[tex]f^-1(x) = (5x-15)/2[/tex]
To find the inverse of a function, you need to switch the roles of the input and output.
So, if we let y = f(x), then the inverse function, denoted as f^(-1)(x), would be x = [tex]f^-1(y)[/tex].
In this case, we can start by setting y = (2x+15)/5.
Then, we can solve for x to find the inverse function:
y = (2x+15)/5
5y = 2x + 15
2x = 5y - 15
x = (5y-15)/2
Therefore, the inverse of f(x) = (2x+15)/5 is [tex]f^-1(x) = (5x-15)/2[/tex].
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In the figure shown,trapezoid RSTU has vertices R(1,3),S(4,3),T(3,1),and U(2,1).
Draw the image RSTU after a dilation with a scale factor of 2,followed by a translation of 2 units down.Label the vertices EFGH
A mower motor rated at 2.0 hp is found to deliver only 1.6 hp when connected to a transmission system. What is the efficiency of the transmission
The efficiency of the motor rated at 2.0 hp and delivering only 1.6 hp to a transmission system is 75%
What is efficiency of the motor used in transmission system?Efficiency of the machine is the ratio of the work input to the machine to the work output of the machine\
This represented mathematically as
= work input / work output * 100 / 1
Form the problem we have that
work input = motor rated at 1.5 hp
work output = motor rated at 2.0 hp
Efficiency = 1.5 / 2.0 * 100 / 1
Efficiency = 0.75 * 100 / 1
Efficiency = 75%
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32) reflection across x=1
The reflection across the line x = 1 will make the coordinates of the points KLM as K'(-3, - 4), L'(1, - 2), M'(1, - 5).
What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.Reflecting functions are functions whose graphs are reflections of each otherGiven is a triangle on the coordinate grid.
The line LM lie along the line {x} = 1. So, the reflection over the line {x} = 1 will ensure that the coordinate of L and M will remain same. The coordinates of point K will become (-3, - 4) from (3, - 4).
Therefore, the reflection across the line x = 1 will make the coordinates of the points KLM as K'(-3, - 4), L'(1, - 2), M'(1, - 5).
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7,3,13,1,7,5 Mode =
Median = Mean = Range =
Answer:
Median= (5+7)/2 = 6 Mean= 6 Range= 12 Mode=7
A area of a rectangle park is 3/5 square mile. the length of the park is 7/8 mile. What is the width of the park
Answer: the width is 24/35 square mile
Jessica has a sack of vegetables.
There are 3 carrots for every 4 potatoes
in the sack.
If there are 12 carrots in the sack, how
many potatoes are there?
16 potatoes
according to the question:
we can formulate it as, (12*4)/3
= 48/3= 16
use the BODMAS rule to solve
that is Brackets Of Division Multiplication Addition Subtraction
so first (12*4) will be calculated.
multiply means adding equal groups
the first value that is used to multiply is called the multiplicand (12)
the second value that is been multiplied is called the multiplier. (4)
the result that we get when we multiply the multiplicand and the multiplier is called the product. (48)
then, divide the product with the denominator
48/3
The division is the process of splitting a specific amount into equal parts.
therefore, 16 potatoes are there.
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Julia had a bag filled with gumballs. There were 1 watermelon, 2 lemon-lime, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
A. Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape
B. Sample space = lemon-lime, watermelon, grape
C. Sample space = 1, 2, 3, 4, 5, 6
D. Sample space = 1, 2, 3
Answer: D. Sample space = 1, 2, 3
Step-by-step explanation:
Answer: D: Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape
Step-by-step explanation:
The amount of flour needed for a recipe is proportional to the number of servings planned. Three servings require 4- 5 cups of flour. Write an equation to represent this relationship. Then identify the constant of proportionality and interpret its meaning.
The equation representing this relationship is y = 1.5x and the constant of proportionality is 1.5.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s. If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
Given that, the amount of flour needed for a recipe is proportional to the number of servings planned.
If a variable x is proportional to the other variable y, then the equation representing the relation is y = kx.
Here y is the amount of flour required and x is the number of servings planned.
When y = 4.5, x = 3.
4.5 = 3k
k = 4.5 / 3 = 1.5
The equation is y = 1.5 x, which represents the relationship between the amount of flour required and the number of servings planned.
Constant of proportionality is 1.5.
This means that the ratio of the y to x is a constant and is equal to 1.5.
Hence the equation representing the situation is y = 1.5x.
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POINTS!!!
37.68 cm³ is the volume of the given figure.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We need to find the volume of the cone which has radius 3 cm and slant height 5 cm
Volume of cone=1/3πr²√S²-r²
S=5 cm and r is 3 cm
Substitute S and r value in formula
=1/3×3.14×(3)²√5²-3²
=1/3×3.14×9√25-9
=1/3×3.14×9√16
=1/3×3.14×9×4
=37.68 cm³
Hence, 37.68 cm³ is the volume of the given figure.
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Melissa will take the 11:50 AM train to San Diego. The train is estimated to arrive in San Diego in 4 hours 26 minutes. What is the estimated arrival
time?
Calculations:
The relationship between the slopes
of the parallel sides is...
The relationship between the lengths of
the non-parallel sides is...
The relationship between the slopes of the parallel sides is m₁ = m₂.
The relationship between the lengths of the non-parallel sides is perpendicular or intersecting.
How to find the slope of a line?The slope of a line can be calculated by taking the tangent ratio of the angle formed by it with the x axis.
The angle between two parallel lines is zero.
This implies that they form same angle with the x-axis.
The slopes of two parallel lines are always equal to each other.
Since, the slope of a line is the tangent of the angle made by it with x axis.
Then, it can be written as m₁ = m₂.
Hence, the relationship between the lengths of the non-parallel sides;
perpendicular or intersecting.
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Answer:
The slopes are equal;The non-parallel sides are congruent (equal)-----------------------------------
The slopes of the parallel sides are equal. We can prove this by finding the slopes:
[tex]m(DG) = (2 - 2)/(1 - (-2)) = 0/3 = 0[/tex][tex]m(EF) = (- 3 - (-3))/(3 - (-3)) = 0/7 = 0[/tex]The slopes are equalWe can see the non-parallel sides have same length. Let us prove this by finding their length:
[tex]ED=\sqrt{(-4+2)^2+(-3-2)^2} =\sqrt{4+25} =\sqrt{29}[/tex][tex]FG=\sqrt{(1-3)^2+(2-(-3))^2} =\sqrt{4+25} =\sqrt{29}[/tex]The sides are equalURGENT!! ILL GIVE
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Question 2
The complete sentence will be;
⇒ The original sphere volume × 125 = The new sphere volume
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A sphere is dilated by a scale factor of to create a new sphere.
Now,
We know that;
The volume of sphere = 4/3 πr³
Here, A sphere is dilated by a scale factor of to create a new sphere.
So, The radius of old sphere = r
Then, The radius of new sphere = 5r
Hence, The volume of old sphere = 4/3 πr³
And, The volume of new sphere = 4/3 π × (5r)³
= 125 (4/3πr³)
Thus, We get;
⇒ The new sphere volume = The original sphere volume × 125
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Which of the following inequalities matches the graph?
x ≤ 5
x ≥ 5
y ≤ 5
y ≥ 5
Answer:
x ≤ 5
Step-by-step explanation:
That inequality best matches the graph.
OK for real this is a hard only verified experts can do this!!!!
The numeric value of the exponential expression in this problem is given by the following option:
A. 2^12.
How to obtain the numeric value of the exponential expression?The exponential expression for this problem is defined as follows:
8^x/2^y.
8 is the third power of 2, hence:
8 = 2^3.
When a term is elevated to two of it's powers, the powers are multiplied, hence:
(2^3)^x = 2^(3x).
Meaning that the exponential expression is then written as follows:
8^x/2^y = 2^(3x)/2^y.
When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:
2^(3x)/2^y = 2^(3x - y).
As stated in the problem, the numeric value of the expression 3x - y is given as follows:
3x - y = 12.
Hence the entire expression is simplified as follows:
2^(3x - y) = 2^12.
Meaning that the correct option is given by option A.
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Answer:A. 2^12.
Step-by-step explanation:i did it and got it right
199. By hand, find coordinates for the points where the line 3x + 2y
2-axis and the y-axis. These points are called the x-intercept and y-intercept, respectively.
Use these points to make a quick sketch of the line.
Step-by-step explanation:
let change the playing yes /no question from direct speech to direct speech
My sister asked me, "Have you seen my dog?" ____________________________________________ Vijay asked "Have you gone to market?" ____________________________________________ My mother asked, "Why are you crying?" ____________________________________________ The rickshaw puller asked me, "Do you speak English?" ____________________________________________
12x - 4y = 80
ax -by = 5
In the system of equations
shown above, a and b are constant
values. If the system has infinite
number of solutions, what is the value
of? a/b?
According to the given information in the question the value of a/b is 5.
What is value?Value is a concept that is difficult to define, but it is fundamental to our lives. It is the basis for our decisions, the way we measure our success, and the way we determine what is important to us. Value is something that can be both tangible and intangible, and it is influenced by the context in which it is perceived. Value is shaped by our beliefs, experiences, and culture, and it is constantly changing. We use value to make decisions, to motivate ourselves, and to create a sense of purpose. Value is ultimately what drives us forward and helps us make sense of the world around us.
This is because when the system has an infinite number of solutions, it means that the two equations are equivalent and that any value of x and y can satisfy the equation. Since the equation 12x - 4y = 80 is the same as ax - by = 5, both equations are equal when a/b = 5.
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All that glitters jewely store marks its prices so it can maximise its profits. What is the persons increase for each item?
The percentage increase in the cost of the jewelry items that All That Glitters Jewelry Store uses to markup its prices to maximize its profits is as follows:
Initial ring = 50%ID bracelet = 100%Earrings = 100%Pins = 25%.What is the percentage increase?The percentage increase shows the relative differences between the original cost prices of the pieces of jewelry and their selling prices.
This percentage increase is otherwise known as the markup.
The markup shows the percent increase by which an item is sold to achieve a profit target.
The formula for computing percent increase is the Increase divided by the original amount multiplied by 100.
All That Glitters Accounting Sheet
Items Cost Price Difference Percent Increase
Initial ring $60 $90 $30 ($90 - $60) 50% ($30/$60 x 100)
ID bracelet $120 $240 $120 ($240 - $120) 100% ($120/$120 x 100)
Earrings $25 $50 $25 ($50 - $25) 100% ($25/$25 x 100)
Pins $36 $45 $9 ($45 - $36) 25% ($9/$36 x 100)
Thus, All That Glitters Jewelry Store uses different markups or percent increases to sell its goods.
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Question Completion:All That Glitters Accounting Sheet
Items Cost Price
Initial ring $60 $90
ID bracelet $120 $240
Earrings $25 $50
Pins $36 $45
What is the percent increase for each item?
What is 1/2xb+9=11 In written form?? Answer needed Thursday January 5th 2023
Answer:
b = 4
Step-by-step explanation:
Solve for b?
1/2b + 9 = 11 Subtract 9 from both sides
1/2b = 11 -9
1/2 b = 2 Multiply both sides by 2
b = 4
Pins were used to fixing a string onto a board. Each pin was placed 30 cm apart. One pin was placed at the start point and one pin at the end of the string. A total of 15 pins were used. What is the length of the string in meters
Answer:
4.5 meters
Step-by-step explanation:
If the pins were placed 30 cm apart, and there were a total of 15 pins, then the length of the string is 30 cm * 15 pins = <<30*15=450>>450 cm.
To convert this length to meters, we divide the number of centimeters by 100: 450 cm / 100 = 4.5 meters.
Therefore, the length of the string is 4.5 meters.
$2.50 more than one-fourth the cost of a pizza
Answer:1/4 x + 2.50$
Step-by-step explanation:
Let us say pizza is x dollars
1/4 of the cost of pizza is 1/4x
plus 2.50$
1/4x+2.50
Consider the expression 4(8x+5)
Answer: 32x+20
Step-by-step explanation:
Answer:2 factors 2 terms
Step-by-step explanation:
What is 420 in exponential form
Answer:
420 = 4.2 x 100 = 4.2 × 102
Step-by-step explanation:
Max conducted a survey of 60 students in which he asked about their favorite school subject. 24 students said math, 12 students said science, 18 students said English.
and 6 students said social studies. Max wants to make a circle graph of these data. What angle measure should he use for the English section
!!!
The angle measure of student's favorite subject, English, is 108°.
What is an angle measure?
When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
Max conducted a survey of 60 students in which he asked about their favorite school subject. 24 students said math, 12 students said science, 18 students said English and 6 students said social studies.
The total angle of circle is 360°.
To find the angle measure of student's favorite subject, English:
The angle subtended by the category = (Amount in the Category ⁄ Total) × 360°
= 18/60 x 360
= 0.3 x 360
= 108°
The circle graph is given in the attached image.
Therefore, 108° is the angle measure of student's favorite subject, English.
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1. Find the value of x and y when,
a) (x 2y) = (5 6)
The value of x and y are 5 and 3 respectively.
How to find coordinates?The value of x and y when (x , 2y) = (5, 6) can be found as follows:
Therefore, the x coordinates of the graph is given as 5 while the double of y coordinates is equals to 6. Then, we have to equate the values as follows:
x = 5
2y = 6
The value of x is known by mere equating.
Hence, let's find the value of y.
2y = 6
divide both sides of the equation by 2
2y / 2 = 6 / 2
y = 3
Therefore, the value of y = 3 and x = 5.
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A sum of money is shared such that Akintola get twice as much as Adeniyi and Bello gets half of Adeniyi's share. Express these amounts in the form of a proportion. If Bello receives 1200naira, how much do Akkntola and Adeniyi each receive?
Answer:
Adeniyi = (2/7)
Akintola = (4/7)
Bello = (1/7)
Step-by-step explanation:
Let x stand for the money that Adeniyi recieves for her share. We can then write expressions for all the lucky recipients:
Adeniyi = x
Akintola = 2x [Akintola gets twice as much as Adeniyi]
Bello = (1/2)x [Bello gets half of Adeniyi's share]
The original amount is the sum of all three shares:
Total = x + 2x + (1/2)x
Total = (3+(1/2))x or = (7/2)x
The proportions for each can be set as the ratio of the individual's amount to the total of (7/2)x.
Adeniyi = x/((7/2)x) = (2/7)
Akintola = 2x/((7/2)x) = (4/7)
Bello = (1/2)x/((7/2)x) = (1/7)
Total = (7/7)
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then graph the equation.
y=8.4 when x=1.2
The equation of variation is y = (Simplify your answer.)
We would obtain the equation as y =7x.
What is the equation?We have to know that when we are talking about a direct variation, the implication of that is that the two variables would tend to be increasing at the same time.
Now, we know that;
y=8.4 when x=1.2
Given that;
y α x
Introducing the constant of proportionality;
y = kx
8.4 = k 1.2
x = 8.4/1.2
x = 7
Then the equation is;
y =7x
This is the equation that has been used to produce the graph in the image attached to the answer given here.
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Select the correct answer.
Which function IS continuous across Its domain?
Answer:D
Step-by-step explanation: It is D because -4 is < to -2
Angela has a pet pig befor the winter started she bought several shipments of food for the pig 250pounds 145 pounds and 200 pounds. From the start of November to through march she feed the pig the same amount of food daily how many pounds did the pig eat each day
The number of pounds of food that the pig ate every day, given that it was the same amount of food daily, was 3. 94 pounds per day
How to find the food eaten ?To find the food that the pigs ate each day, you first need to find the total number of pounds of food that Angela bought and this amount in total is :
= 250 + 145 + 200
= 595 pounds of food
The number of days from the start of November through March is :
= 30 days November + 31 days December + 31 days January + 28 Days February + 31 Days March
= 151 days in total
The amount of food that Angela's pigs ate per day is therefore:
= Total food purchased / Number of days
= 595 / 151
= 3. 94 pounds per day
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Ella has nn nickels and dd dimes. She has at most $1 worth of coins altogether. Write this situation as an inequality.
The inequality equation that shows that Ella has nn nickels and dd dimes. and the worth of the coins is at most $1 altogether is
dd + nn ≤ $1How to find the equation as requiredThe equation to represent the information is written bearing in mind that
10 dimes = 1 dollar = 20 nickels
2 nickels = 1 dime
let the dimes be d and the nickels be n
dd + nn ≤ $1
The term at most means not more than hence the worth of the sum of the coins will be 1$ or less.
we therefore use less than or equal to to represent the equation,
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The situation of Ella's amount in nickels and dimes altogether as an inequality is (5nn + 10dd) ≤ 100.
How to write Ella's nickels and dimes as an inequalityWe shall multiply each number of coins with their value in cents and express them as an inequality less than or greater than 100cents which is the equivalent to $1.
a nickel = 5 cents
a dime = 10 cents
Ella will have;
nn nickels = 5nn cents
dd dimes = 10dd cents
and;
5nn cents + 10dd cents ≤ 100 cents
(5nn + 10dd) cents ≤ 100 cents
divide through by the unit cents, we have;
(5nn + 10dd) ≤ 100.
Therefore, Ella's amount in nickels and dimes can be written as an inequality (5nn + 10dd) ≤ 100 if she has at most $1 worth of coins altogether.
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jack is standing in the queue 1/3rd was in front of him and 5/8th in the back how many students were there in the line?
Answer:
Step-by-step explanation:
24 people
Okay so 1/3 is in front of him, and 5/8 are behind him. We can add these up and see how much is missing, which can only be 1 person, Jack.
1/3+5/8 = 23/24
We got 23/24, and there's 1 person missing, who's Jack!
24 people are in the queue.
