Answer: How to calculate commission. This is a very basic calculation revolving around percents. Just take sale price, multiply it by the commission ...
Step-by-step explanation:
Consider the function g(x) shown below over a domain of [1,∞).
g(x) = 2(x – 1)2 – 3
Part A
Determine g–1(x).
Part B
Identify the domain and range of g(x) and g–1(x). Represent the domains and ranges in inequality, interval, and set notation. Describe the relationship between the domains and ranges of g(x) and g–1(x).
Part C
Graph g(x) and g–1(x). Describe the relationship between the graphs of g(x) and g–1(x).
The inverse of a function may or may not be a function
The function g(x) is given as:
[tex]g(x) = 2(x - 1)^2 - 3[/tex]
(a) Inverse function g^-1(x)
We have:
[tex]g(x) = 2(x - 1)^2 - 3[/tex]
Replace g(x) with y
[tex]y = 2(x - 1)^2 - 3[/tex]
Swap the positions of x and y
[tex]x = 2(y - 1)^2 - 3[/tex]
Add 3 to both sides
[tex]x + 3 = 2(y - 1)^2[/tex]
Divide both sides by 2
[tex]\frac{x + 3}2 = (y - 1)^2[/tex]
Take square roots of both sides
[tex]\sqrt{\frac{x + 3}2} = y - 1[/tex]
Add 1 to both sides
[tex]1 + \sqrt{\frac{x + 3}2} = y[/tex]
Rewrite as:
[tex]y = 1 + \sqrt{\frac{x + 3}2}[/tex]
Express as inverse function of g
[tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]
Hence, the inverse function of g is [tex]g^{-1}(x) = 1 + \sqrt{\frac{x + 3}2}[/tex]
(b) The domain, and the range of g(x) and g^-1(x)
Function g(x)
The function g(x) is a quadratic function.
So, the domain is:
Inequality: [tex]-\infty < x < \infty[/tex]Interval: [tex](-\infty ,\infty)[/tex]Set: {R}The range is:
Inequality: [tex]f(x) \ge -3[/tex]Interval: [tex][-3 ,\infty)[/tex]Set: [tex]\{y|y\ge -3\}[/tex]Function g^-1(x)
The function g^-1(x) is a square root function.
So, the domain is:
Inequality: [tex]x \ge -3[/tex]Interval: [tex][-3 ,\infty)[/tex]Set: [tex]\{x|x\ge -3\}[/tex]The range is:
Inequality: [tex]-\infty < y < \infty[/tex]Interval: [tex](-\infty ,\infty)[/tex]Set: {R}The domain of g(x) is the range of g^-1(x), while the range of g(x) is the domain of g^-1(x).
(c) The graph
See attachment for the graph
Read more about inverse functions at:
https://brainly.com/question/14391067
What is an equation of the line that passes through the points (0, -4) and (-4, 6)?
I got this answer by first using the slope formula, which would result into [tex] \frac{0 - 4}{6 - 0} \\ [/tex]for which the answer would be - ⅔ Then, the y-intercept could be found easily, since you already have it., which is (0,4). Since the format for all linear equations are y=mx+b , in which b means the y-intercept and m means the slope. So then, if you substitute - ⅔ for m and 4 for b , you would get
[tex]y = - \frac{2}{3} x + 4 \\ [/tex]
Which of the following is not true about the mean of a set of data?
The mean can be less than the minimum data value.
The mean can be the same value as the median.
The mean can be different from all the data values.
The mean can be one of the data values.
Answer:
i think the answer is -> "the mean can be less than the minimum data value."
Step-by-step explanation:
mean means the average and by finding the average you need to add up all your set values then divide it, so with that being said the mean will always need to be higher than the lowest data set of value.
Challenge elementary school has 800 students. Every Wednesday, 12% of the students stay after school for chess. How many students attend chess club on Wednesday?
Answer:
Its 96 bro :) 96 students
Step-by-step explanation:
Basically yeah, 800 is 100% of the population yeah. So just multiply 800 times 12%. 800 x 12% is 96.
96 = 12% of 800, I hope this helps!
A photographer charges $12 for a set of 20 pictures. Each picture cost the same amount. At this rate, how many pictures cost $30?
Answer:
Step-by-step explanation:
20/12 = 1 2/3
30 ÷ 1 2/3
= $18
(6x²+2x-1)-(8x²-x-5)
Answer:
-2x^2 + 3x + 4
Hope this helps. :D
Step-by-step explanation:
Pls give brainliest.
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
Answer:
It's the first one. We notice that for every package there are 36/3 = 12 pencils. Therefore for 4 packages there will be 4*12 = 48 pencils.
For what integer value of x is f(x) = -10 if f(x) = - 4x + 2?
Answer:
x = 3
Step-by-step explanation:
Given the linear function, f(x) = -4x + 2, for which we must determine the integer value of x that will provide an output of f(x) = -10:
Solution:The first step is to substitute the output value, f(x) = -10, into the given function, and solve for its corresponding input value, x:
f(x) = -4x + 2
-10 = -4x + 2
Subtract 2 from both sides:
-10 - 2 = -4x + 2 - 2
-12 = -4x
Divide both sides by -4 to solve for x:
[tex]\displaystyle\mathsf{\frac{-12}{-4}\:=\:\frac{-4x}{-4} }[/tex]
x = 3
Hence, when x = 3, f(x) = -10.
Double-check:Substitute the value of x = 3 into the original function:
f(x) = -4x + 2
f(3) = -4(3) + 2
f(3) = -12 + 2
f(3) = -10 ⇒ f(x) = -10.
Therefore, the input value of x = 3 gives an output value of f(x) = -10.
10. John is mixing paint.He uses black, green and blue in the ratio 6:3: 1. How much of black green and blue paint is needed to make a mixture of paint of 500ml.
The given ratio becomes 6x : 3x : x.
6x = black paint
3x = green paint
x = blue paint
6x + 3x + x = 500
10x = 500
x = 500/10
x = 50
6x = 6(50) = 300
3x = 3(50) = 150
x = 50
Answer:
300 ml of the black paint.
150 ml of the green paint.
50 ml of the blue paint.
Help please
:Ccccccccccccccccccccccccc
Answer:
1. false
2. true
Step-by-step explanation:
sorry if wrong
(0, 2), (1,7) create a equation that passes through each pair of points
Answer:
y = 5x + 2
Step-by-step explanation:
Given the equation 5x + 2
Plug in 0
y = 5(0) + 2
y = 2
(0,2)
Given the equation 5x + 2
Plug in 1
y = 5(1) + 2
y = 7
(1,7)
A red die is tossed and then a
green die
is tossed. What is the probability that
the red die shows an even number and
the green die shows an even number?
Make sure your answer is reduced.
Answer: 1/4
Step-by-step explanation:
There are three even numbers and three odd numbers on a 6 sided dice
The probability of rolling an even number on the red die is: p(red with even) = 3 / 6, or 1 / 2, since there are six numbers on a die.
The probability of rolling an even number on the green die is the same as the probability of rolling an even number on the red die, or 3 / 6, or 1 / 2.
Since rolling the red die and rolling the green die are independent events, to find the probability of both occurring, you need to multiply the individual probabilities.
P(of both red and green even) = 1/2 * 1/2, or 1/4.
Answer:
3/4
Step-by-step explanation:
This is what I got for Acellus
If the triangles are similar, which must be true? StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction.
The correct relation between the triangles if the triangles are similar is, [tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex].
Given that,
Consider [tex]\rm \triangle RST[/tex] and [tex]\rm \triangle RYX[/tex].
Triangle RST is shown.
Line XY is drawn parallel to side ST within triangle RST to form a triangle [tex]\rm \triangle RYX[/tex].
We have to determine,
If the triangles are similar, which must be true?
According to the question,
Consider [tex]\rm \triangle RST[/tex] and [tex]\rm \triangle RYX[/tex].
Triangle RST is shown.
The relationship between the triangles is line XY is drawn parallel to side ST within triangle RST to form [tex]\rm \triangle RYX[/tex].
The point X on side RT and point Y on side RS in [tex]\rm \triangle RYX[/tex].
Then,
The [tex]\rm \triangle RST[/tex] is similar to [tex]\rm \triangle RYX[/tex], the corresponding ratio of their sides are equal,
[tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex]
Hence, The correct relation between the triangles if the triangles are similar is, [tex]\dfrac{RY}{RS} = \dfrac{RX}{RT} = \dfrac{XY}{TS}[/tex].
For more details about Triangle refer to the link given below.
https://brainly.com/question/13858149
Answer:
B.
Step-by-step explanation:
Edge 2022
Please answer with an explanation
Answer:
-2(1-2p)
Step-by-step explanation:
-7-4p-(-5)
-(-5)=5
=-7-4p+5
=5-7-4p
=-2-4p
=-2(1-2p)
I need help asap pls
Answer:
d? Kerana ianya tidak sama kaki
1. How many small squares are in Step 10?
Image below
A. 10
B. 11
C. 90
D. 110
Answer:
110 squares
Step-by-step explanation:
= 10 x 11
= 110 small squares.
From the question,
Step one : • • = 1(2) small squares
Step two : • • • = 3 squares in two layers = 2(3) = 6 small squares
• • •
Step three : • • • • = 4 squares in 3 layers = 3(4) = 12 small squares
• • • •
• • • •
what comes after this:
2:4
4:8
8:10
_:_
Hint: Times two (x2) if you answer right then you shall get 30 points which is half of mine
You answer it you get 15 points so answer away
Answer:
16:20??
Lol I think it's wrong sorry.
Step-by-step explanation:
Please help please please
Answer:
39
Step-by-step explanation:
284-5(7)²
284-(5×49)
284-245
39
Answer:
The Answer Is 70
Step-by-step explanation:
So first you have do the parentheses, (2+5) = 7
Then do the exponents [tex]7^{2}[/tex] 7.7 = 49
Next do the Multiplying 49.5= 214
Finally Subtract 284-214=70
I Hope This Helps You :)
The diagram shows a rectangle 15cm long and 13cm wide.It has been split into four smaller rectangles. write the area of each small rectangle on the diagram.
[tex]195 cm^{2}[/tex]
Area of each splited rectangles =[tex] \frac{195cm{}^{2} }{4} [/tex]
=[tex]48.75 {cm}^{2} [/tex]
!! PLEASE MARK ME THE BRAINLIEST!!AND I'M REALLY VERY SORRY IF MY ANSWER IS WRONGKindly help out with this question!
Step-by-step explanation:
33+22+90=145
180-145=35
x=180-35
x=145
Please help me solve for n
To solve for N, you have to work backwards
1. Take off the absolute sigh
the absolute sign only means that the answer must be positive. So that means N could equal to positive and Negative
2. What is 1x6?
This process is called inverse operation. Where you have division, you have multiplications. The answer is 6.
3. The answer is 6 or negative 6, in the fact that -6 would equal to six in the absolute sign.
I hope this helped! If it's wrong blame me!
part A :A rocket scientist needs to find the overall thrust of a new rocket design. The rocket has two stages: Stage A and Stage B. Stage A’s thrust is defined by the expression 11.2x + 6.4 and Stage B’s thrust is defined by the expression 7.4x − 2.9.
Part b: An engineer accidentally reads the blueprints incorrectly and installs the Stage B thrusters upside-down. What is the combined thrust of the rocket if Stage A is firing normally, but Stage B is applying reverse (negative) thrust?
Answer:the answer is that if thruster b is going the opposite way it will stay in 1 place as thruster a is firing up to make the rocket fly if thruster b is going the opposite way it will just hover with that being said that's the answer
Step-by-step explanation:
Hannah's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=7.1x+55 where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the yy-value when x=1?
Answer:
Expected score with 1 hour of homework
Step-by-step explanation:
549.5 to 1 decimal place
Answer:
It is still 549.5
Step-by-step explanation:
Rounding to 1 decimal place is just rounding by the tenth place
So it is still 549.5
Hope this helps!
A town has two shopping malls. A survey conducted on the shopping preferences of the town's residents showed that 62% of the residents visit Comet Mall, 73% of the residents visit Star Mall, and 48% of the residents visit both malls. The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is
Using Venn probabilities, it is found that:
The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is 0.87 = 87%.In this problem, the events are:
Event A: Visits Comet Mall.Evenet B: Visits Star Mall.In this problem:
62% of the residents visit Comet Mall, hence [tex]P(A) = 0.62[/tex].73% of the residents visit Star Mall, hence [tex]P(B) = 0.73[/tex].48% of the residents visit both malls, hence [tex]P(A \cap B) = 0.48[/tex]The probability of either is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Hence:
[tex]P(A \cup B) = 0.62 + 0.73 - 0.48 = 0.87[/tex]
The probability that a resident is chosen at random shops at either Comet Mall or at Star Mall is 0.87 = 87%.You can learn more about Venn probabilities at https://brainly.com/question/25698611
Answer:
87%.
Step-by-step explanation:
The probability that a resident chosen at random shops at either Comet Mall or at Star Mall is 87%.
What is (f •g)(x)
f(x)= -3x^2-5x
g(x)=5x
Answer:
sorry I didnt get you. whats the mean of ^ symbole.
A planet has a circular orbit around a star. It is a distance of 65,000,000 km from the centre of the star. It orbits at an average speed of 65,000 km/h. How many Earth days does it take the planet to orbit the star? Give your answer to 2 sf.
Answer:
Step-by-step explanation:
Orbit = 2*pi * r
r = 65000000 km
Orbit = 65000000 * 2 * 3.14
Orbit = 406 200 000 km
d = 406 200 000
s = speed = 65000 km / hr
t = time = d / s
t = 406,000,000 / 65000
t = 6280 hours.
1 day = 24 hours.
t = 6280 / 24 = 261.67 days
if 10 seeds are planted, what is the probability that exactly 3 don't grow?
Answer:
10:7
Step-by-step explanation:
take 10 as it is and it becomes 10
then,10-3 it is because when 3 don't grow it subtracts and becomes 7
I don’t anderstands but i wanna help
will mark brainleist pls help
Step-by-step explanation:
Angle c + angle d = 180° ( linear pair)
given,
angle c = 5x + 9
angle d = 5x - 6
now,
5x + 9 + 5x - 6 = 180
10x + 3 = 180
10x = 180 - 3 = 177
10x = 177
x = 177/10 = 17.7
so,
angle C = 5x + 9 = 5(17.7) + 9 = 97.50°
angle D = 5x - 6 = 5(17.7) - 6 = 82.50°
Hope this answer helps you dear! take care!.