If the graphs of both functions are symmetric with respect to the line y = x, then we say that the two functions are inverses of each other.
The inverse function is represented by f⁻¹ with regards to the original function f and the domain of the original function becomes the range of the inverse function.
The range of the given function becomes the domain of the inverse function the injective function is the reflection of the original function with reference to the line y = x and is obtained by swapping (x, y) with the (y, x).
There are a few steps to find an Inverse Function:
For the given function f(x) = ax+b, replace f(x)=y, to obtain y = ax + b.Interchange the x with y and the y with x in the function y=ax+b to obtain x=ay+b.Here solve the expression x = ay + b for y. And we obtain y = (x - b/aFinlly replace y = f-1(x), and we have f-1(x) = (x - b)/a.To know more about inverse graph function:
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-12 + 3m= m - 2
thanku
[tex] - 12 + 3m = m - 2[/tex]
[tex]3m - m = - 2 + 12[/tex]
[tex]2m = 10[/tex]
[tex]m = \frac{10}{2} \\ [/tex]
answer: [tex]m = 5[/tex]
What is sublimation class 9?.
Sublimation is the straight transition from a solid state of materials to a vapor state upon heating (without becoming liquid).
When a substance changes from one state to another, as as from a solid to a gas, this transition, transformation, or conversion is referred to as sublimation.
Sublimation is the procedure through which a material is converted from its solid to gaseous phase without moving to its liquid form. At a temperature and pressure below the substance's triple point, this process, an endothermic phase transition, takes place. The opposite of this process, in which a gas is transformed straight into a solid state, is desublimation or deposition.
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please help with thus
Evaluate the following expreion when a = 5 and b = 1. Then, plot the reulting value on the provided number line
The solution of the expression 12 + [2 - (4 × a²)] ÷ 7 + b with the given values of a and b (using BODMAS) is -1 .
Given,
Equation is : 12 + [2 - (4 × a²)] ÷ 7 + b
Values of a and b are; 5 and 1 respectively
Substitute the values of a and b into the equation
12 + [2 - (4 × 5²)] ÷ 7 + 1
Using BODMAS :
solve the expression that is in the bracket first :
⇒ 12 + [2 - 100] ÷ 7 + 1
⇒ 12 + [-98] ÷ 7 + 1
Solve the division next :
⇒ 12 - 14 + 1
Solve the addition next :
⇒ 13 - 14
Solve the subtraction next :
⇒ -1
Therefore, the solution of the expression with the given values of a and b is - 1
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the sum of two numbers is 157. the difference between the two numbers is 5. what are the two numbers.
hope it helps you
Step-by-step explanation:
hope it helped you
What is the y-intercept of Y 10x 9?.
The y-intercept is (0,9)
The y-intercept of a linear equation in the form of y = mx + b is represented by the constant term, b. In this case, the y-intercept is 9. This means that the line represented by this equation crosses the y-axis at the point (0, 9).
To find the y-intercept, we can substitute x = 0 into the equation, y = 10x + 9 and we get:
y = 10(0) + 9
y = 9
So the y-intercept is (0,9)
A linear equation is an equation that can be written in the form of y = mx + b, where m is the slope (or rate of change) and b is the y-intercept (the point where the line crosses the y-axis).
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A small business has one team that installs new swimming pools and four employees that clean and maintain pools. Which of
the following is a service that is provided by this business to its customers? (1 point)
O the employees who clean and maintain pools
O the new swimming pools
O the team that installs the new pools
O pool cleaning
Answer:
the correct answer would be "the team that installs the new pools" and "the employees who clean and maintain pools" are services provided by this business to its customers, as they are actively performing tasks for the customer related to swimming pools.
O pool cleaning is a service that is provided by this business to its customers.
The correct option is C. The team that installs the new pools.
What is the business to the customer?Business-to-consumer (B2C) refers to the process of selling goods and services directly between an organization and the customers who will ultimately use them. The majority of businesses that sell directly to customers are referred to as B2C businesses.
The correct answer would be "the team that installs the new pools" and "the employees who clean and maintain pools" are services provided by this business to its customers, as they are actively performing tasks for the customer related to swimming pools. Pool cleaning is a service that is provided by this business to its customers.
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Brian draws a drinking glass on graph paper using the scale shown below. The glass has a length of 8 units in the drawing. What is the height of the actual glass? HELP PLEASE!
The height of the actual glass is equal to 10 cm.
What is scale factor?In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures such as drinking glasses, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Scale factor = 2/2.5
For the height of the actual glass, we have:
2/2.5 = 8/x
x = (2.5 × 8)/2
x = 20/2
x = 10 cm.
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The quare root of a certain number i approximately 8. 1066. The certain number i between what 2 integer?
The given number lies between 64 and 81
what is square root?A value that, when multiplied by itself, equals the original number is said to be the square root of a number. The character "√" stands for it. For instance, since 4 × 4 is 16, the square root of 16 is 4. Although a number's square root can be positive or negative, the positive value is more frequently utilized. To determine a distance or length, it is also used in mathematics.
given that square root is approximately 8.1066
let the value of the number be x
so √x>8 and √x<9
=> 8 < √x < 9
squaring on the both side we get
64 < x < 81
so the number lies between 64 and 81
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How do you write a product of a mixed number?.
A product of mixed numbers is a fraction or a natural number.
We know that a mixed number is a number consisting of a natural number and a proper fraction.
It is a combination of a natural number and fraction
We can say that a mixed number can be written as [tex]a\frac{b}{c}[/tex]
where a, b and c are non-zero real numbers with c > b
When we need to multiply two mixed numbers, first we change each mixed number to an improper fraction. Then multiply the numerators.
Then we multiply the denominators. And simplfy the resultant fraction if needed.
Consider two mixed numbers [tex]2\frac{1}{4} , 3\frac{2}{5}[/tex]
After converting given mixed numbers into an improper fractions we get,
[tex]2\frac{1}{4} =\frac{9}{4} , 3\frac{2}{5}=\frac{17}{5}[/tex]
So the product of given mixed numbers would be,
[tex]2\frac{1}{4} \times 3\frac{2}{5}[/tex]
[tex]=\frac{9}{4} \times \frac{17}{5} \\\\=\frac{153}{20}[/tex]
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6-27: On graph to the right, graph each line in the system shown belowWhat is the point of intersection ? Does more one exist? How do you know for sure? y = - x + 2; y = 3x + 6
The point of intersection for the two lines [tex]y = -x + 2[/tex] and [tex]y = 3x + 6[/tex] is [tex](2,4).[/tex]
To find the point of intersection, you can set the two equations equal to each other and solve for x and y.
[tex]y = -x + 2[/tex]
[tex]y = 3x + 6[/tex]
[tex]-x + 2 = 3x + 6[/tex]
[tex]-4x = 4[/tex]
[tex]x = -1[/tex]
then substitute [tex]x = -1[/tex] in any of the equation
[tex]y = -x + 2[/tex]
[tex]y = -(-1) + 2[/tex]
[tex]y = 1 + 2[/tex]
[tex]y = 3[/tex]
So the point of intersection is [tex](-1,3)[/tex].
It is possible that there may be more than one point of intersection, but in this case, there is only one point of intersection.
To be sure that there is only one point of intersection, you could graph the two lines and visually check if they intersect at only one point.
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What expression is equivalent to the given expression?
Consider this expression.
-3x^2 - 24x - 36
__(x + __)(x + __)
A. 3
B. -3
A1. 2
B1. -2
C1. -4
D1. 4
A2. 6
B2. 9
C2. -9
D2. -6
Answer: A. -3
A1. -2
A2. -6
Step-by-step explanation:
The expression -3x^2 - 24x - 36 can be factored into the form (ax + b)(cx + d) by using the technique of grouping or by using the factoring by grouping method.
The factored form of -3x^2 - 24x - 36 is
( -3x - 6)( x + 6)
So the answer is:
A. -3
A1. -2
A2. -6
Is an isosceles triangle always 90 degrees?.
No, an isosceles triangle is not always 90 degrees
Two of a triangle's sides must be the same length for the triangle to be considered isosceles. The third side, which is not equally long as the first two, is referred to as the base. The angle at the vertex opposite to the base is obtuse, acute, or right angle and the angles at the vertex opposite to the base are congruent.
Not all angles in an isosceles triangle are 90 degrees. A triangle with equal-length sides is called an isosceles triangle, although the angles at the vertex opposite the equal sides might be of any degree. The isosceles right triangle, the golden triangle, the faces of bipyramids, and some Catalan solids are all examples of isosceles triangles.
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Last week Rachel used 42. 5 pounds of sugar in her bakery. This week she used 26 pounds of sugar. What is the percent change of the amount of sugar used?
The percentage change in the amount of sugar used is 38.8%
Sugar used the previous week = 42. 5 pounds
Sugar used this week = 26 pounds
Calculating the difference between two amounts of sugar -
Sugar used the previous week - Sugar used this week
= 42.5 - 26
= 16.5 pounds.
To calculate the change in percentage, the differential amount is to be multiplied by 100 to express the result as a percentage, which is required to determine the percent change in the amount of sugar utilised.
Calculating the per cent change -
Differential sugar amount / Sugar used in previous week x 100
= 16.5 / 42.5 x 100
= 38.8%.
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Si solo estuvieran escritos los nombres de los números les serviria tomar en cuenta el número de palabras de cada número para ordenarlos
Yes, it is possible to order a list of numbers by their number of words. To do this, you will need to count the number of words in each number, then order them in ascending or descending order based on this number.
Here is an example of how to do this:
1. Count the number of words in each number. For example, the number “twenty-nine” has two words (“twenty” and “nine”).
2. Order the numbers from least to greatest or greatest to least based on the number of words. For example, “nine” has one word, so it would come before “twenty-nine” which has two words.
3. Place the numbers in order from least to greatest or greatest to least.
This method can also be used to order numbers that are written in words or numbers that are written in numerals. However, if the numbers are written in numerals, you will need to convert them to words before you can count the number of words.
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Evaluate the function
Find f(3) if f(x) = 8x+3
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{f(x) = 8x + 3}\\\mathsf{f(x) = 8x + 3}\\\mathsf{f(x) = 8(3) + 3}\\\mathsf{f(x) = 24 + 3}\\\mathsf{f(x) = 27}\\\\\huge\text{Therefore, your answer could possibly be: }\\\huge\boxed{\mathsf{f(x) = 27}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Answer:
[tex] \sf \: f(3) = 27[/tex]
Step-by-step explanation:
Given function,
→ f(x) = 8x + 3
Now the value of f(3) will be,
→ f(x) = 8x + 3
→ f(3) = 8(3) + 3
→ f(3) = 24 + 3
→ [ f(3) = 27 ]
Hence, the value of f(3) is 27.
18.4x - 2.1y +9.6 - (-1.2x) + 3.4
19.6x -2.1y + 13 is a simplified form of the 18.4x - 2.1y +9.6 - (-1.2x) + 3.4 equation.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given expression 18.4x - 2.1y +9.6 - (-1.2x) + 3.4
Simplifying using PEMDAS
=> 18.4x - 2.1y +9.6 - (-1.2x) + 3.4
First, we will open the bracket
=> 18.4x - 2.1y +9.6 + 1.2x + 3.4
Calculating the like terms
=> 19.6x -2.1y + 13
Therefore, a simplified form of the given equation is 19.6x -2.1y + 13.
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What is an inequality in math example?.
An inequality in math is a statement that compares two values using an inequality sign. Inequalities can be used to describe a range of values, such as greater than, less than, greater than or equal to, and less than or equal to.
For example, the inequality 7 > 5 states that the value 7 is greater than the value 5. This type of inequality is known as a strict inequality, meaning that the values must be greater or less than one another in order for the statement to be true.
Another type of inequality is a non-strict inequality, which uses the symbols “≥” and “≤”. Here, "greater than or equal to" and "less than or equal to" are the appropriate definitions. For example, the inequality 5 ≤ 7 states that the value 5 is less than or equal to the value 7. This type of inequality allows the values to be equal to each other, rather than just strictly less or greater than one another.
Inequalities are used in a variety of mathematical equations, including linear equations, quadratic equations, and polynomial equations. They can also be used to solve for unknown values, such as the solution to an equation. Inequalities are also used to describe ranges of values, such as the range of numbers on a number line.
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pls help ASAP
List the three tubes — top, seat, and down tube — in order from shortest to longest. Explain your reasoning. (4 points; 1 point for list, 3 points for explanation)
Answer:
Part 1
The triangle is an isosceles triangle because it has no equal sides. The measurement of B will equal 95°.
Part 2. from shortest to longest1. seat tube2. top tube3. down tubeStep-by-step explanation:
Part 11.It has no equal sides
2.180° in a triangle, added the other degrees given, then subtracted 180 by the added degree sum.
Part 2you figure out the shortest to longest side by looking at the degrees.
Where 30° is, the opposite line from it is the seat tube . Meaning its the shortest. use the same tactic for the others. Opposite of 55° is top tube. Finally Opposite of 95° is the down tube.
Hope this helps! Good Luck!
I tried to simplify the answers as well as explaining it at the same time. I know when I have graded assignments they check them all for plagiarism. If you still a little confused I can help and be a little more in depth.
MP3,
What is the product of 3a²b and -2ab³?
the answer is number 4, you are basically multiplying everything together. 3×-2=-6 and for the letters (i forgot the term to call them) you just add them together which gives the answer on number 4.
Can you follow this and give me the answers for the missing numbers?
Answer:
+ (5x + 9y = -5)
Step-by-step explanation:
+ (2x + 5y = -9)
+ ( 3x + 4y = 4)
+ (5x + 9y = -5)
Steven has a rope that is 6 ft long. He cuts it into 9 pieces, as shown in the model.
The model shows that there are 9 pieces that are each 2/3 ft long.
Which division equation represents the situation?
The (arithmetic operation)division equation at B (6/(2/3)=9) represent the situation.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.
The four basic arithmetic operations in Maths, for all real numbers, are:
Addition (Finding the Sum; ‘+’)
Subtraction (Finding the difference; ‘-’)
Multiplication (Finding the product; ‘×’ )
Division (Finding the quotient; ‘÷’)
As
Model having length 6 feet is divided into 9 pieces.
Therefore,
6/9=2/3
hence,
6/(2/3)=9
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I need this answered NOW!!!!
10 POINTS!!!!
Answer: y = −1/2x + 2 is the answer to the slope-intercept form of the graph.
Step-by-step explanation:
I hope this helps!!
Find the angle between the forces given the magnitude of their resultant. (Hint: Write force 1 as a vector in the direction of the positive x-axis and force 2 as a vector at an angle with the positive x-axis. Round your answer to one decimal place.)
Force 1 Force 2 Resultant Force
50 pounds 75 pounds 100 pounds
Answer:
75.5°
Step-by-step explanation:
You want the angle between a 50 pound force and a 75 pound force given that their resultant is a 100 pound force. Force 1 is aligned with the +x axis, and Force 2 is in the first quadrant.
Law of CosinesThe forces and their resultant form a triangle such that the angle opposite the resultant is the supplement of the angle between the forces. We can find the angle opposite the resultant using the law of cosines:
c² = a² +b² -2ab·cos(C)
cos(C) = (a² +b² -c²)/(2ab)
C = arccos(a² +b² -c²)/(2ab) = arccos((50² +75² -100²)/(2·50·75))
C = arccos(-1875/7500) = arccos(-1/4) ≈ 104.48°
The angle between the vectors is the supplement of this:
angle12 = 180° -104.48° = 75.52° ≈ 75.5°
The angle between the forces is about 75.5°.
Vega wants to prove that the segment joining midpoints of two sides of a triangle is half the length of the third side. Select the appropriate rephrased statement for Vega's proof.
Here are the answer choices:
Let P and Q represent the intersections of two triangle sides. Consequently, the third side's length is divided in half by the length of the section that connects P and Q.
Vega is attempting to prove that the segment joining the midpoints of two sides of a triangle is equal to half the length of the third side. To do this, she must first identify the two midpoints of any given triangle. Let P and Q be the midpoints of two sides of the triangle. She must then demonstrate that the segment connecting P and Q is equal to half the length of the third side. To do this, Vega must calculate the distance between P and Q and then compare it to the length of the third side. If the two measurements are equal, then Vega will have proven her point. This statement can be rephrased as "the length of the segment connecting P and Q is equal to half the length of the third side."
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If 8 pounds of peanuts cost $12 how much does 1 pound of peanuts cost? Use the answer to find how much 10 pounds cost
Please help
Answer: 1.5
Step-by-step explanation: 12/8=1.5
Answer:
One pound of peanuts costs 1 dollar and 50 cents.
Ten pound of peanuts costs 15 dollars.
Step-by-step explanation:
1. If 8 pounds of peanuts cost $12 how much does 1 pound of peanuts cost?
One pound of peanuts costs 8 times less:
$12 : 8 = $1.5 = 1 dollar and 50 cents
2. Use the answer to find how much 10 pounds cost:
Ten pounds of peanuts will cost 10 times more than one pound:
$1.5 x 10 = $15
What are the 3 angles of an isosceles right triangle?.
An isosceles right triangle has a right angle (90 degrees) and two congruent acute angles(45 degrees).
A triangle's isosceles quality is characterised by its two equal-length sides. The third side which is not equally long as the first two is referred to as the base. The legs are the two equal sides. The vertex opposite the base has an obtuse, acute, or straight angle, and the angles at that vertex are congruent.
A right angle of 90 degrees and two congruent acute angles make up an isosceles right triangle (45 degrees). A right triangle has three angles, two of which are acute and one of which is always a right angle (90 degrees). Because the two legs of an isosceles right triangle are congruent, the two acute angles are likewise congruent. An isosceles right triangle, therefore, has angles of 90 degrees, 45 degrees, and 45 degrees.
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A ceiling measures 24 feet by 26 feet. You need to install ceiling tiles measuring 2 feet by 4 feet in size. How many ceiling tiles are required?
The total number of ceiling tiles required is 78
Measurement in the ceiling = 24 feet by 26 feet.
Measurement of the tiles = 2 feet by 4 feet
Mathematicians use units of measurement, rules, and formulas to calculate various measurement parameters, including area, volume, length, perimeter, surface area, time, etc. The process of comparing a physical quantity with a recognised standard quantity of the same kind is called comparison.
Calculating the total number of tiles required -
= Measurement in the ceiling / Measurement of the tiles
= 24 x 26 / 2 x 4
= 624 / 8
= 78
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Is the inverse of a square root function a parabola?.
The inverse of a square root function looks like a half parabola when we plot it on the graph.
Curved graphs of square root functions are typical. In actuality, the curve above is a parabola's half that is lying on its side. On a graph of the equation y² = x, it represents one half of the parabola.
A quadratic function is defined as f(x) = ax² + bx + c, where a, b, and c are all integers and an is not equal to zero. The graph of a quadratic function has the form of a parabola.
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The degree of the polynomial function f(x) is 3.
The roots of the equation f(x) = 0 are -1, 0, and 4.
-
Which graph could be the graph of f(x)?
Answer: The graph that could be the graph of f(x) is a parabola that opens upwards, with a vertex at (2,-4) and x-intercepts at x = -1 and x = 4. Since the degree of the polynomial function f(x) is 3 and the roots are -1, 0, and 4, the polynomial function is a cubic function and its graph is a parabola.
The roots of a polynomial function are the x-coordinates of the x-intercepts of the graph of the function. Therefore, since the roots of the equation f(x) = 0 are -1, 0, and 4, the graph of f(x) will have x-intercepts at x = -1 and x = 4.
The fact that the vertex is at (2, -4) mean that the parabola will open upwards and pass through the point (2, -4)
It's important to note that, if the polynomial function has a degree greater than 3, there may be multiple graphs that could represent the polynomial function, as long as they have the same roots.
Step-by-step explanation:
