2. Graph the inverse of the function, then determine if the inverse is a function.
Part I: The graph of F(x) is shown below. On the same grid, draw the graph of
the inverse of F(x). (2 points)
Part II: Is the inverse a function? Explain your answer. (3 points)
Answers
The inverse of the function f(x)= x^2 is a function.
The graph of the inverseThe equation of the function is
f(x)= x^2
Rewrite as:
y = x^2
Swap x and y
x = y^2
Make y the subject
[tex]y = \sqrt x[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt x[/tex]
So, the inverse of f(x)= x^2 is [tex]f^{-1}(x) = \sqrt x[/tex]
See attachment for the graph
Is the inverse a function?The inverse is a function.
This is so because it passes the vertical line test
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Related Questions
a card is drawn from a deck of cards. event A is that the card obtained is a 2 and B is that the card is a spade. these event do not overlap.
true
false
Answers
Event A and Event B are events that do not overlap. This statement is false.
Do events A and B overlap?Two events overlap if there is a chance that both events occur together. A spade has a number 2. Thus, it is possible to pick a spade that has the number 2 on it. Thus, these events are dependent events.
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16 / 4 * (3 - 1)
a) 2
b) 4
c) 8
Answers
Hello,
if :
[tex] \frac{16}{4(3 - 1)} = \frac{16}{4 \times 2} = \frac{16}{8} = 2[/tex]
if :
[tex] \frac{16}{4} \times (3 - 1) = 4(3 - 1) = 4 \times 2 = 8[/tex]
Answer:
Hello! The answer is c) 8.
Step-by-step explanation:
To solve this question, we need to follow the order of operations. This can be done through PEMDAS - parentheses, exponents, multiplication, division, addition, and subtraction.
First, we need to solve what's in the parentheses:
[tex]\frac{16}{4} * 2[/tex]
Now we can multiply and we get:
[tex]\frac{32}{4}[/tex]
This can be further simplified by doing 32 ÷ 4 to get 8.
Therefore, the answer is c) 8
Solve the system using elimination. ''x-3y=9 and -x+3y=-9
Answers
Answer:
Infinitely many solutions.
Step-by-step explanation:
Let's solve your system by elimination.
x−3y=9;−x+3y=−9
x−3y=9
−x+3y=−9
Add these equations to eliminate x:
0=0
Answer:
Infinitely many solutions.
the set of ordered pairs represents a function
(1, 3) (2, 9) (k, 12) (5, 9) (8, 0)
Which of these could be the value of k
Answers
Answer:
12
Step-by-step explanation:
because it digit havbeen given ad k
PLEASE NEED HELP
2 graphs. Graph A: a dotted line goes from (1, 0) to (1, 0.25), is solid and horizontal to (2, 0.25), is dotted to (2, negative 0.1875), is solid and horizontal to (6, negative 0.1875), and then is dotted to (6, 0). Graph B. A line goes from (negative 5, 0) to (negative 3, 0.25), and then decreases to (3, 0).
Which statement about the graphs is true?
Graph A is a valid density curve because the part of the graph from 2 to 6 is below the horizontal axis.
Graph A is not a valid density curve because the part of the graph from 1 to 2 is above the horizontal axis.
Graph B is not a valid density curve because part of the horizontal axis has negative values.
Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
Pictures posted below
Answers
Answer: Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
The last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.
A few fundamental principles apply to density curves:
A density curve's area beneath it represents probability.A density curve's area under it equals one.Base x height in a uniform density curve equals one.The likelihood that x = a will never occur.The likelihood that x < a is the same as that of x ≤ a.Following the rules above, we can see from graph B that the curve is above the horizontal axis. That shows that the probabilities are positive which is a necessity. Moreover, the area under the curve must also be 1. That is also satisfied.
Hence, the last statement "Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1." is the correct statement.
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Jessica has half of her investments in stock paying a 7% dividend and the other half in a stock paying 13% interest. If her total annual interest is $780, how much does she have invested?
Answers
Answer:
$7800
Step-by-step explanation:
The total interest earned can be found by summing the earnings from each of the investments.
SetupLet x represent the total amount invested. Then Jessica's earnings are ...
(x/2)(0.07) +(x/2)(0.13) = 780
SolutionSimplifying the equation gives ...
(x/2)(0.07 +0.13) = 780
0.10x = 780
x = 7800 . . . . . . . . divide by 0.10
Jessica has $7800 invested.
Given a sample variance of 6, what is the approximate sample standard deviation?
Answers
The sample standard deviation is 2.45.
What is the sample standard deviation?Standard deviation measures the spread of a dataset around its mean. The variance measures the average degree to which each data point differs from the mean.
The standard deviation is the square root of the variance.
Standard deviation = √6 = 2.45
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Dan was getting rs. 100 for 5 years at an interest rate of 5%. Find the accumulated value of annuity at the end of 5 years
Answers
The future value of the annuity after the end of 5 years is $552.56.
Given that, r =5%= 0.05, 5 years = 5 yearly payments, so n = 5, and P = $100.
What is the annuity formula?The formula to find the annuity formula [tex]FV=\frac{P \times ((1+r)^{n}-1 )}{r}[/tex].
Now, [tex]FV=\frac{100 \times ((1+0.05)^{5}-1 )}{0.05}[/tex]
⇒FV = 100 × 55.256
⇒FV = $552.56
Therefore, the future value of the annuity after the end of 5 years is $552.56.
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A researcher surveyed 67 business majors
Answers
Answer:
Whats the question then?
Step-by-step explanation:
What is the LCM of 4 and 18
Answers
Answer:
36
Explanation:
Multiples of 4 are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64,...
Multiples of 18 are:
18, 36, 54, 72, 90, 108, 126, 144,...
The least common multiple of 4 and 18 is 36.
100 cubed as a power of 10
Answers
Answer:
100
Step-by-step explanation:
10^2 is 100 therefore it is 100
56. Thermometer A reads xº.
Thermometer B reads 2° below the
reading on thermometer A.
Thermometers C and D each read 4°
less than twice the reading on
thermometer B. What is the average
temperature, in degrees, of the 4
thermometers?
E. x - 4
2
F. x - 4
G. 3x 9
445
H. 3x - 9
What is the answer
Answers
All the options are incorrect. the required average is (3x-9)/2.
Thermometer A reads xº.
Thermometer B reads 2° below the reading on thermometer A = x-2
Thermometers C and D each read 4° less than twice the reading on thermometer = 2(x-2)-4
Average of the values is the ratio of total sum of values to the number of values.
As per question,
A=x
B = x-2
C.D = 2(x-2)-4= 2x-8
Average = A + B + C + D /4
= x+x-2+2x-8+2x-8/4
= 6x-18/4
= 3x-9/2
Thus, the required average of temperature = 3x-9/2.
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What is cos 60°?
1
.06
2
30⁰
Answers
PLEASE HELP ASAP I NEED TO PASS SUMMER SCHOOL ASAP
ILL MARK BRAINLIEST
Answers
Your value would be
Something like 7
A map has the scale 1/3inch = 8 miles. If city a and city b are 12 inches apart on my map then how far apart are the city’s in real life
Answers
12 ÷ 1/3 =
12 x 3/1 =
12 x 3 =
36 miles
What are m and b in the linear equation y = 28x + 8?
Answers
Answer:
Step-by-step explanation:
y = mx + b is the formula to figure out your question
Now, the equation ( y = 28x + 8)
Already shows the m and b
m = 28
b = 8
Hope this helps! :)
If not ask me in the comments about your question and I’ll answer
The side of a square is x units. Which one of following expressions represents the perimeter?
Answers
if the perimeter=s+s+s+s
=x+x+x+x
Julio es un alumno que faltó a las clases por ayudar a su familia a elaborar y vender quesos. Decidió sacar fotocopias al cuaderno de su compañero. Si cada fotocopia vale S/ 0.30 y debe calcular cuánto dinero necesita para pagar las fotocopias. Identifica cada variable, expresa como función, grafica y responde: ¿Cuánto pagará por 29 copias?
Es urgente por favor
Answers
Aplicando el concepto de precio unitario, concluimos que Julio debe pagar 8.70 soles peruanos por la producción de 29 fotocopias de los apuntes de un compañero.
¿Cuánto dinero debe pagar Julio por las fotocopias?
En esta situación, Julio debe pagar por 29 fotocopias de los apuntes de un compañero suyo. El monto a pagar es el producto del número de copias y el coste unitario de cada fotocopia, es decir:
x = (0.30 PEN) · (29)
x = 8.70 PEN
Aplicando el concepto de precio unitario, concluimos que Julio debe pagar 8.70 soles peruanos por la producción de 29 fotocopias de los apuntes de un compañero.
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Find the measure of
Answers
Answer:
B. 30
Step-by-step explanation:
3x + 2x + x = 180 (angle sum of a triangle is 180)
6x = 180
x = 30
Answer:
B. 30
Step-by-step explanation:
3x + 2x + x = 180
6x = 180
x = 180/6
x = 30
Ross has $750 in a bank account that earns 9% in annual interest. Select an equation that represents this scenario.
PLS HELP
Answers
cos 0 = . Find tan 0.
Answers
Answer:
b
Step-by-step explanation:
15/8
Solve using the distributive property of whole numbers.
27,345 x 113 x-27,345 x 13
Answers
Answer:
2,734,500
Step-by-step explanation:
27,345 × 113 - 27,345 × 13 ← factor out 27,345 from each term
= 27,345(113 - 13)
= 27,345 × 100
= 2,734,500
Solve the triangle. Round your answers to the nearest tenth
Answers
Explanation:
Context:A triangle has 180 degrees total
Step 1: add 119 plus 27 which makes 146
Step 2:Subtract 146 from total value of triangle which is 180 so 180-146=34
What are the exact steps to solve for the x-intercepts of f(x)= −4x2 + 4x + 8? What about −9 = x2 + 6x? Please explain thoroughly
Answers
Answer:
x-intercepts: (-1, 0) and (2, 0)
x-intercept: (-3, 0)
Step-by-step explanation:
Given quadratic function:
[tex]f(x)=-4x^2+4x+8[/tex]
The x-intercepts of a quadratic function are the points at which the curve crosses the x-axis ⇒ when y = 0
Therefore, to find the x-intercepts of the given function, set the function to zero:
[tex]\implies -4x^2+4x+8=0[/tex]
Factor out -4:
[tex]\implies -4(x^2-x-2)=0[/tex]
Divide both sides by -4
[tex]\implies x^2-x-2=0[/tex]
Rewrite the middle term as -2x + x:
[tex]\implies x^2-2x+x-2=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-2)+1(x-2)=0[/tex]
Factor out the common term (x - 2):
[tex]\implies (x+1)(x-2)=0[/tex]
Zero Product Property: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):
[tex]\begin{aligned}(x+1) & = 0 & \quad \textsf{ or } \quad \quad (x-2) & = 0\\\implies x & = -1 & \implies x & = 2\end{aligned}[/tex]
Therefore, the x-intercepts are (-1, 0) and (2, 0).
---------------------------------------------------------------------------------------
Given quadratic equation:
[tex]-9 = x^2 + 6x[/tex]
Add 9 to both sides:
[tex]\implies x^2+6x+9=0[/tex]
Rewrite the middle term as 3x + 3x:
[tex]\implies x^2+3x+3x+9[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+3)+3(x+3)=0[/tex]
Factor out the common term (x + 3):
[tex]\implies (x+3)(x+3)=0[/tex]
[tex]\implies (x+3)^2=0[/tex]
Square root both sides:
[tex]\implies (x+3)=0[/tex]
Solve for x:
[tex]\implies x=-3[/tex]
Therefore, the x-intercept is (-3, 0).
As the function has a repeated factor (multiplicity of two), the curve will touch the x-axis at (-3, 0) and bounce off.
Sonia works at a bakery. The function f(x) represents the amount of money Sonia earns per loaf, where x is the number of loaves she makes. The function g(x) represents the number of bread loaves Sonia bakes per hour, where x is the number of hours she works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 9x2 + 1
g of x equals the square root of the quantity 2 x cubed
Answers
A function assigns the value. The function f(g(x)) represents the amount that Sonia will earn per hour by baking bread.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given f(x)=9x²+1 and g(x)=√(2x³). Therefore, the value of f(g(x)) will be,
[tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]
= 9(2x³) + 1
= 18x³ + 1
The function f(g(x)) represents the amount that Sonia will earn per hour by baking bread.
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A linear function f(x) on a table. How do I find a solution for the value of f(4)?
x | f(x)
3 | -3.5
4 |
5 | 5.5
6 | 10
7 | 14.5
Answers
If 5(x-6y) = 50y,what is the value of x in terms of y? PLS EXPLAIn
E. 16y
F. 15y
G. 11 2/5y
H.11y
EXPLAIN CORRECT ANSWER AND EXPLANATION GETS BRAINIEST
Answers
Answer:
E. 16y
Step-by-step explanation:
Given equation:
5(x - 6y) = 50y
Expand the brackets using
Distributive Property for subtraction: a(b - c) = ab - ac
⇒ 5 · x - 5 · 6y = 50y
⇒ 5x - 30y = 50y
Add 30y to both sides:
⇒ 5x - 30y + 30y = 50y + 30y
⇒ 5x = 80y
Divide both sides by 5:
⇒ 5x ÷ 5 = 80y ÷ 5
⇒ x = 16y
evaluate if y=4 and z= -2 7y+z=?
Answers
Answer:
26
Step-by-step explanation:
7(4)+-2
28-2=26
Step-by-step explanation:
y = 4 and z = -2
[tex] = 7y + z[/tex]
[tex] = 7 \times 4 + ( - 2)[/tex]
[tex] = 28 - 2[/tex]
[tex] = 26...[/tex]
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
All the roles have now been cast, and the lead actors playing the following parts are gathered around a large circular table for their first read: Jean Valjean, Inspector Javert, Thénardier, Enjolras, Marius, Fantine, adult Cosette, adult Éponine, and Madame Thénardier. It is your job to seat these 9 actors, the 3 producers, and the director around the table.
If the 9 actors must sit together, how many ways are there to seat the 13 people around the table?
8,709,120
362,880
6,227,020,800
259,459,200
Answers
There are 8,709,120 ways to arrange the people around the table
How to determine the number of ways?The given parameters are:
People = 13
Actors = 9
If the actors must seat together, then the actors must be grouped as 1.
The 9 actors can be arranged in 9! ways
Now, we have 1 group + 4 individuals.
This equals 5 people (in theory)
The 5 people can be arranged in 5! ways
So, the number of ways is
Ways= 9! * 5!
Evaluate
Ways = 8,709,120
Hence, there are 8,709,120 ways to arrange the people around the table
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6. If x and y are positive integers, and
3x + 2y = 21, what is the sum of all
possible values of x?
Answers
An equation is formed of two equal expressions. The sum of all possible values of x is 16.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
3x + 2y = 21
3x = 21 - 2y
x = (21-2y)/3
Since the value of x is needed to be positive, the value of 2y must not exceed 21. Also, the value of (21-2y) must be a multiple of two.
Now, the values of y that will satisfy the given condition in the equation are 0, 3, 6, and 9.
Further, the sum of the possible values of x are,
Sum = 7 + 5 + 3 + 1 = 16
Hence, the sum of all possible values of x is 16.
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