Yes , the given function is an inverse function which is given by [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f-1 or F-1.A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.An inverse function returns the original value that the function provided the output for.We have given a function [tex]f(x)=\frac{2x^2}{5} +1[/tex]. ....(1)
Let y = f(x)
[tex]y=\frac{2x^2}{5} +1\\y-1=\frac{2x^2}{5} \\\\\frac{5(y-1)}{2} =x^2\\\\\sqrt{\frac{5(y-1)}{2} } =x[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]x=f^{-1}(y)[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]
We can check that this is really an inverse function or not
Putting in [tex]x=\sqrt{\frac{5(y-1)}{2} }[/tex] equation (1) , we get
[tex]f(f^{-1}(y))=\frac{2(\sqrt{\frac{5(y-1)}{2} })^2}{5} +1\\\\\y=\frac{2\frac{5(y-1)}{2} }{5} +1\\\\y=\frac{5(y-1)}{5} +1\\\\y=y-1+1\\\\y=y[/tex]
As LHS = RHS which means inverse function is correct .
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Fill in the blank to find an equivalent fraction to 8/9 = ?/9
Answer:
Due to the fact that the denomonator is the same your answer will be 8/9 but if there was a different denominator you would need to find the least common multiple. Dont forget anything you do to the bottom has to be done to the top
Step-by-step explanation:
Hope this helps!!
hii pls help, extra points for a sure and correct answer!!
Answer:
The answer is supposedly 0.25
write an algebraic expression for the word phrase c divided by 7
Answer:c=7
Step-by-step explanation:
Look at the picture pleaseee
What is an equation of the line that passes
through the point (1, 3) and is parallel to
the line 3x + y = 9?
Answer: y=-3x+6
Step-by-step explanation:
simplify ax+by=c into slope intercept which is y=mx+b
y=-3x+9.
since slopes are the same in parallel equations, graph the point (1,3) and go up 3, and left 1. the y intercept should be 6. I went left one because it's a negative slope, so in order for the line to be negative, you'd go left, not right. y= -3x+6
A dozen donuts (12) at the local bakery cost $19.20. At this rate, how much does 1 donut cost?
How much do 7 donuts cost?
Answer: 1 Donut would be $1.6 and 7 donuts would be $11.2
I'm thinking of a number and if I add 3 and divide
by 2, I get -4, what is my number?
Answer:
x= -11
Step-by-step explanation:
(x+3)/2 = -4
multiply both sides by 2
x+3 = -8
move 3 to other side through subtraction
x = -11
Compare -√7 and 3.12345.... Justify your reasoning.
HELP PLEASE
If we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that there are two numbers which are -√7 and 3.12345.
Let's compare the,.
We know that an irrational number is a number which can't be expressed other than using roots.
Here -√7 is an irrational number and if we represent that in decimal form then it can be written as :
-√7 = - 2.6467
Now , as this number is negative decimal number it is less than the other number given which is 3.12345 because 3.12345 is a positive decimal number. And we know that value of a positive number is always greater than a negative number.
i.e.,
3.1245 > -√7
Therefore , if we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.
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f(x) = 9x² +5; find f(10)
Answer:
f(10) = 905
Step-by-step explanation:
f(x) = 9x² +5; find f(10)
~Substitute x with 10
9(10)^2 + 5
~Solve exponent first
9(100) + 5
~Multiply
900 + 5
~Add
905
Best of Luck!
The answer is:
f(5) = 905Work/explanation:
To evaluate the given function, plug in 5 for x:
[tex]\bf{f(x)=9x^2+5}[/tex]
[tex]\bf{f(10)=9(10)^2+5}[/tex]
Remember, exponents first. So we square 10 first.
[tex]\bf{f(10)=9\cdot100+5}[/tex]
Multiply, then add:
[tex]\bf{f(10)=900+5}[/tex]
[tex]\bf{f(10)=905}[/tex]
Therefore, the answer is 905.What is the correct solution to the given equation?
Solve for 4X + 5 = 25
Answer:5
Step-by-step explanation:
4x + 5 = 5.. if its addition you take away the number if its subtraction you add the number.. take away 5 from 25.. 4 times 5 is 20
Kloe has 24 sunflowers, 16 roses, and 48 white carnations. She wants to make flower arrangements with the same number of each flower. How many flower arrangements can she make? How many of each type of flower is in a flower arrangement?
Kloe can make 4 flower arrangement
The number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations.
The number of flower arrangements can be calculated as follows;
The first step is to calculate the HCF between the three numbers
24= 6 × 4
16= 4 × 4
48= 12 × 4
The HCF is 4
Hence the number of flower arrangement is 4 and the number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations
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a person leaves home at 8:00 am and drives to a destination at a rate of 40 miles per hour. the person returns at a rate of 25 miles per hour and arrives at 2:30 pm. how far was the destination?
Answer:
100mi
Step-by-step explanation:
a) Work out (8 × 10³) × (2 × 10¹) Give your answer in standard form.
Answer:
[tex]1.6 \times 10^5[/tex]
Step-by-step explanation:
[tex](8 \times 10^3) \times (2 \times 10^1)\\\to (8 \times 2) \times (10^3 \times 10^1) \text{ / Remember rule: } a^m \times a^n = a^{m + n}\\\to 16 \times 10^{3 + 1}\\\to 16 \times 10^4\\\to 1.6 \times 10 \times 10^4\\\to 1.6 \times 10^{1 + 4}\\\to 1.6 \times 10^5[/tex]
What are the solutions of each equation? Check your answers.
(c). ln 2 x+ln 3=2
According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.
Therefore, the given expression is [tex]ln2+ln3=2[/tex]
The values get multiplied in addition. Therefore, the above expression can be written as:
Expression = [tex]ln(6)=2[/tex]
Using logarithmic definition, we can write:
[tex]6 = e^{2}\\e = \sqrt{6},-\sqrt{6}[/tex]
The solution for the given expression is [tex]e = \sqrt{6},-\sqrt{6}[/tex]
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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Simplify each rational expression. State any restrictions on the variables.
x²+8 x+16 / x²-2 x-24
According to the question, the given rational expression is as follows:
Expression = [tex]\frac{x^{2} +8x+16}{x^{2} -2x-24}[/tex]
Simplify the numerator as well as denominator by doing factors which is shown below:
[tex]x^{2} +8x+16=x^{2} +4x+4x+16=(x+4)(x+4)[/tex]
Similarly, denominator factors are as follows:
[tex]x^{2} -2x-24=x^{2} -6x+4x-24=(x-6)(x+4)[/tex]
Now, substituting these values in the given expression, we get:
[tex]\frac{x^{2} +8x+16}{x^{2} -2x-24} = \frac{(x+4)(x+4)}{(x-6)(x+4)}=\frac{x+4}{x-6}[/tex]
Therefore, the final answer for the given expression is [tex]\frac{x+4}{x-6}[/tex].
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(b) Suppose a rocket, as designed, cannot provide enough velocity to achieve a stable orbit. Could alterations to the rocket make a stable orbit achievable? Explain.
The rocket moves really fast with high speed.
What is rocket ?A projectile that receives thrust from a rocket engine is known as a rocket (from the Italian rocchetto, which means "bobbin/spool"). All of the propellant carried by the rocket is used to create the exhaust from its engine.
In actuality, the absence of an atmosphere in space allows rockets to operate more effectively.
Due to their ability to reach Earth's escape velocity, multistage rockets can reach any maximum altitude. Rockets may produce significant accelerations and are powerful, light, and lightweight when compared to airbreathing engines.
In order for rockets to go forward and function in the vacuum of space, their action-reaction engines quickly discharge exhaust in the opposite direction.
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Tickets for an Amtrak train cost $17 for children and $36 for adults. Josie paid $2,297 for a total of 77 tickets. How many children tickets and how many adult tickets did Josie buy?
Adult tickets costs $63.8
Children tickets costs $13.2
How to calculate the amount of adult and children tickets ?Let x represent the adult tickets and y to represent the cost of children tickets
x + y= 77..........equation 1
36x + 17y= 2,297........equation 2
From equation 1
x= 77-y
Substitute 77-y for x in equation 2
36(77-y) + 17y = 2297
2772 - 36y= 2297
-36y= 2297-2772
-36y= -475
y= 475/36
y= 13.2
Substitute 13.2 for y in equation 1
x + 13.2 = 77
x= 77-13.2
x= 63.8
Hence adult tickets costs $63.8 and children tickets costs $13.2
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Which of the following will result in a rational number? select all that apply. A, 1 sqare root of 4/ + 5/12 B. 1 square root of 9/7 + 7/15 C. square root of 2 - 5/7 D. square root of 2/7 ÷ 5/7
Answer:
A. & B.
Step-by-step explanation:
Square root of 4 is 2, and the square root of 9 is 3. These are rational, and adding fractions keeps them rational.
But the square root of 2 is irrational, and subtracting or dividing will not make them rational.
Hope this helps! :)
help please im so lost. can somebody please explain!!!!?
Answer:
Step-by-step explanation:
Depreciation means value falling
10 is the scrap value which means the value that will remain after the product is properly used up.
depreciation for one year will be calculeted through
(original value - scrap value)/ no of years of use
(500 - 10)/3
= 163 is the annual rate of depreciation
If no scrap value is given, then you will simply divide the value by the no. of years of use
b. annual depreciation = 163
original value = 500
500 - 163(x) = worth of the poster after x years
worth remaining after a certain no. of years is also known as net book value.
What adds to be the bottom number but also multiplies to be the top? The top is 36 and the bottom is 12.
Answer:
The required number is 6. 6+6=12. 6×6=36.
Step-by-step explanation:
Write each equation in exponential form.
log₂1/2=-1
The answer to this question is 1/2
Logarithmic scale: A measurement scale in which the position is marked using the logarithm of a value rather than the actual value.
A logarithmic equation includes a logarithm in the variable x.
An exponential equation is one in which the variable is represented by an exponent. A logarithmic equation is one in which the logarithm of a variable-containing expression is used.
For logarithmic equations, log b (x) = y is equivalent to b^y = x such that x > 0, b > 0 and b is not equal to 1.
In the given problem, b = 2, x = 1/2, and y = -1.
b =2
x = 1/2
y = -1
Substituting the values of b, x and y into the equation b^y = x;
2^(-1) = 1/2
therefore, the value of the given equation log₂1/2=1 is 1/2.
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Write each expression in simplest form. 2 √32 x²+3 √72 x²
Simplest form of expression is an expression written in its simplest of terms without changing the original value of the expression. There should be no like terms or parentheses.
In the given expression, there are two like terms and no parentheses. Hence, we solve for eliminating the like terms to find the simplest form of expression.
In order to eliminate the like terms, we need solve the square root terms to its simplest form.
√32=√2x2x2x2x2=4√2
√72=√2x2x2x3x3=6√2
Hence, the expression becomes,
2*4√2 x2+3*6√2 x2
Simplifying,
8√2 x2+18√2 x2
Adding the like terms,
(8+18)√2 x2
26√2 x2
Hence, the simplest form of expression 2 √32 x²+3 √72 x² is 26√2 x2.
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Evaluate each expression for the given value of the variable.
x³ + x²; x=2)
After evaluating the expression we get 12.
Given, x³ ₊ x²
Finding the value of an algebraic expression when a specified number is used to replace the variable is known as evaluating the expression. In order to evaluate an expression, we first replace the expression's variable with the given number, then we streamline the expression using the order of operations.
A procedure called evaluation involves analyzing a program critically. It entails gathering and studying data regarding a program's operations, features, and effects. Its objective is to assess a program, enhance its effectiveness, and/or provide information to help with programming decisions.
substitute the value of x =2
2³ ₊ 2²
= 8 ₊ 4
= 12
hence we get the answer as 12.
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If f(x)=-x^2-1, and g(x)=x+5, then f(g(x)) =
Answer:
-8x^2+2x+5
Step-by-step explanation:
Distributive Property
Simplify the expressions, and match the expressions that are equal in value.
arrowBoth
arrowBoth
By applying the laws of indices to each of the expression, the simplified expressions are matched as follows:
5³ ÷ 5⁻¹ ⇔ 5⁴5⁻⁴ ⇔ 1/5⁴What is an exponent?An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.
What are the laws of indices?In Mathematics, laws of indices can be defined as the standard principles and rules that are used for simplifying a mathematical equation or expression that involves powers of the same base.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to evaluate an expression, you should apply the PEMDAS rule, where operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the operations of addition or subtraction would be performed from left to right.
By applying the laws of indices to each of the expression, the simplified expressions are as follows:
5³ ÷ 5⁻¹ = 5⁽³ ⁻⁽⁻¹⁾ = 5⁽³ ⁺ ¹⁾ = 5⁴ ⇒ 5³ ÷ 5⁻¹ = 5⁴
5³ × 5⁻¹ = 5⁽³ ⁺ ⁽⁻¹⁾ = 5⁽³ ⁻ ¹⁾ = 5²
a⁻ⁿ = 1/aⁿ ≡ 5⁻⁴ = 1/5⁴
5⁻³ ÷ 5⁻¹ = 5⁽⁻³ ⁻⁽⁻¹⁾ = 5⁽⁻³ ⁺ ¹⁾ = 5⁻²
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Complete Question:
Directions: Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Simplify the expressions, and match the expressions that are equal in value.
5³ ÷ 5⁻¹
5³ × 5⁻¹
5⁻⁴
1/5⁴
5⁻³ ÷ 5⁻¹
Jillian volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen worked and the total amount of money she collected for the tickets she sold.
Tickets (t) Money (m)
10 $25.00
8 $20.00
6 $15.00
4 $10.00
Based on the table, write an equation for the relation between the number tickets Jillian sold and the amount of money she collected.
t= 2.50mt= 2.50m
t=m2.5t is equal to m over 2 point 5
tm = 25tm = 25
m=25tm is equal to 25 t
The equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.
How to compute the equation?It should be noted that there's a constant relationship between the figures that are given.
This can be illustrated as:
= 25/10
= 2.5
Therefore, the equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.
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Find the area of a triangle with the given base b and height h . b=6 in., h=15 in.
A square with side length ppp has an area of 169169169 square centimeters. The following equation shows the area of the square.
p^2 = 169p
2
=169p, squared, equals, 169
What is the side length of the square in centimeters?
Answer:
Side = 13 cm
Step-by-step explanation:
To find the side of the square:
Area = 169 square cm
[tex]\sf \boxed{\bf Side = \sqrt{area}}[/tex]
[tex]\sf = \sqrt{169}\\\\ = \sqrt{13*13}\\\\ =13 \ cm[/tex]
Write the expanded form, the standard form, and the exponent form for each multiplication problem. Look for the patterns as you fill in the blanks.
Requirements:
1- You have to do every single problem shown inside the photo
2- Answers before 8:15AM
3- No fooling around or giving wrong answers.
Thank you :)
1. 10 * 10 * 10 = 1000 = 10^3
2. 10 * 10 * 10 * 10 = 10,000 = 10^4
3. 10 * 10 * 10 * 10 * 10 = 100,000 = 10^5
4. 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10,000,000 = 10^7
5. Summary
Multiplication Exp on first factor Exp on 2nd factor Exp on product
10^1 * 10^2 1 2 3
10^1 * 10^3 1 3 4
10^2 * 10^3 2 3 5
10^4 * 10^3 4 3 7
6. Multiplying two powers of ten, the product can be found by adding up the exponential values, the sum will be the exponent of the product and the base remain ten.
What are powers of ten?This refers to the exponential value of 10. Hence we can say that power as used in mathematics, is also called exponents.
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If QS bisects
x=
m
m
m
The measure of PQT = 142.
We know what ray QS bisects angle PQT. If you draw out angle PQT and ray QS you can see that angle PQS is congruent to angle SQT. Because of the definition of angle bisector. This also means that angle SQT is half of PQT. Because of this we know that we can set the measure of PQT equal to 2 times the measure of SQT.
So we can set up and solve the following equation as such:
2(8x-25) = 9x +34
16x - 50 = 9x +34
7x -50 = 34
7x = 84
x = 12
Again I this doesn't seem to be your final answer. To find the answer the measures of each angle you're going to want to plug 12 in for x for one of the angles. So I'll do it for angle SQT.
8(12) - 25
96 -25
71
So the measure of angle SQT should be 71. Therefore since QS bisects PQR, the measure of angle PQS should also be 71. The measure of PQT should be double that which makes it 142.
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