Give an equation for the transformation that maps the graph of f onto the graph of g.
Answers
[tex]g(x)=cf(b(x-h))+k[/tex]
g(x) is the transformed functionf(x) is the original functionc = vertical stretch (negative = reflect about the x-axis)b = horizontal stretch (negative = reflect about the y-axis)h = horizontal translation (negative = moves left)k = vertical translation (negative = moves down)Solving the Question
We know that only a vertical translation and horizontal translation were applied to the graph. How?
The slopes of each segment remained the same, indicating that there was no vertical or horizontal stretchTo identify what values of h and k to use, identify the translations applied to one of the points:
(1,2) ⇒ (4,4)
It moved 3 units rightIt moved 2 units upTherefore:
h = 3k = 2Plug this into the equation:
[tex]g(x)=cf(b(x-h))+k\\g(x)=f(x-h)+k\\g(x)=f(x-3)+2[/tex]
Answer[tex]g(x)=f(x-3)+2[/tex]
Related Questions
What is the value of x in the image below.
Answers
Answer:
16xthe equal parts squares
Step-by-step explanation:
if that is correct let me know of the ewuation
which of the following set of numbers could represent the three sides of a right triangle? {60,63,87} {57,76,94} {42,56,69} {36,78,85}
Answers
Answer:
{60,63,87}
Step-by-step explanation:
PLEASE HELP NEEDED URGENTLY!
. A birdbath and stand are made from
3 cylinders. The top and bottom cylinders
have radius 22 cm and height 13 cm.
The middle cylinder has radius 15 cm and
height 40 cm. The “bath” has radius 15 cm
and depth 2 cm. The birdbath and stand are
to be tiled. Calculate the area to be tiled.
Answers
Answer:
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>>Mayank made a bird - bath for his garden
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Mayank made a bird-bath for his garden in the shape of cylinder with a hemispherical depression at one end as shown in figure. The height of the hollow cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath. (Take π=22/7)
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Updated on : 2022-09-05
Solution
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Verified by Toppr
Let r be the common radius of the cylinder and hemisphere and h be the height of the hollow cylinder.
Then r=30cm;h=1.45m=145cm
Total surface are of the bird-bath = curved surface area of the cylinder + curved surface area of the hemisphere
=2πrh+2πr
2
=2π(h+r)
=2×
7
22
×30(145+30)cm
2
=3.3m
2
help me with this, please
Answers
Answer: B.) 240 / 100
Step-by-step explanation:
A percentage is x / 100
For example, 4% = 4 / 100.
So 240% is 240 / 100.
You deposit $2000 each year into an account earning 5% interest compounded annually. How much will you have in the account in 30 years?
Answers
There will be amount of $8,880.43 in the account in 30 years.
What is compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Let A be the final amount.
Principal = $2000
r = rate = 5%
n = number of compounding in a year = 4
t = number of years the principal will be compounded = 30
The formula for compound interest:
[tex]A=P(1 +\frac{r}{n})^{nt}[/tex]
[tex]A=2000(1 +\frac{0.05}{4})^{4 \times 30}[/tex]
A = $8,880.43
I will have $8,880.43 in the account in 30 years.
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draw the image of quadrilateral ABCD under a translation by 5 units to the right
Answers
The image of the quadrilateral ABCD when translated to the right by 5 units is given as attached. When translated, the new coordinates are given as follows;
A' = (4,2)
B' = -1,1)
C' = (-2,-2)
D' = 5, -5)
What is a translation in Math?A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction.
There are several forms of translation:
When we flip a figure over a line, we call this reflection.Rotation is the process of rotating a figure to a specific degree around a point.When we dilate, we enlarge or contract a figure.Learn more about translation:
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The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function T (t) = StartFraction 4 t Over t squared + 1 EndFraction, where t represents time elapsed. What is the meaning of the horizontal asymptote for this function?
Answers
The horizontal asymptote of T(t)=0 means that the temperature will not increase above 98.6F as time elapses.
Given,[tex]T(t)=\frac{4t}{t^2+1}\\[/tex]
where, t represents time elapse it means 't' reaches to infinity
In function [tex]\lim_{n \to \infty} f(n)[/tex], f(n) is called as horizontal asymptote of the function.
then the above equation can be written as
[tex]T(t)=\lim_{t \to \infty}\frac{4t}{t^2+1}\\\\=\lim_{t \to \infty}\frac{4t}{t(t+\frac{1}{t})}\\\\=\lim_{t \to \infty}\frac{4}{(t+\frac{1}{t})}\\\\=\frac{4}{\infty +0}\\\\=0[/tex]
Hence,the horizontal asymptote of T(t) is 0 it means there is no increase in the temperature above 98.6F.
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There are two solutions for the quadratic equation, 9x^2 + 4 = 0. Which of the choices below describes the solutions.
A. One real and one complex solution
B. Two real solutions
C. Two complex solutions.
Answers
Answer:
C. Two complex solutions.
Step-by-step explanation:
[tex]1. \ 9x^2+4=0;\\x^2=-\frac{4}{9};\\x=_-^+ \frac{2}{3} i;[/tex]
2. two complex solutions, the correct answer is C.
At Westville High School there are 315 seniors and 389 juniors. 65% of the seniors have parking passes and 42% of the juniors have parking passes. The statistics teacher selects a SRS of 30 seniors and a separate SRS of 30 juniors. Let ^ps-^pj be the difference in the sample proportic seniors and juniors that have parking passes.
a. What is the shape of the sampling distribution of ^ps-^pj? Why?
b. Find the mean of the sampling distribution.
c. Calculate and interpret the standard deviation of the sampling distribution.
d. What is the probability that the difference in sample proportions (senior-junior) of students with parking passes is greater than 30%?
Answers
a. The shape of the distribution is normal, by the Central Limit Theorem.
b. The mean is of: 0.23.
c. The standard error is of: 0.125, meaning that the sample proportions differ by around 0.125 from the mean of 0.23.
d. The probability is of: 0.2877 = 28.77%.
What is the distribution of differences?By the Central Limit Theorem, as each sample has at least 10 successes and at least 10 failures, the shape of the distribution is normal.
For each sample, the mean and the standard error are given as follows:
Seniors: [tex]p_S = 0.65, s_S = \sqrt{\frac{0.65(0.35)}{30}} = 0.087[/tex]Juniors: [tex]p_J = 0.42, s_J = \sqrt{\frac{0.42(0.58)}{30}} = 0.09[/tex]Hence for the distribution of differences, the mean and the standard error are given as follows:
Mean: 0.65 - 0.42 = 0.23.Standard error: s = sqrt(0.087² + 0.09²) = 0.125.What is the probability?Using the z-score formula, the probability that the difference is greater than 30 is one subtracted by the p-value of Z when X = 0.3, hence:
Z = (0.3 - 0.23)/0.125
Z = 0.56
Z = 0.56 has a p-value of 0.7123.
1 - 0.7123 = 0.2877 = 28.77%.
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The recipe also calls for 3/4 cup of snot for every 6 cat
whiskers. If she has 10 cat whiskers, how many cups of
snot will she need?
Answers
Answer:
1.25
Step-by-step explanation:
3/4 snot = 6 cat
/6 /6
______________
0.125 snot = 1 cat
*10 *10
______________
1.25 snot = 10 cat
6. Rodrigo is attending a 4-year college. As a freshman, he was approved for a 10-year, federal
unsubsidized student loan in the amount of $5,300 at 4.29%. He knows he has the option of
beginning repayment of the loan in 4.5 years. He also knows that during this non-payment
period, interest will accrue at 4.29%. (Round all monthly payment calculations to 2 decimal
places.)
a. How much interest will Rodrigo accrue during the 4.5-year non-payment period?
b. If Rodrigo decides to make no payments during the 4.5 years, the interest will be
capitalized at the end of that period. What will the new principal be when he begins
making loan payments?
How much interest will he pay over the life of the loan?
c. Suppose Rodrigo only paid the interest during his 4 years in school and the 6-month
grace period. What will he now pay in interest over the term of his loan?
Answers
Rodrigo will accrue 1023.17 interest during the 4.5-year non-payment period.
Define interest.The simplest way to compute interest is as a percentage of the principal. For instance, if you agreed to borrow $100 from a buddy with 5% interest, the interest you would pay would only be 5% of $100: $100(0.05) = $5. Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.
Given,
For calculating interest:
Interest = Principal ×rate × time
Principal = 5300
Rate = 0.0429
Time = 4.5
Interest = 5300 × 0.0429 × 4.5
Interest = 1023.17
Rodrigo will accrue 1023.17 interest during the 4.5-year non-payment period.
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A scientist divided 1/2 of an ounce of liquid protein evenly among 4 cell sample. How
much liquid protein did she put in each cell sample
Answers
The amount of liquid protein in each cell sample is 1/8 ounce
How to determine the ounce of liquid?From the question, we have the following parameters that can be used in our solution:
Ounce of liquid = 1/2 ounce
Number of samples = 4 cells
From the above parameter, we can calculate the amount of liquid protein in each cell sample
Amount = Ounce of liquid /Number of samples
Substitute the known values in the above equation
So, we have the following equation
Amount = (1/2)/4
Evaluate the quotient
Amount = 1/8
Hence, the amount is 1/8 ounce
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Kendra is printing out copies of a presentation. It takes 5 minutes to print a color copy and 1 minute to print a black-and-white one. She wants to spend under 47 minutes on printing. Write an inequality that represents the number of minutes Kendra could spend printing each type of copy.
Answers
The inequality statement for Kendra is written as 5y + x < 47 minutes
How to write the inequality to suit KendraInformation given in the question
It takes 5 minutes to print a color copy
1 minute to print a black-and-white one
She wants to spend under 47 minutes on printing
Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using equal to
let x represent the number of black-and-white printed
let y represent the number of colored copy printed
under 47 minutes means less than 47 minutes
5y + x < 47 minutes
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Suppose y varies inversely with x, and y=-3 when x=13 What is an equation for the inverse variation?
Answers
Answer:
y = - 39/xStep-by-step explanation:
Inverse variation equation:
y = k/x, where k- constant of variationGiven x = 13, y = - 3Find the value of k- 3 = k/13k = - 3*13k = - 39The equation is:
y = - 39/xAnswer:
y = -39/x
Step-by-step explanation:
Formula we use,
→ y = k/x
→ k = xy
Now the value of k will be,
→ k = xy
→ k = 13 × (-3)
→ [ k = -39 ]
Then the inverse equation is,
→ y = k/x
→ -3 = -39/13
→ [ y = -39/x ]
Hence, the answer is y = -39/x.
Which of the graphs does not belong with the others ? Explain your reasoning.
Answers
Answer:D
Step-by-step explanation:
It is a monomial and the others and not
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answers
Answer:
Alternate exterior
Congruent
4
Step-by-step explanation:
The given angles are alternate exterior angles and alternate angles has equal measures so they are also congruent which means to find the value of x:
20x = 80 divide both sides 20
x = 4
what is 3/7 divide by 1/14
Answers
Answer:
6/1 is what i got, is that a right answer?
Step-by-step explanation:
3/7 by 1/14
2*3/1*1 over 14 =6/1 over 14 simplified 3/7.
vn: Do What's Next ces start with the terms 2 and 8. he next two terms of the arithmetic sequence 2, 8, 2, 48. he next two terms of the geometric sequence 2, 8, o possible next terms of a sequence 2, 8, ric nor arithmetic. t
Answers
One possible pair of next terms: 0, 1
A second possible pair of next terms: 14, 32
What is arithmetic progression?
The difference between two successive words in an arithmetic progression sequence, often known as A.P., is always the same. The common difference is the term for the constant. It is a technique for calculation that has been used for centuries to get precise results for everyday calculations such as measurements, labelling, and other kinds of everyday calculations. The word "arithmos" in Greek, which simply means "numbers," is where the phrase first appeared.What is Geometric progression?
When one term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence.The difference of these numbers is 6, so the next two terms of an arithmetic sequence would be 8+6 = 14, and 14+6 = 20.
The ratio of these numbers is 4, so the next two terms of a geometric sequence would be 8×4 = 32, and 32×4 = 128.
Any pair of numbers can be used that is not (14, 20) or (32, 128).
The next two terms could be 0 and 1, or they could be 14 and 32.
2, 8, 0, 1 . . . is a sequence of no particular type
2, 8, 14, 32 . . . is a sequence of no particular type
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At a sale, suits were sold for $72 each. This price was 45% of a suit's original price. How much did a suit orginlly cost
Answers
At a sale, suits were sold for $72 each and this price was 45% of a suit's original price which means that suit originally cost $160.
What is Percentage?This is referred to as a number or ratio that can be expressed as a fraction of 100.
Selling price = $72 which is 45% of a suit's original price.
Therefore, 45/100 × X = $72.
45X = 7200
X = 7200/45 = $160.
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hello whats 6.75 ft to inches ..... could use some help
Answers
Answer:81
Step-by-step explanation:
cus you need multiply the length value by 12
6.75x12 equal 81
Two different proportional relationships are represented by the equation and the table.
Answers
The rate of change in proportion A is lower than the rate of change in proportion B.
What is a proportional relationship?A proportional relationship is used to illustrate the relationship the variables.
In this case, the proportion A is given as y = 9x.
Proportion B will be:
= 34.5 / 3
= 11.5
This will be illustrated as y = 11.5x
Therefore, it can be seen that B had a higher proportion than A.
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4^(2x-3)=8^(x-4)
I don't understand the problem please give steps Thank You
Answers
The solution to the problem is X =-6
What is simplify?Simply in mathematics is reducing the problem or fraction into basic form
Simplify the equation by finding the root of the equation
[tex]2^{2(2x-3)}[/tex]= [tex]2^{3(x+4)}[/tex]
Divide the side of the equation by each other
{2(2x-3)} = {3(x- 4)}
Open the bracket by multiplying the right hand side and left by their coefficient.
4x -6 = 3x - 12
Collect the like terms and the unknow X be on the left side
4x-3x = 6-12
x = -6
Therefore, the solution to the problem is X =-6
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A car is purchased for $38,000. Each year it loses 20% of its value. After how many years will the car be worth $10,600 or less?
Answers
After 4.6 years the car's worth will be $10,600 or less.
According to the question,
We have the following information:
A car is purchased for $38,000. Each year it loses 20% of its value.
Now, we will first find 20% of 38,000:
(20*38000)/100
$7600
Now, each year the decrease in the price will be $7600.
So, we have the following arithmetic progression:
38000, 30400, ...
Now, following formula is used to find the nth term of an A.P:
an = a+(n-1)d where a is the first term and d is the common difference
10,600 = 38000+(n-1)-7600
10600-38000 = -7600n+7600
-27,400 = -7600n+7600
-7600n = -27400-7600
-7600n = -35000
n = 35000/7600
n = 4.6 years
Hence, after 4.6 years the car will be worth $10,600 or less.
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the product of three, x, and y
Answers
This is pretty simple because all you have to do to find this product is to write it out as 3xy. These are still multiplied, making it the product.
Answer:
it is equal to 5⃣ hope that m not wrong
Sara takes 45 minutes to make 3 bracelets. At this rate, how long will it take Sara to make 21 bracelets?
Group of answer choices
225 minutes
315 minutes
135 minutes
270 minutes
Answers
Answer:
315 minutes
It takes 15 minutes for 1 bracelet. 15 minutes multiplied by 21 bracelets is 315. Lmk if you need more help
Answer: 315 minutes.
Step-by-step explanation:
To solve this, we need to find out how long it takes to make one bracelet first.
If it takes 45 minutes to make 3 bracelets, we need to divide 45 by 3, which gives us 15.
This means it takes 15 minutes to make one bracelet.
Now, we need to multiply 15 by 21.
15 x 21 = 315.
This means it will take 315 minutes to make 21 bracelets.
May I have assistance I’ll give you brainliest no links or I will report you
Answers
The equation of the line is y = -68.7x - 5.1 when the slope is 68.7 and the y - intercept is -5.1.
Equation of the line
Basically, the equation of the line refers the mathematical equation that gives the relation between the coordinate points lying on that straight line.
The general form of the equation of the line is
y = mx + c
where
m refers the slope
c refers the y intercept
Given,
Here we have the value of slope is -68.7 and the y intercept is -5.1.
Now, we have to write the equation of the line.
Here we have the value of
Slope = -68.7
y- intercept = - 5.1
So, the equation of the line is written as,
=> y =-68.7x - 5.1
Therefore, the equation of the line with the given slope and intercept is
y = -68.7x -5.1
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Peter's Party Zone sells cups in packages of 666 and plates in packages of 888.
Shaniya is hosting a birthday party for her little sister and wants to have the same number of each item.
What is the least number of packages of plates Shaniya needs to buy?
Answers
Least number of packages of plates Shaniya needs to buy=24
Based on the given problem above, it is mentioned that in one pack of cups has 6 and one pack of plates has 8. Therefore, the least number of packages of plates that Shaniya needs to buy is 3 packages and for the cups, it would be 4 packages. 4 x 6 is 24 cups, and 3 x 8 would be 24 plates.
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4.2 x 10^8 is how many times the value of 2.1 x 10^2
A. 2 x 10^4
B. 2 x 10^6
C. 2.1 x 10^6
D. 2.1 x 10^4
Answers
4.2 x 10^8 is 2*10^6 times the value of 2.1 x 10^2 when division is performed.
How can the number of times can be calculated?The concept that will be used to solve the question is division operation.
We were given 4.2 x 10^8 which is greater than 2.1 x 10^2
The operation can be expressed as :
4.2 x 10^8 =( n *2.1 x 10^2)
where n = the number of times that 4.2 x 10^8 is greater than 2.1 x 10^2
Then make n the subject of the formular which is
n = 4.2 x 10^8/2.1 x 10^2
n = 2*10^6
Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.
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What is the answer to this??
If you know basic geometry I think this should be simple
Answers
sqrt(3^2+2^2)=c
c=sqrt(13)
Answer: sqrt(13)
What is the expression in rational exponent form? (^4√ 8^3)^1/3?
Answers
The simplified form of the expression ( ⁴√( 8³ ) )^1/3 in rational exponents forms is 8^1/4.
How to convert expressions to rational exponents forms?Given the expression in the question;
( ⁴√( 8³ ) )^1/3
To convert to rational exponent form, apply the exponent rule;
ⁿ√aˣ = a^x/n
Hence;
( ⁴√( 8³ ) )^1/3 = 8^3/4
So we have,
( 8^3/4 )^1/3
Now, apply the power rule to multiply the exponents.
(a^m)^n = a^mn
( 8^3/4 )^1/3
8^( 3/4 × 1/3 )
8^( 3×1/4×3 )
Multiply 3 and 1
8^( 3/4×3 )
Multiply 4 and 3
8^( 3/12 )
Cancel out the common factor of 3 and 12; 3
8^( 1/4 )
8^1/4
Therefore, the simplified of the expression is 8^1/4.
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