Identify the transformations of the function ƒ(x) = log22(x + 6) from the base graph g(x) = log2(x).There are two transformations: 1. a vertical stretch of the curve by a factor of 2 and 2. a shift to the right of 12 units.There are two transformations: 1. a horizontal compression of the curve by a factor of 2 and 2. a shift to the left of 12 units.There are two transformations: 1. a vertical compression of the curve by a factor of 2 and 2. a shift to the left of 12 units.There are two transformations: 1. a horizontal stretch of the curve by a factor of 2 and 2. a shift to the right of 12 units.
Answers
ANSWER:
B. There are two transformations: 1. a horizontal compression of the curve by a factor of 2 and 2. a shift to the left of 12 units.
STEP-BY-STEP EXPLANATION:
We have the following function:
\(\begin{gathered} f(x)=\log_22(x+6)\rightarrow\log_2(2x+12) \\ \\ g(x)=\log_2(x) \end{gathered}\)We have to add or subtract within the logarithm it represents a horizontal shift, in the case of adding the added amount moves to the left and if it is subtracted it moves that amount to the right. In this case it adds 12, which means that it moves to the left by 12 units.
When multiplying inside the function, by a value k, there is a horizontal change, in a factor k. If this value is greater than one it would be horizontal compression but if the value is between 0 and 1 it would be horizontal stretch.
In this case, it is multiplied by 2, which is greater than 1, which means that there is a horizontal compression of factor 2.
Which means that the correct answer is B. There are two transformations: 1. a horizontal compression of the curve by a factor of 2 and 2. a shift to the left of 12 units.
Related Questions
What is the cost of a pair of shoes if they retail for $18.50, have a tax of 6%, and you have a coupon for 20% off after taxes
Answers
Answer:
$15.69
Step-by-step explanation:
multiply the retail price by 1.06 to get the price after taxes.
find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer
john and jack divided there math homework.John solved twice as many problems as jack plus 1 more problem how many problems did each boy solve if there are 28 assigned problems?
Answers
Answer:
John: 19
Jack: 9
Step-by-step explanation:
Answer:
Jack = 9
John = 19
Step-by-step explanation:
Let the number that Jack solved = N
Then John solved 2N + 1
So
N + 2N + 1 = 28
3N = 28 - 1
3N = 27
N = 27 / 3 = 9 = number Jack solved
2(9) + 1 = 19 = number John solved
Solve help? That's it really.
Answers
Answer:
1).00390625
2).216
3).0231481481481
Step-by-step explanation:
What are the solutions to the quadratic equation 4(x + 2)2 = 36 x = −11 and x = 7 x = −7 and x = 11 x = −5 and x = 1 x = −1 and x = 5
Answers
Answer:
c
Step-by-step explanation:
edge2020
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
What is a Quadratic Equation?
Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given that;
4(x + 2)² = 36
4( x(x + 2) + 2(x+2) ) = 36
4( x² + 2x + 2x + 4 ) = 36
4( x² + 4x + 4 ) = 36
4x² + 16x + 16 = 36
4x² + 16x + 16 - 36 = 0
4x² + 16x - 20 = 0
We can further simply ( divide through by 4 )
x² + 4x - 5 = 0
Hence,
a = 1b = 4c = -5x = (-b±√(b² - 4ac)) / (2a)
x = (-4±√(4² - (4 × 1 × -5)) / (2×1)
x = (-4±√(16 - (-20)) / (2)
x = (-4±√(16 + 20)) / (2)
x = (-4±√(36)) / 2
x = (-4±6)) / 2
Hence
x = (-4-6)) / 2 and x = (-4+6)) / 2
x = -10/2 and x = 2/2
x = -5 and x = 1
The solutions to the quadratic equation 4(x + 2)² = 36 is x = -5 and x = 1.
Hence, option c) x = -5 and x = 1 is the correct answer.
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A calf raiser mixes a batch of milk replacer for 15 calves. Each calf gets two
quarts of milk replacer. If the calf raiser uses 960 oz. of replacer and needs to
add 34 as much water as milk replacer, how many ounces of water does she need?
Answers
Answer:
The calf raiser uses 960 oz of milk replacer for 15 calves, so each calf gets 960 oz / 15 = 64 oz of milk replacer.
To convert this to quarts, we need to divide by 32 (since there are 32 oz in a quart)
64 oz / 32 oz/quart = 2 quarts
Each calf gets 2 quarts of milk replacer and the calf raiser needs to add 34 as much water as milk replacer
So the total amount of water she needs is 2*34 = 68 quarts
To convert the quarts of water to ounces we need to multiply by 32 (since there are 32 oz in a quart)
68 quarts * 32 oz/quart = 2176 oz of water.
So the calf raiser needs 2176 ounces of water to mix with the milk replacer for 15 calves.
What is the best way to combine
the sentences below using a
participle phrase?
Sam wondered if the students
really understood the material. He
decided to investigate.
A. Sam decided to investigate whether or not the
students really understood the material.
B. Wondering if the students really understood
the material Sam decided to investigate.
C. Wondering if the students really understood
the material, Sam decided to investigate.
nternational Academy of Science. All Rights Reserved.
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A
O
Need an answer
Answers
C. Wondering if the students really understood the material, Sam decided to investigate.
Option C is the best way to combine the sentences using a participle phrase because it captures the cause-and-effect relationship between Sam's wondering and his decision to investigate in the best way.
Answer:
C. Wondering if the students really understood the material, Sam decided to investigate.
Step-by-step explanation:
This sentence correctly uses a comma to separate the participle phrase from the main clause, providing clarity and maintaining grammatical correctness.
NEED ASAP!! ILL GIVE YOU 30 points!!
Hopt decided to sell some mimstoons (x) and kents (y). Altogether,
she planned to sell at least 8 items.
Write an inequality showing the above constraint.
Answers
Answer:
X+Y is greater then or equal to 8
Step-by-step explanation:
In total she wants to sell at least 8 items which implies shes willing to sell more (so greater or equal to) then it's adding X+Y bc those are the items that she is selling
If you owe your friend $3 and you have $15, which expression would help you find out how much money you would have left?
Answers
Answer:
12
Step-by-step explanation:
15 - 3 = 12
Answer:
both of them are right
Step-by-step explanation:
Find the length of the third side. If necessary, write in simplest radical form.
2√34, 6
Answers
The length of the third side is 2√34 + 6.
We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.
Let x be the length of the third side. Then we have:
2√34 + 6 > x
Subtracting 6 from both sides, we get:
2√34 > x - 6
Adding 6 to both sides, we get:
x < 2√34 + 6
Therefore, the length of the third side must be less than 2√34 + 6.
To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:
2√34 + 6 = x
If this is true, then the given sides can form a triangle.
Simplifying the equation, we get:
x = 2√34 + 6
The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.
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Patrick Company expects to generate free-cash of $120,000 per year forever. If the firm's required return is 12 percent, the market value of debt is $300,000, the market value of preferred stock is $70,000, and the company has 100,000 shares of stock outstanding. What is the value of Patrick's stock?
Answers
Step-by-step explanation:
Patrick Company expects to generate free-cash of $120,000 per year forever. If the firm's required return is 12 percent, the market value of debt is $300,000, the market value of preferred stock is $70,000, and the company has 100,000 shares of stock outstanding. What is the value of Patrick's stock
present ages of two children are 2 and 5 years the rspectively. After how long will the sum of their square ages be 45.
Answers
Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.
Calculating the duration to get the sum to 45Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.
Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;
let x represent the number of years from now when the sum of square of their respective age will be
45.(x + 2)² + (x + 5)² = 45
Expanding the brackets;
x² + 4x + 4 + x² + 10x + 25 = 45
2x² + 14x + 29 = 45
2x² + 14x + 29 - 45 = 0
2x² + 14x - 16 = 0
Solving the quadratic equation for x;
x = 1, x = -8
Taking the positive value, the value of x is 1
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Jennifer wants to have a graduation party that will cost at least $375. If Jennifer can save $52 a month, how many months will she need to to be able to afford the party? Which inequality represents this situation.
1. 52 < 375m
2. 375 > 52m
3. 52 > 375m
4. 375 < 52m
Answers
Answer:375<52m
Step-by-step explanation:
jennifer will want at least 375 so you could get more and 52 is about per month m so 375<52m
Answer:
4. 375 < 52m
Step-by-step explanation:
In this inequality, "m" represents the number of months Jennifer will need to save in order to afford the party. The left side of the inequality, 375, represents the cost of the party, which Jennifer wants to be able to afford. The right side of the inequality, 52m, represents the amount of money Jennifer saves per month multiplied by the number of months, which should be more than or equal to the cost of the party for her to afford it!
Hope this helps, thank you.
∠X = 89°, ∠Y = 90°, ∠Z = ?
Answers
∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°
→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°
→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°
→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°
angle Y and W are supplementary angles
so
→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°
angle X and Z are supplementary angles
so
→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°
Therefore, the answer is
∠Z=40°
In a two candidate election, Amanda received 7 times as many votes as Joshua. If a total of 16 votes were cast, then how many votes did Joshua receive?
Answers
Answer:
2 votes
Step-by-step explanation:
It is 7 times joshua so we can write that as 7j
16 is the total so we are going to put an equal sign before that
7j=16
To solve, isolate j
To do that divide by 7 on each side
you get 2.28 votes but you can't have a fraction of a person voting so it would be 2 votes
Ellie has 49 books. Franklin has more books than Ellie. Write an expression that shows how many books Franklin has.
Answers
Answer:
49 < x
Step-by-step explanation:
Write an inequality.
Let x be franklin's books
so then,
49 < x is the inequality
7. Sapna travelled 48 km to meet her parents. She travelled the first 18 km by car and the remaining distance by train. Find the fraction of the journey sapna travelled by car and train
Answers
The fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
We know that fraction is an expression in mathematics used to denote the division of two whole numbers.
Given that the total distance = 48 km.
The distance Sapna traveled by car = 18 km.
So, the fraction is = distance traveled by car/total distance = 18/48 = 3/8
The distance Sapna traveled by train = 48 - 18 km = 30 km.
So, the fraction is = distance traveled by train/total distance = 30/48 = 5/8
Therefore the fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
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Translate each into an algebraic expression
5 times k
A) 5k
B) k+5
C) k divided by 5
D) 5-k
Answers
Answer:
A) 5k
Step-by-step explanation:
anything near a number like that is usually times. Like 7g would be 7xg!
What is the value of x? Round to the nearest tenths place.
Answers
Answer:
ok x should be 30
Step-by-step explanation:
Write the steps to graph the line from the equation.
y= 4x - 1
Answers
The graph of the given equation is attached below.
We are given the equation:-
y = 4x - 1
First we will find the x and y intercepts of the line.
Putting x = 0 to find the y-intercept of the graph, we get
y = 4*0 - 1
y = -1
Hence, the coordinates of the point will be (0,-1).
Putting y = 0 to find the x-intercept of the graph, we get
0 = 4x - 1
1 = 4x
x = 1/4
Hence, the coordinates of the point will be (1/4,0).
My plotting these coordinates on the graph and then joining the line passing through it, we will get our desired graph.
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se the drawing tool(s) to form the correct answer on the provided graph.
A barrel in Jim's yard contains 60 gallons of water. Water leaks out of the barrel at a rate of 1 gallon every 10 minutes.
Create and graph the solution set of the equation for the gallons of water, y, remaining in the barrel in terms of the number of minutes elapsed, x
Answers
Answer:
it will take 10 hours for the barrel to empty out
Step-by-step explanation:
n a certain city, it was found out that there are 100 residents who are employed
in the office of the city mayor. They are classified as follows:
48 female employees
46 married employees
34 employees with more than 15 years of service
19 married females
18 married with more than 15 years of service
17 female with more than 15 years of service
8 married female with more than 15 years of service
Questions:
1.How many are married female employees with less than 15 years of service?
2.How many are married male with more than 15 years of service?
3.How many are female single employees with more than 15 years of service?
4.How many are married female with more than 15 years of service?
5.How many are male single employees with less than 15 years of service?
Answers
Answer:
1. 11 married females because out of the 19 married, only 8 had more than 15 years of service and 19 - 8 = 11.
2. 10 married males because of out the 18 married with more than 15 years of service, 8 were females and 18 - 8 = 10.
3. 9 single females because out of the 17 with more than 15 years of service, 8 were married and 17 - 8 = 9.
4. 8 married females because it literally says, "8 married female with more than 15 years of service".
gotta go hope this helps sry
I need help with this question
Answers
Answer:
5/7
Step-by-step explanation:
ratio of boys to girls---> 2:5
ratio sum: 2+5=7
girls ratio =5/7
OR
total of people in 7th grade choir=28
hence, no of girls in 7th grade choir=5/7 × 28
=20
proportion of girls in choir= 20/28 = 5/7
Robert can mow a 600 square lawn in 1 hour and 20 minutes. How many lawns in the same size's can he mow in 8 hours?
Answers
Jake and Joshua have new jobs selling gift cards at a local convenience store at the cash register, but their pay is different. Jake earns a foundational wage of $15 per hour, as well as $3 for each gift card sold. Joshua gets $4 for each gift card sold and earns a foundational wage of $10 per hour. If they each sell a certain number of gift cards in one hour, they will end up earning the same amount of pay. How many gift cards would that make up to?Write a system of equations, graph them, and type the solution
Answers
The payment for Jake will be given by
\(p=15+3x\)Where "p" is the payment and "x" is the number of gif cards sold.
And the payment for Joshua will be
\(p=10+4x\)Now we have two equations, we can graph them
The intersection of the two graph is at (5, 30), that means that when they sell 5 gift cards in a hour they will both be pay $30, that's when they both ea
What is the value of k?
Answers
9514 1404 393
Answer:
k = 10
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angles.
115° = (4k +5)° +(6k +10)°
115 = 10k +15 . . . . . . . . . . . divide by °, simplify
100 = 10k . . . . . . . . . . . . subtract 15
10 = k . . . . . . . . . . . . . . divide by 10
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.3,5,7,...
Answers
Step 1:
Arithmetic sequence
In an Arithmetic Sequence the difference between one term and the next is a constant.
Geometric sequence
Geometric Sequences. In a Geometric Sequence each term is found by multiplying the previous term by a constant.
Step 2
The sequence is 3 , 5 , 7
\(\begin{gathered} \text{Common difference = 2nd term - 1st term or 3rd term - 2nd term} \\ \text{= 5 - 3 = 2} \\ =\text{ 7 - 5 = 2} \end{gathered}\)Final answer
Since the common difference is constant, the sequence is Arithmetic sequence.
PLEASE ANSWER THIS QUESTIO NOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
2.65 pounds/week
Step-by-step explanation:
(13 1/4) / 5
13.25 / 5
= 2.65 pounds/week
Answer:
2.65 lbs per week
Step-by-step explanation:
13.25 is how many pounds
5 weeks is the length of time
pounds/length of time
13.25/5 = 2.65
2.65 lbs per week
Probability of dependent
Events
Answers
Dependent events: The likelihood of one event happening influences the likelihood of the other event happening.
What are dependent events?
When the result of one event affects the result of another, two events are said to be dependent events.
The likelihood of two connected events is the sum of the probabilities of the occurrences X and Y that happen after X.
The likelihood of one event does influence the likelihood of the other happening.
For instance, the likelihood of drawing another King decreases if you remove a King from a deck of cards without replacing it.
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simplify the expression 10x - 8x + 2 + 10
Answers
Answer:
2x + 12
Explanation:
10x - 8x = 2x, 2 + 10 = 12, so the simplified answer is 2x + 12
Divide: 7 5/6 ÷ 2/3 need help
Answers
To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.
Step 1: Convert the mixed number to an improper fraction:
7 5/6 = (6 * 7 + 5) / 6 = 47/6
Step 2: Multiply the improper fraction by the reciprocal of the fraction:
47/6 ÷ 2/3 = 47/6 * 3/2
Step 3: Simplify the fraction if possible:
47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12
Step 4: Simplify the fraction further, if necessary:
141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4
Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.