36
B = 19.
51 students had signed up for a Language Arts course, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 36
A + 5 + 14 + 4 = 51
A = 28.
Considering that there are 279 students, and supposing 40 did not sign for any course, we have that:
A + B + C + (A ∩ B) + (B ∩ C) + (A ∩ C) + (A ∩ B ∩ C) + 40 = 279.
28 + 19 + C + 5 + 8 + 14 + 4 + 40 = 279
118 + C = 279
C = 161
161 students signed up for only Math, considering that 40 did not sign for any.
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