So if you're asked to graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse. Just look at all those values switching places from the f(x) function to its inverse g(x) (and back again), reflected over the line y = x.
The equation of the line across which all inverses reflect is y = x. This reflection principle applies to linear functions, hyperbolas, and other mathematical relations where inverses can be found by interchanging the roles of x and y.
The equation of the line that all inverses reflect across is y = x. This is because when you are finding the inverse of a function, you swap the x and y variables, thus mirroring the original function across the line y = x. If you have a linear function in the slope-intercept form (y = mx + b), and you find its inverse, assuming the function is one-to-one and therefore has an inverse, you would essentially swap the x and y coordinates, resulting in the equation of its inverse. This process reflects each point of the original function across the line y = x.
As an example, for a line with an equation y = -x + 1, the inverse when reflected across the line y = x would result in swapping x and y to get x = -y + 1, which when solved for y, gives the inverse function's equation. Conversely, for a function expressed in another form, such as a hyperbola or a set of simultaneous linear equations, the principle is the same: to find the inverse, interchange the roles of the dependent and independent variables. For instance, a hyperbola described by y = a - b/x could have its inverse derived by interchanging x and y, leading to the inverse relation x = a - b/y.
It takes three painters 4 hours to paint 1 classroom.How many hour does it talk 1 painter to paint to classrooms?
It takes 1 painter 24 hours to paint two class rooms
Step-by-step explanation:
When some worker do a job together, then
The number of worker is varies inversely with the time to finish the job, because 2 workers take time less than 1 worker to finish the same jobWhen y varies inversely with x, then x y = k, where k is constantIf 5 workers finish a job in 2 hours, then 10 workers finish the same job is 1 hour because 5 × 2 = 10 × 1∵ It takes three painters 4 hours to paint 1 classroom
∵ It takes 1 painter x hours to paint 1 class room
- Equate 3 × 4 by 1 × x because they will do the same job
∴ 3 × 4 = 1 × x
∴ 12 = x
∴ It takes 1 painter 12 hours to paint 1 class room
We need to find it takes 1 painter to paint two class room
∵ The painter will paint 2 class rooms
∵ He takes 12 hours to paint 1 class room
- Multiply his time in one class room by 2
∵ 12 × 2 = 24
∴ It takes 1 painter 24 hours to paint 2 class rooms
It takes 1 painter 24 hours to paint two class rooms
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what is triangular number
Answer:
Theory
Step-by-step explanation:
A triangular number or triangle number counts objects arranged in an equilateral triangle. The nth triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers , starting at the 0th triangular number, is 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...
There are 4, 000 books in the towns library. Of these, 2, 600 are fiction. Write a percent equation that you can use to find the percent of the books that are fiction. Then solve your equation.
The percent equation showing the fiction books is y = 0.65x showing that among the 4,000 books in the library, 2,600 are fiction.
An equation is a mathematical representation of the equality of two expressions.
The number of books in the town's library = 4,000
The number of fiction books = 2,600
The number of nonfiction books = 1,400 (4,000 - 2,600)
The percentage of fiction books to the total number of books = 65% (2,600/4,000 x 100)
Let the total number of books in the library = x
Let the number of fiction books = y
Equation:
y = 0.65x
y = 2,600 (0.65 x 4,000)
10/3 = 5y how do I find y
Answer: y= 2/3
Step-by-step explanation:
Divide 10 by 5 and you get the 2 so you keep the denominator and it makes 2/3
How do u solve 4(3x-1)=9-x
Answer:
x = 1
Step-by-step explanation:
Well the first step is to apply the distributive property:
4(3x - 1) is equal to (12x - 4). You DISTRIBUTE a '4' to what is inside the parentheses.
And btw, to make it easier, you can make 9 - x so that x is first. For example, (-x + 9). They're both the same thing, just written differently.
Your new equation is 12x - 4 = -x + 9. You want to now solve the equation.
Add the (-x) to both sides. It cancels out on the right side and you add it to 12x on the left side.
[If there's no number in front of a variable, you can always just put 1 in order to make it easier]
12x + 1x = 13x. Your new equation is 13x - 4 = 9. This should look very familiar. You simply add 4 to both sides. 9 + 4 = 13
Finally, 13x = 13. Divide 13 ÷ 13 to get 1.
x = 1
21 divided by 14 and checking with Multiplication
Answer:
21 divided by 14 is 1.5
and
1.5 x 4 = 21
The calculated division of the numbers 21 divided by 14 is 3/2
How to calculate the division of the numbersFrom the question, we have the following parameters that can be used in our computation:
21 divided by 14
When represented as an equation, we have
21 divided by 14 = 21/14
Divide 21 by 14
So, we have the following result
21 divided by 14 = 3/2
Using the above as a guide, we have the following:
the result is 3/2
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Ethan says that the value of 40.7 is 10 times the value of 4.07 is be correct?
Answer:
He is correct
Step-by-step explanation:
multiplication and division are inverse operations so lets divide to see if he is correct
40.7/10=4.07
he is correct
Since the result tallies with Ethan's assumption, hence the result of Ethan is correct.
According to Ethan, he assumed that the product of 10 and 4.07 is 40.7, we are to check if the calculation of Ethan is correct.
To do that, we will have to multiply 10 with 4.07 as shown below:
[tex]= 10 \times 4.07 \\= 10 \times \frac{407}{100}\\=\frac{4070}{100} \\=40.70[/tex]
Since the result tallies with Ethan's assumption, hence the result of Ethan is correct.
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One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Find the two numbers.
One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Then the two numbers are 5 and 7
Solution:
Given that one number is 7 less than a second number.
Twice the second number is 1 less than 5 times the first.
Need to determine two numbers.
Let assume first number be represented by variable x and second number be represented by variable y.
As first number is 7 less than a second number, adding 7 to first number will give us second number
=> x + 7 = y ------ (1)
[tex]\begin{array}{l}{\text { Twice of second number }=2 \times \text { second number }=2 \times y=2 y} \\\\ {\text { 5 times the first number }=5 \times \text { first number }=5 \times x=5 x}\end{array}[/tex]
As given that Twice the second number is 1 less than 5 times the first , if we 1 to twice of second number we will get 5 times first number ,
=> 2y + 1 = 5x ------ (2)
On substituting value of y as x + 7 from equation 1 into equation 2 , we get
2(x + 7) + 1 = 5x
=> 2x + 14 + 1 = 5x
=> 2x – 5x = -15
=> -3x = -15
x = 5
Substituting x = 5 in equation (1) to get value of y
=> y = 5 + 7 = 12
Hence first number is 5 and second number is 12
Tours of the art museum are offered every 1/3 hr from 10:00 A.M. until closing at 4:00 P.M. How many tours are offered each day?
Answer: 3 Each hour × (difference in 10 am and 4 pm= 5) = 15.
Step-by-step explanation:
Answer:
18 tours are offered
Step-by-step explanation:
So 1/3 of a hour is 20 mins, so every 20 mins a tour is offered so we know 1 hour equals to 3 tours offered so
10:00 to 11:00 is 3, 11:00 to 12:00 is 3, 12:00 to 1:00 is 3, 1:00 to 2:00 is 3, 2:00 to 3:00 is 3, 3:00 to 4:00 is 3.
6 hours times 3 equals, 18 tours are offered
Label each pair of triangles with the postulate or theorem that proves the triangles are congruent.
Answer:
Δ MNO ≅ Δ PQR by ASA postulate
Step-by-step explanation:
Δ MNO and Δ PQR are congruents because:
1. Their included sides MN and PR are equal (22 units = 22 units)
2. Their angles ∠M and ∠P are equal (100° = 100°)
3. Their angles ∠N and ∠Q are equal (35° = 35°)
Now, we can conclude that Δ MNO ≅ Δ PQR by ASA postulate.
4. If the expression 25y^2- 70y+d is a perfect square, where d is a constant, find the
value of d.
Answer:
d = 49
Step-by-step explanation:
Given that the expression is a perfect square of the form
(ay - b)² = a²y² - 2aby + b²
Then comparing like terms
a²y² = 25y², that is
a² = 25 ⇒ a = 5
and -2aby = - 70y, thus
2ab = 70, that is
2(5)b = 70
10b = 70 ⇒ b = 7
b² = 7² = 49
Hence
25y² - 70y + d = (5y - 7)² = 25y² - 70y + 49
Thus d = 49
Four times a number,y,increased by eight
I'm assuming your teacher wants you to translate the given sentence into an algebraic expression.
y = some unknown number
4y = 4*y = four times a number y
4y+8 = four times a number, y, increased by 8
Answer: 4y+83tenths - 3 twentieth
Answer:
0.15
Step-by-step explanation:
Given expression
3 tenths- 3 twentieth
⇒
[tex]=\frac{3}{10} -\frac{3}{20} \\=\frac{6}{20} -\frac{3}{20}\\=\frac{6-3}{20} \\=\frac{3}{20} \\=0.15[/tex]
Therefore value of given expression is 0.15
A company makes four different types of candles. The ratio of fragrance to wax for each type of candle is shown in the tables below.
Answer:
the answer is type 2
Step-by-step explanation:
ok so you first have to find the ratio of all of them and for type 1 it is 40 to 1 for type 2 it is 50 to 1 type 3 is 25 to 1 and type 4 is 30 to 1 so there for type two has the biggest ratio of fragrance to wax
The required table that has a higher ratio of fragrance to wax is type 2.
As given in the question, a company makes four different types of candles. The ratio of fragrance to wax for each type of candle is shown in the tables.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
For Type 1
The ratio of Fragrance to wax.
= 20 / 0.5 = 40 / 1
For Type 2
The ratio of Fragrance to wax.
= 150 / 3 = 50 / 1
For Type 3
The ratio of Fragrance to wax.
= 250 / 10 = 25
For Type 4
The ratio of Fragrance to wax.
= 30 / 1
Now,
50 > 40 > 30 > 25
Type 2 > type 1 > type 3 > type 4
Thus, the required table that has a higher ratio of fragrance to wax is type 2.
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You rotate a triangle 90° counterclockwise about the origin. Then you translate its image 1 unit left and 2 units down. The vertices of the final image are (-5,0),(-2,2) and (-2,-1) . What are the vertices of the original triangle?
Answer:
The coordinates of the original triangle are (2,4). (4,1) and (1,1)
Step-by-step explanation:
About the origin, I have to rotate a triangle 90° counterclockwise. Then I translate its image 1 unit left and 2 units down.
The vertices of the final image are (-5,0), (-2,2), and (-2,-1).
We need to get the vertices of the original triangle.
So, start from a triangle with vertices (-5,0), (-2,2), and (-2,-1) and do the reverse to get the original triangle.
So, we will translate the image triangle by 1 unit right and 2 units up and we will get the triangle with vertices (-5 + 1, 0 + 2), (- 2 + 1, 2 + 2) and (- 2 +1, - 1 + 2) ≡ (-4,2), (-1, 4) and (-1,1).
Now, we have to rotate this intermediate triangle by 90° clockwise.
Therefore, the coordinates of the original triangle are (2,4). (4,1) and (1,1) (Answer)
{Since, for 90° rotation the coordinates of all the vertices will interchange their location (i.e. x-value to y-value and y-value to x-value) and a negative sign will be added to the y-coordinate of the interchanged coordinates}
Seniors at a high school were asked what color car they drive. The results were put in a circle graph. The measure of each central angle is shown. If a senior is chosen at random from this school, find the probability of each response.
What Color Is Your Car?
Car color is not red or blue.
options:
0.51
0.47
0.53
0.49
Answer:
P(The color of the car is red) is 0.32 .
P(The color of the car is white) is 0.34 .
P(The color of the car is silver) is 0.19 .
P(The color of the car is blue) is 0.15 .
P(car color is not red or blue) is 0.53 .
Step-by-step explanation:
We know that total angle subtended at the center by a complete circle is
360° .
According to the question,
P(The color of the car is red)
= [tex]\frac {115.2}{360}[/tex]
= 0.32
P(The color of the car is white)
= [tex]\frac {122.4}{360}[/tex]
= 0.34
P(The color of the car is silver)
= [tex]\frac {68.4}{360}[/tex]
= 0.19
P(The color of the car is blue)
= [tex]\frac {54}{360}[/tex]
= 0.15
So
P(car color is not red or blue)
= 1 - (0.15 + 0.32)
= 0.53
Answer:
0.53 is the correct answer.
Step-by-step explanation:
Is the expression 3(x+1 1/2)-3 equivalent to 3x+1 1/2
Answer:
No
Step-by-step explanation:
3(x+11/2)-3 = 3x + 33/2 -3 = 3x + (33-6)2 = 3x + 27/2
The expression 3(x+1 1/2)-3 is equivalent to 3x+1 1/2 once the distributive property is applied and the constants are combined.
The expression 3(x+1 1/2)-3 is not equivalent to 3x+1 1/2. To determine the equivalency, we need to apply the distributive property to the expression on the left-hand side. The distributive property states that we can multiply the outside term by each term inside the parentheses. Thus, the expression 3(x+1 1/2) becomes 3x + 4 1/2. When we subsequently subtract 3 from 4 1/2, we get 1 1/2, which results in the final expression of 3x + 1 1/2. This confirms the expressions are equivalent.
Domain and Range Mapping Diagrams
Determine whether each diagram depicts a function or not.
Function
VOON
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Solve for u.
3u+4u = 56
Answer:
8
Step-by-step explanation:
3u+4u=7u
7u=56
u=8 because you divide
Answer:
U=8
Step-by-step explanation:
3u+4u=56
7u=56
u=8
Solve the following inequality. Show and explain your work
3(x-6)+2>5x-4
Answer:
x< (-6)
Step-by-step explanation:
If you have any questions about the way I solved it,don't hesitate to ask
q.15ab with step pls
Answer:
(a) The cost of 1 model house A = $24
(b) YES, with $200 Victor can purchase 3 A model & 4 B model houses.
Step-by-step explanation:
Let us assume the cost of model house B = $ m
So, the cost of model house A =$ ( m - 6)
So, the price of 5 A model house = 5 x ( Rate of 1 model house A)
= 5(m-6)
And, the price of 3 B model house = 3 x ( Rate of 1 model house B)
= 3 x (m) = 3 m
So, the cost of 3 B house + 5 A house = 5(m-6) + 3 m
⇒5(m-6) + 3 m = $210
or, 5 m - 30 + 3 m = 210
or, 8 m = 240
or, m = 30
So, the cost of 1 B house = m = $30
And the cost of 1 house A = (m -6) = (30 - 6) = $24
Now, The cost of 3 A model + 4 B model
= 3( 24) + 4(30) = 72 + 120 = 192
So, The cost of 3 A model + 4 B model = $192 and $192 < $200
Hence, YES, with $200 Victor can purchase 3 A model + 4 B model houses.
The perimeter of a basketball court is 90 meters and the length is 6 meters longer than twice the width. What are the length and width?
The length of basketball court is 32 meters and width is 13 meters.
Step-by-step explanation:
Perimeter = 90 meters
Let w be the width
Length = l = 2w + 6
As basketball court are in rectangular shapes, therefore,
Perimeter = 2(length+width)
[tex]90=2(2w+6+w)\\90=2(3w+6)\\90=6w+12\\90-12=6w\\6w=78[/tex]
Dividing both sides by 6;
[tex]\frac{6w}{6}=\frac{78}{6}\\w=13\ meters[/tex]
Length = 2w+6
[tex]l=2(13)+6\\l=26+6\\l=32\ meters[/tex]
The length of basketball court is 32 meters and width is 13 meters.
Keywords: perimeter, rectangles
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(–x^2y^3m)^5 write the monomial in standard form
Answer:
-m^5*x^10*y^15
Step-by-step explanation:
remember alphabetical order
The standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is (–x²y³m)⁵. The standard form of the number will be written as,
E = (–x²y³m)⁵
Solve the exponents and simplify.
E = -m⁵x¹⁰y¹⁵
Therefore, the standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.
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Use the array to solve the problem 8x9
Answer:
72
Step-by-step explanation:
multiply
Answer:
72
Step-by-step explanation:
This is 6 grade homework please help me
Answer:
what is the problem?
Step-by-step explanation:
Answer:
What work do you need help with tag a photo or write it out.
The length of a rectangle is three times width. If the perimeter of the rectangle is 40cm, find its length and width?
Answer:
width = 5
length = 15
Step-by-step explanation:
width: x
length : 3x
x + 3x + x + 3x = 40
8x = 40
x = 5
width = 5
length = 15
The drawing below has four lines . How many lines does it have
Answer: I think you answered your own question
Step-by-step explanation:
Diana has an end table in the shape of a right triangle. The triangular tabletop is twice as high as it is wide at the base. If the area of the tabletop is 4 square feet (4ft2), what is the width of the base of this triangular tabletop in feet?
Answer:
The width of the base is 2.828 feet
Explanation:
Given the area of the table top is 4 square feet
The triangular table top is twice as high as it is wide at the base
Therefore, we can say that height = base
Area of a right angled triangle is calculated by, Area = ½ * base * height
In this case, height = base
Therefore, area =[tex]\frac{1}{2}\times (base)^2[/tex]
Substituting the values,
4 = [tex]\frac{1}{2}\times (base)^2[/tex]
[tex](base)^2[/tex] = 8
Base = 2√2 = 2 * 1.414 = 2.828 feet
Therefore, the width of the base is 2.828 feet
If on a scale drawing 75 feet are represented by 45 inches, then a scale of 1/5 inch represents how many feet?
Answer:
1/3 or 0.33 feet
Step-by-step explanation:
This question can be easily answered by using simple proportions.
If 75 feet are represented by 45 inches on a scale, then the scaling factor from feet to inches is 45/75, or from inches to feet is 75/45
If we have 1/5 inch and want feet, just multiply by 75/45 to get
1/5*75/45=1/3=0.33 feet
Answer:
1/3 feet
Step-by-step explanation:
We are given that
On a scale drawing
45 inches represented =75 feet
We have to find a scale of 1/5 inch how many feet represents.
To find the value in feet represented by a scale of 1/5 inch we will use unitary method.
Using unitary method
45 inches represents =75 feet
1 inch represents =[tex]\frac{75}{45}[/tex] feet
1/5 inch represents =[tex]\frac{75}{45}\times \frac{1}{5}[/tex] feet
1/5 inch represents=[tex]\frac{1}{3}[/tex] feet
Hence, a scale of 1/5 inch represents 1/3 feet
euben's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Reuben $5.70 per pound, and type B coffee costs $4.30 per pound. This month, Reuben made 167 pounds of the blend, for a total cost of $820.30. How many pounds of type A coffee did he use?
Answer:
The quantity of type A coffee is 73 pounds
The quantity of type B coffee is 94 pounds .
Step-by-step explanation:
Given as :
The price of Type A coffee costs = $ 5.70 per pound
The price of Type B coffee costs = $ 4.30 per pound
The total quantity of coffee does Reuben purchases = 167 pounds
The total cost of the coffee for 167 pounds = $ 820.30
Let The quantity for type A coffee = a pounds
And The quantity of type B coffee = b pounds
Now, According to question
a + b = 167 pounds And
$ 5.70 × a + $ 4.30 × b = $ 820.30
Now solving equations
5.70 × ( a + b ) = 5.70 × 167
or, 5.70 a + 5.70 b = 951.9
Now ,
( 5.70 a + 5.70 b ) - ( 5.70 a + 4.30 b ) = 951.9 - 820.30
or, ( 5.70 a - 5.70 a ) + ( 5.70 b - 4.30 b ) = 131.6
Or, 0 + 1.4 b = 131.6
∴ b = [tex]\frac{131.6}{1.4}[/tex]
I.e b = 94 pounds
Put the value of b to get a value
So, a = 167 pounds - b
Or, a = 167 - 94
∴ a = 73 pounds
Hence The quantity of type A coffee is 73 pounds
And The quantity of type B coffee is 94 pounds . Answer