The graph below shows a transformation of y
- 2x
Write the equation for the graph in the comment
Answers
Answer:
[tex]y=-2^{(x+2)}+1[/tex]
Step-by-step explanation:
Equation of the parent function of the graph attached is,
y = [tex]2^{x}[/tex]
Let the equation of the transformed function function shown in the graph be,
y = a(2ˣ) + b
Now we will find the values of a and b by substituting the points lying on the curve.
For (-2, 0),
0 = a(2⁻²) + b
[tex]\frac{a}{4}+b=0[/tex] ------(1)
For (0, -3),
-3 = a(2⁰) + b
a + b = -3 --------(2)
Subtract equation (1) from equation (2),
(a + b) - ([tex]\frac{a}{4}+b[/tex]) = 0 + 3
[tex]\frac{3a}{4}=3[/tex]
a = -4
From equation (2),
-4 + b = -3
b = 1
Therefore, equation of the transformed function will be,
[tex]y=-4(2^x)+1[/tex]
[tex]y=-2^{2}(2^x)+1[/tex]
[tex]y=-2^{(x+2)}+1[/tex]
Graph transformation is the process by which an existing graph is modified to produce a variation of the proceeding graph.
Equation of transformed graph is, [tex]y=-2^{x+2}+1[/tex]
Here, equation of original graph is given, [tex]y=2^{x}[/tex]
Let us consider, equation of transformed graph is, [tex]y=m(2^{x} )+n[/tex]
Since, given graph passing through points (-2,0) and (0,-3)
Substituting above points into equation.
We get two equation,
m +4n = 0
m + n = -3
After solving, we get m= -4 and n = 1
So, equation becomes [tex]y=-2^{x+2}+1[/tex]
Learn more:
https://brainly.com/question/10510820
Related Questions
Jill has not been able to maintain the $1,000 minimum balance required to avoid fees on her checking account. She wants to switch to a different account with a fee of $0.20 per check and a $12.50 monthly maintenance fee. Jill wants to estimate the fees for her new account. Below is a summary of the checks she has written from May to August. What is the mean number of checks Jill wrote per month during the last four months? Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account. Estimate the total monthly fees Jill will pay each month for the new checking account.
Answers
Step-by-step explanation:
Kindly find attached a summary of the checks she has written from May to August.
A. What is the mean number of checks Jill wrote per month during the last four months
mean= (14+19+23+24)/4
mean= 80/4
mean= 20 checks
B. Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account.
the expression for the total is given as
y=12.50+0.2x
y=12.50+0.2(20)
y=12.50+4
y=16.5
=$16.5
C. Estimate the total monthly fees Jill will pay each month for the new checking account.
May= 12.50+0.2(14)
May=12.5+2.8= 15.3
June= 12.50+0.2(19)
June=12.5+3.8= 16.3
July= 12.50+0.2(23)
July=12.5+4.6= 17.1
August= 12.50+0.2(24)
August=12.5+4.8= 17.3
total will be = 15.3+16.3+17.1+17.3= $66
A:20
B:$4.00
C:$16.50
A: 14+19+23+24/4 = 20
B: 20/.2 = 4
C: 12.50+4= 16.50
Find the value of x.
Answers
Answer:
12
Step-by-step explanation:
1. the rule: 3:6=6:x;
2. if 3/6=6/x, then x=12.
the temperature at noon was -3°C. By 10 Pm on the same day the temperature decrease by 5.4° what was the temperature at 10 pm
Answers
Answer:
-8.4
Step-by-step explanation:
Answer:
Probbly -8.4
Step-by-step explanation:
6th grade math I mark as brainliest
Answers
In a study using 50 foreign-language vocabulary words, the learning rate L (in words per minute) was found to depend on the number of words already learned, x, according to the equation L(x) = 20 – 0.4x
Answers
Here is the complete question
1. State coordinates of x axis
2. State coordinates of y axis
3. State the slope
4. Graph the function
5. Is learning rate increasing or decreasing?
Answer:
1. (50,0)
2. (0,20)
3. Slope = -0.4
4. Check attachment for graph
5. Learning rate is decreasing
Step-by-step explanation:
1.
L(x) = 20-0.4x
20 = 0.4x
x = 20/0.4
x = 50
(50,0)
2
For y coordinate;
L(0) = 20-0.4(0)
= 20
(0,20)
3.
Slope,
Y = -0.4x+20
We compare with
Y = mx+c
m = -0.4
Intercept c = 20
4. Check attachment
5. The slope is negative at m = -0.4 therefore the rate of learning is on a decline. As number of words learnt increases, learning rate falls.
Answer:
Step-by-step explanation:
How do we know if a function is a parabola like for instance, this one x^2 + x?
Answers
QUESTION 16
What is the value of m If the ratios 3:18 and m:42 are in
proportion?
Answers
Answer:
[tex]m = 7[/tex]
Step-by-step explanation:
Given
[tex]3:18 = m:42[/tex]
Required
Solve for m
[tex]3:18 = m:42[/tex]
Convert to fraction
[tex]\frac{3}{18} = \frac{m}{42}[/tex]
Multiply both sides by 42
[tex]42 * \frac{3}{18} = \frac{m}{42} * 42[/tex]
[tex]42 * \frac{3}{18} = m[/tex]
[tex]m = 42 * \frac{3}{18}[/tex]
[tex]m = \frac{42 * 3}{18}[/tex]
[tex]m = \frac{126}{18}[/tex]
[tex]m = 7[/tex]
A farm has 56 horses and sheep in all. There are 8 fewer sheep than horses. How many horses are there on the farm?
Answers
Answer:
32 Horses
Step-by-step explanation:
32-8=24
There are 32 horses and 24 sheep (As you can see there are 8 fewer sheep than horses)
I sort of guess and checked:
I tried to think of 2 numbers that added to 56 but one number was 8 less than the other one.I figured out that 32 and 24 fit this description :)A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-10x^2+600x-3588
y=−10x
2
+600x−3588
Answers
Answer:
Step-by-step explanation:
The maximum profit will be found in the vertex of the parabola, which is what your equation is. You could do this by completing the square, but it is way easier to just solve for h and k using the following formulas:
[tex]h=\frac{-b}{2a}[/tex] for the x coordinate of the vertex, and
[tex]k=c-\frac{b^2}{4a}[/tex] for the y coordinate of the vertex.
x will be the selling price of each widget and y will be the profit. Usually, x is the number of the items sold, but I'm going off your info here for what the vertex means in the context of this problem.
Our variables for the quadratic are as follows:
a = -10
b = 600
c = -3588. Therefore,
[tex]h=\frac{-600}{2(-10)}=30[/tex] so the cost of each widget is $30. Now for the profit:
[tex]k=-3588-(\frac{(600)^2}{4(-10)})[/tex] This one is worth the simplification step by step:
[tex]k=-3588-(\frac{360000}{-40})[/tex] and
k = -3588 - (-9000) and
k = -3588 + 9000 so
k = 5412
That means that the profit made by selling the widgets at $30 apiece is $5412.
Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].
What is the maximum profit?
Maximum profit, or profit maximisation, is the process of finding the right price for your products or services to produce the best profit.
Here given that,
A company sells widgets. The amount of profit, [tex]y[/tex], made by the company, is related to the selling price of each widget, [tex]x[/tex], by the given equation.
As the maximum profit found in the vertex of the parabola,
Here, [tex]x[/tex] will be the selling price of each widget and [tex]y[/tex] will be the profit.
The number of items sold is [tex]x[/tex].
So, the quadratic equation is:-
[tex]a = -10b = 600c = -3588.[/tex]
Therefore, so the cost of each widget is $[tex]30[/tex].
For the profit:-
[tex]k = -3588 - (-9000) andk = -3588 + 9000 sok = 5412[/tex]
Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].
To know more about the maximum profit
https://brainly.com/question/16755335
#SPJ2
The width of a rectangle
is 11 feet longer than the
length. The perimeter of the
rectangle is 70 feet. Find
the length and the width
Answers
Answer:
Hello! The answer to this problem is Length= 27 and Width= 8
Step-by-step explanation:
2(11+2x) +2x = 70
6x + 22 = 70
6x = 48
x = 8
In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it was
determined that 20% of all stock investors are retired people. In addition, 40% of all U.S. adults invest in mutual funds. Suppose a random sample of 25 stock investors is taken What is the probability that fewer than 4 are retired people
Answers
Answer:
a) 0.1108
(b) 0.0173
Step-by-step explanation:
We are given that 20% of all stock investors are retired people. A random sample of 25 stock investors is taken.
Firstly, the binomial probability is given by;
where, n = number of trails(samples) taken = 25
r = number of successes
p = probability of success and success in our question is % of
retired people i.e. 20%.
Let X = Number of people retired
(a) Probability that exactly seven are retired people = P(X = 7)
P(X = 7) =
= = 0.1108
(b) Probability that 10 or more are retired people = P(X >= 10)
P(X >= 10) = 1 - P(X <= 9)
Now, using binomial probability table, we find that P(X <= 9) is 0.98266 at n = 25, p = 0.2 and x= 9
So, P(X >= 10) = 1 - 0.98266 = 0.0173.
cuál es el denominador común de las fracciones?
Answers
Answer:
?????????????????????????
Step-by-step explanation:
Fraction Multiplication and División:Question 4
Tina has $72 to spend on new t-shirts. If each t-shirt costs $12,
how many different t-shirts can Tina buy? Set up a fraction to
determine how many t-shirts Tina can buy. Then solve.
Answers
Answer: 6 T-shirts
Step-by-step explanation:72/12=6
The frequency of the red eyes (p allele) in fruit flies is 63% what is the frequency of the white eye allele (9 allele)?
37%
47%
57%
23%
Answers
Answer:
[tex]q = 37\%[/tex]
Step-by-step explanation:
Given
Red Eyes
[tex]p = 63\%[/tex]
Required
Determine Frequency of White Eyes (q)
In probability;
[tex]p + q = 1[/tex]
Make q the subject
[tex]q = 1 - p[/tex]
Substitute 63% for p
[tex]q = 1 - 63\%[/tex]
[tex]q = 37\%[/tex]
Answer:
37%
Step-by-step explanation:
Point J is on line segment IK. Given JK = 2x, IJ = 5x, and IK = x + 6, determine the numerical length of JK.
Answers
Answer:
[tex]JK = 2[/tex]
Step-by-step explanation:
Given:
[tex]JK = 2x[/tex]
[tex]IJ = 5x[/tex]
[tex]IK = x + 6[/tex]
Required
Solve for JK.
Since J is on IK, we have:
[tex]IK = IJ + JK[/tex]
[tex]x + 6 = 5x + 2x[/tex]
[tex]x + 6 = 7x[/tex]
Collect Like Terms
[tex]7x - x = 6[/tex]
[tex]6x = 6[/tex]
Solve for x
[tex]x = 6/6[/tex]
[tex]x = 1[/tex]
Substitute 1 for x in [tex]JK = 2x[/tex]
[tex]JK = 2 * 1[/tex]
[tex]JK = 2[/tex]
What are the true and false statements for If two planes intersect, then their intersection is a line. Include converse, inverse and contrapositive.
Answers
Answer and Step-by-step explanation:
Solution:
Statement:
If two planes intersect their intersection is a line.
Suppose that
P =if two planes intersect.
q = then their intersection is line.
¬p = if two planes do not intersect.
¬q = then their intersection is not a line.
Converse:
If two planes intersect their intersection is a line.
P → q
Inverse:
If two planes do not intersect, then their intersection is not a line.
¬p → ¬q
Contrapositive:
If two planes intersection is not a line, then they do not intersect.
¬q → ¬p
how do I write an equation in standard form with the points (3,3) (0,-3) (2,-3)
Answers
-3-3= -6 2-3=-1
-6/-1=6
Y=6x+b
3=6 x 3
3=18
Subtract both sides by 18
B=-15
Answer= y=6x-15
The theory that it is reasonable to chose the simpler theory when choosing between two competing theories of equal explanatory value is
Answers
Answer:
Occam’s razor theory.
Step-by-step explanation:
This theory is known as Occam’s razor theory.
It's a theory based on the principle whereby we give precedence to simplicity. It states that out of two competing theories, the one with the simpler explanation of an object should be embraced over the other. The reason is that the philosopher William of Ockham said that "objects are not meant to be multiplied beyond absolute necessity.”
This definition resonates with what is explained in the question.
Thus, the theory is as explained.
How many people are in the set Cn D?
4
6
36
38
Answers
Answer: A.) 4 people
Step-by-step explanation:
What is the leading coefficient of a third degree polynomial function that has an output of 1,272 when x=2, and has zeros of −6, 7i, and −7i?
Answers
Answer:
The leading coefficient is 3
Step-by-step explanation:
Polynomials
Given the roots of a polynomial x1,x2,x3, it can be expressed as:
[tex]p(x)=a(x-x1)(x-x2)(x-x3)[/tex]
Where a is the leading coefficient.
We are given the roots x1=-6, x2=7i, x3=-7i, thus:
[tex]p(x)=a(x+6)(x-7i)(x+7i)[/tex]
Operating the product of the conjugated imaginary roots:
[tex]p(x)=a(x+6)(x^2+49)[/tex]
Knowing p(2)=1,272 we can find the value of a
[tex]p(2)=a(2+6)(4+49)=1,272[/tex]
Operating:
[tex]a(8)(53)=1,272[/tex]
[tex]424a=1,272[/tex]
Solving:
[tex]a=1,272/424[/tex]
a=3
The leading coefficient is 3
Answer:
3
Step-by-step explanation:
Does anyone have the answer?
Answers
Answer:
hi to what. good bye???????
suppose the retail price of an automobile is $28,000 in 1998 and that it increase at 3% per year. a) write a equation exponential function y=a(1 +r) b) use the model to predict the retail of the automobile in 2016
Answers
Answer:
......................................
A sinking fund is established to discharge a debt of $30,000 in 5 years. If deposits are made at the end of each 6-month period and interest is paid at the rate of 4%, compounded semiannually, what is the amount of each deposit?
Answers
Answer:
what you have to do is do 30000 * 5 and then do 6 divided by the number and then four times that number and whatever the answer you get be your answer hope this help
If 10% of x is 20, what is 23% of x? A. 33 B. 46 C. 200 D. 230
Answers
Answer:
B. 46
Step-by-step explanation:
20*10=200
200*0.23=46
Anyone know this because I need help !!!!
Answers
Answer: 90 clockwise rotation
Step-by-step explanation:
you can take any point and replace its (x,y) to (y,-x) otherwise called the 90 clockwise conversion and it will map figure C onto figure C'
A bookshelf at a bookstore is 3 feet 9 inches wide. There are 18 copies of the same book on the shelf, which fit the shelf exactly. What is the width of 1 of the books?
Answers
Answer:
2.5 inches
Step-by-step explanation:
Given
Shelf Width = 3ft 9in
Copies = 18
Required
Determine the width of each book
This is calculated by dividing the shelf width by the number of copies.
Width = Shelf Width ÷ Copies
Width = (3 ft 9in) ÷ (18)
[Convert with to inches]
Width = (3 * 12 + 9) ÷ (18)
Width = (36 + 9) ÷ (18)
Width = 45 ÷ 18
Width = 2.5 inches
Hence, the width of each book is 2.5inches
Solve the following system of equations for X..
3x – 2y = 8
2x + 2y = 7
Help
A)3
B)-3
C)15
D)1
Answers
Answer:
x = 3
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Select the correct answers.
Mila is at a flea market. She has $50 in her wallet. She decides that she will spend $15 on jewelry, $20 on a pair of jeans, $5 on a T-shirt, and $10 on something to eat. She likes a one-of-a-kind T-shirt, but the seller is not ready to sell it for less than $8. She thinks of five ways to deal with this situation. Which two choices indicate a trade-off?
She will try to find another seller selling the T-shirt for a lower price.
She will give up on the T-shirt and use the money to buy better jeans.
She will use some of the money she received from her aunt on her birthday.
She will pay the seller $5 and promise to pay the remainder on another day.
She will buy the T-shirt for $8 and not order juice at lunch.
Answers
Answer:
1and3
Step-by-step explanation:
Simplify the expression 4x+3(5y+x
Answers
Answer:
Step-by-step explanation:
4x + 3(5y + x)
= 4x (5y + x) + 3 (5y + x)
= 20xy + 4x² + 15y + 3x
Describe the similarities and differences between a bar graph and a histogram.
Answers
Answer:
Bar graphs are used with nominal or ordinal scores; histograms are used with interval or ratio scores.
Step-by-step explanation: