Answers
Solution:
Given:
The graph of the function h(x)
Picking any point on the graph as shown below,
Picking point (0,2) on the graph of the function h(x)
[tex]\begin{gathered} x=0 \\ y=2 \\ \\ \text{Hence, the point of the inverse function is gotten by interchanging the coordinates of the point } \\ ^{}^{} \end{gathered}[/tex][tex]\begin{gathered} \text{If the point of h(x) is }(x,y),thenh^{-1}(x)\text{ is (y,x)} \\ \\ \text{Hence, at (0,2) on h(x)}, \\ h^{-1}(x)\text{ will have the point (2,0)} \\ \\ \text{Also, at (1,0) on h(x),} \\ h^{-1}(x)\text{ will have the point (0,1)} \end{gathered}[/tex]Therefore, a point on the graph of the inverse function of h(x) is (2,0).
Another point on the graph of the inverse function of h(x) is (0,1).
Related Questions
1. The polynomial function F(x) = x² + 6x + 8 has a known factor of (x + 4). Rewrite F(x) as a product of
linear factors.
Answers
Answer:
f=12
Step-by-step explanation:
F(4) = 4^(2) + 6(4) + 8
Korey is planning to open a comic book store. His store will cost $12,500 to open and will come with an $8,000 total annual operational cost. If his store makes $12,000 in profit during the first year, and profits increase by 6% each year from then, how long will it take for Korey to see an overall profit in his business (where total profits exceed total expenses)? A = P (1 + r) superscript t
Answers
It will take 3 years for Korey to see an overall profit in his business.
What is a percentage?A percentage is a number or ratio that represents a fraction of 100.
We have,
Cost of the store to open = $12500
Cost of the operational cost = $8000
Profit store makes each year = $12000
Profit increase each year = 6%
Profit = Income - Total cost
First-year:
Profit = 12000 - (12500 + 8000) = -8500
There is no profit in the first year.
2nd year:
Profit = 2 x (12000 + 6% of 12000) - (12500 + 2 x 8000)
= 25440 - 28500
= -3060
There is no profit in the second year.
Third-year:
Profit = 3 x (12000 + 6% of 12000) - (12500 + 3 x 8000)
= 38160 - 36500
= 1660
We see that there is a profit of 1600 in the third year.
Thus,
It will take 3 years for Korey to see an overall profit in his business.
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f(n) = 4n+ 3
g(n) = n³-3n
Find (f - g)(n)
Answers
Answer:
[tex]-n^3+7n+3[/tex]
Step-by-step explanation:
[tex](f-g)(n)=f(n)-g(n) \\ \\ =4n+3-n^3+3n \\ \\ =-n^3+7n+3[/tex]
7. What is the equation of the line in slope intercept
form that passes through (6,8) and (-2,4)
Answers
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{6}}} \implies \cfrac{ -4 }{ -8 } \implies \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{6}) \\\\\\ y-8=\cfrac{ 1 }{ 2 }x-3\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 2 }x+5 \end{array}}[/tex]
Answer them please. I need help ASAP!!!!!
Answers
Answer:
A. -26, -12.7, -9/2, 2/100, 7, 11 1/4, 41/2, 35
B. |-12.7| = 12.7, |-11 1/4| = |-45/4| = 45\4
B Optional 45/4 = 11.25 as decimal form
Step-by-step explanation:
For the mixed fractions you have to divide it. For the whole fraction
11 1/4
1. 11 x 4=44
Then add the 1. 44+1=45
The denominator doesn't change
45/4 then divide if it ask for the decimal form which is 11.25.
I'm not entirely sure of the answers. Good luck :)
Can some one solve this
Answers
A(2,12) and B(-1,17)
Slope of the line that is parallel to AB is given by formulae y2-y1/x2-x1
=> m = 17-12/-1-2 = 5/-3=-5/3
Also parallel lines run in same direction and hence have same slope!
Can somebody help me with 7 and 8
Answers
The vertices of parallelogram MNOP after a rotation of 180° are: M' (-1, -7), N' (-8, -5), O' (-4, -2), and P' (3, -4).
A counterclockwise rotation of 270° to triangle GHI would produce an image with this vertices: G' (-2, 0), H' (-6, -7), and I' (-8, -3).
How to determine the vertices of the image?In this exercise, you are required to rotate parallelogram MNOP by 180° and triangle GHI by 270° in a counterclockwise direction. In Geometry, the rotation of parallelogram MNOP 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the vertices (-x, -y):
(x, y) → (-x, -y)
Point M' = (1, 7) → Point M' = (-(1), -(7)) = (-1, -7).
Point N' = (8, 5) → Point N' = (-(8), -(5)) = (-8, -5).
Point O' = (4, 2) → Point O' = (-(4), -(2)) = (-4, -2).
Point P' = (-3, 4) → Point P' = (-(-3), -(4)) = (3, -4).
In Geometry, the rotation of triangle GHI by 270° about the origin in a counterclockwise direction would produce a point that has the vertices (y, -x):
(x, y) → (y, -x)
Points at G = (0, -2) → Points at G' = (-2, 0)
Points at H = (7, -6) → Points at H' = (-6, -(7)) = (-6, -7).
Points at I = (3, -8) → Points at I' = (-8, -(3)) = (-8, -3).
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4 x 10 to the power of 5
Answers
Answer:
400000
Step-by-step explanation:
Have a Good Day!
Write an equation of the line that passes through(0, -2) and(4,10)
Answers
Answer: y = 3x -2
Step-by-step explanation:
1) slope formula
y2 - y1 / x2 - x1
2) find the y's and x's
y2 = 10
y1 = -2
x2 = 4
x1 = 0
3) plug them into the equation
10 - (-2) / 4 -0
10+2/4
12/4
4) simplify
slope = 3
5) write out equation
y = 3x + b
6) plug in coordinates
(0,2)
-2 = 3(0) + b
7) find the y intercept
-2 = b
8) plug in y intercept
y = 3x -2
84 km a centímetros
Alguien sabe como se resuelve
Answers
8400000cm
84 kilometer is 8400000 centimeter.
How to convert kilometer to centimeter?In the International System of Units, a Centimeter or centimeter is a unit of length equal to one hundredth of a meter, with centi being the SI prefix for a factor of 1/100.A centimeter is a metric length measurement unit. One centimeter equals ten millimeters or one meter. A cheerio is typically one centimeter in diameter.One kilometer equals 1000 meters. When we need to travel from one location to another, we use kilometers to calculate the distance. Kilometers can be used to calculate the distance between cities or the distance traveled by a plane.
Here given 84 km ,
We know that 1 km = 1000 meter
so 84 km = 84 x 1000 meter
= 84000 meter
and 1 meter = 100 cm
so here 84000 meter = 84000 x 100 cm
= 8,400,000 Centimeters
∴ 84 km = 8400000cm
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Javen babysat his little brother on
Saturday and made $66.50. He
babysat for 7 hours. How much
money did he earn per hour? Help
Answers
Answer:
$9.50
Step-by-step explanation:
9.5
7 66.5
63
35
35
0
Hopes this helps please mark brainliest
Answer: 9.50
Step-by-step explanation:
I calculated and estimated a solution to this problem.
Its 9.50
figure it out ig thats how I did it.
Ivan borrowed money from a credit union for 5 years and was charged at an annual rate 9% .The total interest that he paid was $2700.How much money did he borrow
Answers
The formula to calculate the total interest paid is:
[tex]I=P((1+r)^n-1)[/tex]Where:
• I, is the total interest paid
,• P, is the amount borrowed
,• r, is the interest rate
,• n, is the times that the interest was compounded
Solving this formula for P,
[tex]\begin{gathered} I=P((1+r)^n-1) \\ \\ \Rightarrow P=\frac{I}{(1+r)^n-1} \end{gathered}[/tex]Using the data given,
[tex]\begin{gathered} P=\frac{2700}{(1+\frac{9}{100})^5-1} \\ \\ \Rightarrow P=5012.77 \end{gathered}[/tex]Therefore, we can conclude that he borrowed $5,012.77
Y=5575•(0.65)^ta. What is the initial value? b. What is the decay factor?
Answers
a) Initial Value = 5575
Decay factor = 0.35
Explanation:The given expression is:
[tex]Y\text{ = 5575}\times(0.65)^t[/tex]a) What is the initial value
The initial value of Y will take place when t = 0
Substituting t = 0 into the given equation:
[tex]Y\text{ = 5575}\times(0.65)^0[/tex][tex]Y=\text{ 5575 }\times\text{ 1 = 5575}[/tex]The initial value is Y = 5575b) What is the decay factor
The value of a substance due to an exponential decay is given by the general expression:
[tex]Y=A(1-r)^t[/tex]Where A = original/Initial value, and r = decay rate
Comparing the above equation with the given equation shown below:
[tex]Y=5575(0.65)^t[/tex]It is clear from the comparison of both equations that A = 5575 and :
1 - r = 0.65Solving for r:r = 1 - 0.65r = 0.35The decay factor is 0.35Kyle and Nadim are on the same space on a board game they are playing. Kyle moves back 2 spaces in one turn and moves back 3 more spaces in his second turn. Nadim has remained in the same place. What integer represents Kyle’s location relative to Nadim’s location on the game board?
Answers
The integer -5 represents Kyle’s location relative to Nadim’s location on the game board.
It is given in the question that Kyle and Nadim are on the same space on a board game they are playing. Kyle moves back 2 spaces in one turn and moves back 3 more spaces in his second turn while Nadim remained in the same place.
We have to find the integer that represents Kyle’s location relative to Nadim’s location on the game board.
We usually denote going ahead by the positive sign and the going back by the negative sign.
Hence, Kyle moving back 2 spaces and then again moving back 3 spaces is equal to moving back 5 spaces which will be represented by the integer -5.
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WILL GIVE BRAINLIST TO BEST ANSWER PLUS EXTRA POINTS
A company rents a Popcorn machine. Customers are charged a fixed amount plus a rate based on the number of hours the machine is rented. The company uses the function shown below to determine the total charges, in dollars, for the customer.
ƒ (x) = 40 + .15x
What does f(x) represent?
What does the 40 represent?
What does the 0.15 represent?
What does the ‘x’ represent?
Answers
1. F(x) represents the total cost function for renting a Popcorn machine.
2. The 40 in the equation represents the Fixed Cost per day of the rental.
3. The 0.15 represents the variable cost per hour.
4. The x represents the number of hours the machine is rented.
What is a function?A function is a mathematical expression, rule, or law defining the mathematical relationship between the independent variable and the dependent variable.
Mathematical functions are used to define the mathematical relationships that show how the dependent variable can be determined, given an independent variable. They are written with the equal sign (=).
Thus, we can conclude that the rental cost function ƒ (x) = 40 + .15x shows the total amount that a customer would be charged each day for renting a Popcorn machine.
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please help trying to do a test
(x + 1) a factor of 2x ^ 4 - 9x ^ 3 - 20x ^ 2 + 147x - 180 Find out by using the Factor theorem.
Answers
Answer:
Step-by-step explanation:
4
PAWEZZE HELP ASAP FOR 20 POINTS
Answers
Answer:
the 2nd one
Step-by-step explanation:
please help I will give you brainliest
Answers
Answer:
Both the line right before the 2 and the line right before the one
Step-by-step explanation:
11. What is the least common
70 ?
multiple of 30, 40, and
Answers
Answer:
i think 840 i searched it up
Step-by-step explanation:
Point T and point U are shown below.
What are the coordinates of the midpoint of
point T and point U?
Y
U (4, 12)
T(4,2)
Answers
work it out pleasee :)
Answers
Answer:
18
Step-by-step explanation:
18 is the HCF of 36 and 90 , then
[tex]\frac{36}{90}[/tex] ( divide numerator/ denominator by 18 )
= [tex]\frac{2}{5}[/tex] ← in simplest form
Answer for (4)(4+2^2-4) ???
Answers
It's no small feat to travel 160,000,000km, to visit 200 million children, in 800 million homes, in only 34 hours... Luckily Santa has magic on his side. If he visits 200,000,000 children in 34 hours, How many Kids per hour.
Answers
Answer
Santa visits 5,882,353 kids per hour
Explanation
The mathematical expression to get the number of kids visited per hour is
[tex]\text{Number of kids visited per hour = }\frac{Total\text{ number of kids}}{Total\text{ number of hours available}}[/tex]Total number of kids = 200,000,000 kids
Total number of hours available = 34 hours
[tex]\begin{gathered} \text{Number of kids visited per hour = }\frac{200000000}{34} \\ =5,882,352.94 \\ =5882352\text{ kids per hour to the nearest whole number} \end{gathered}[/tex]Hope this Helps!!!
Given θ is in the third quadrant, φ is in the second quadrant, sinθ=-5/13, and tanφ=-8/15. Find the value of tan(π+θ)1) 12/52) 13) 5/12
Answers
Based on historical data, three hospital trauma centers in ontario have 50, 30, and 20 percent of cases. the probability of a case resulting in a malpractice lawsuit in each of the three hospitals is .001,.005, and .008 respectively. if the malpractice suit is filled, what is the probability that it originated in hospital 1?
Answers
The probability that if a malpractice suit is filed, it originated in hospital 1 = P(B1|A) =
To solve this problem we will use Baye's theorem which states
P(B1 |A) = P(A/B1)P(B1) / P(A|B1)P(B1) + P(A|B2)P(B2) + P(A|B3)P(B3) (1)
where P(A|B) is the probability of event A occurring given that event B has already taken place.
Probability of hospital 1 having the case = P(B1) = 50
Probability of hospital 2 having the case = P(B2) = 30
Probability of hospital 3 having the case = P(B3) = 20
Probability of case resulting in malpractice in hospital 1= P(A/B1) =0.001
Probability of case resulting in malpractice in hospital 2= P(A/B2) =0.005
Probability of case resulting in malpractice in hospital 3= P(A/B3) =0.008
The probability that if a malpractice suit is filed, it originated in hospital 1 = P(B1|A)
Using equation (1)
P(B1|A) = (0.001)(50) / (0.001)(50) + (0.005)(30) + (0.008)(20)
= 0.05 / ( 0.05 + 0.15 + 0.16 )
= 0.05 / 0.36
= 0.138
Problem based on Bayes's theorem
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Which of the following functions translates the graph of the parent function f (2) = 2? left 2 units?
Answers
f (x) = x^2, translated left ,2 units
Is a parabola
Vertex is at (0,0)
left translation is (x +2)
(-2 + 2)= 0
Then answer is
Option A ) h(x)= (x+2)^2
solve for x of the triangle
Answers
Answer:
[tex]x=3[/tex]
Step-by-step explanation:
Since on one side of the triangle, both of the side halves are equal, then 5x-4 and 3x+2 are equal.
[tex]5x-4=3x+2[/tex]
We can just use simple algebra to find x.
[tex]5x-4=3x+2\\5x=3x+6\\2x=6\\x=3[/tex]
5 is not more than x
Answers
"not more" means "less than or equal to". We just have to use the inequality sign "less than or equal to" which means 5 is less than or equal to x.
Having said that, we can express the statement as follows
[tex]5\leq x[/tex]f(x)=-3x+12find f(-6)
Answers
Answer:
f(-6)=18d
Step-by-step explanation:
Answer:
-3x-72f
Step-by-step explanation:
Can some one help please I don’t know their
Answers
Answer: 2 complex solutions; the discriminant is less than zero
Step-by-step explanation:
When the D<0 there are no real solutions because the quadratic does not intercept the x-axis on the graph.
