3. What transformations on the graph f(x) = logg x result in the graph of g(x) = -log (x+5)?
4. What transformations on the graph f(x) = log3 x result in the graph of g(x) = -log(x) + 4?
Answers
The transformation that results in the graph of g(x) is: g(x) = -f(2x) + 4 = -log3(2x) + 4.
To transform the graph of f(x) = logg x into the graph of g(x) = -log (x+5), we need to apply the following transformations:
a) Reflection about the x-axis: This reflects the original graph across the x-axis. This transformation changes the sign of the function, which turns f(x) into -f(x).
b) Horizontal translation: This shifts the graph horizontally to the left or right. To shift the graph of f(x) to the left by 5 units, we need to replace x with (x + 5) in the function. This gives us f(x + 5).
Therefore, the transformation that results in the graph of g(x) is: g(x) = -f(x + 5) = -logg(x + 5).
To transform the graph of f(x) = log3 x into the graph of g(x) = -log(x) + 4, we need to apply the following transformations:
a) Reflection about the x-axis: This reflects the original graph across the x-axis. This transformation changes the sign of the function, which turns f(x) into -f(x).
b) Vertical translation: This shifts the graph up or down. To shift the graph of -f(x) up by 4 units, we need to add 4 to the function. This gives us -f(x) + 4.
c) Horizontal scaling: This stretches or compresses the graph horizontally. To compress the graph of -f(x) horizontally by a factor of 1/2, we need to multiply x by 2. This gives us -f(2x) + 4.
Therefore, the transformation that results in the graph of g(x) is: g(x) = -f(2x) + 4 = -log3(2x) + 4.
Learn more about transformation here
https://brainly.com/question/10904859
#SPJ11
Related Questions
Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
Answers
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
Read more about area here:https://brainly.com/question/27440983
#SPJ1
What is the MEAN of the data set below?(0.2,0.8,0.4,0.3,0.4,0.4,0.4,0.8,1.3)
Answers
Answer:
5/9
Step-by-step explanation:
we add all of the values and divide by the total number in this case 9, all of them add to make 5 so we do 5÷9 to get 5/9
Calculate the distance between the points KL if L is located on the origin and K is 3 units to the left of y-axis and 5 units upwards from the x-axis.
Answers
Answer:
answer must be √34 in my opinion.
!! URGENT !! The following data points represent the number of points the Hawaii Eagles football team scored each game.
17
,
33
,
28
,
23
,
10
,
42
,
3
17,33,28,23,10,42,317, comma, 33, comma, 28, comma, 23, comma, 10, comma, 42, comma, 3
Using the data, create a histogram.
Answers
Answer:
See image.
Step-by-step explanation:
Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.
3 and 10 fall in 0-15, so thats 2 values
17, 23, and 28 fall in 15-30, so thats 3 values,
33 and 42 fall in 30-45, so thats 2 values.
The scale on a map reads 1/2 inch = 30 miles. If two cities on the map are 5 % inches apart, find the actual distance between the cities.
Answers
Answer:
3 miles
Step-by-step explanation:
5% of one inch = 0.05 inches
0.5/30 = 0.05/x
0.5x = 1.5
x = 3
Notice how you can also simply divide 30 by 10 in this case? :)
A scale drawing of a lake has a scale of 1 cm to 80 m. If the actual width was f the lake is 1,000 m, what is the width of the lake on the scale drawing?
Answers
Answer:
12,5 centimeters.
Step-by-step explanation:
We take the following proportion
\(\frac{1 cm}{80m} = \frac{x}{1000m}\)
Which becomes:
\(1000 = 80x\)
And then, we clear out the variable x:
\(\frac{1000}{80}=\frac{100}{8}=\frac{50}{4}=12,5\)
And this means that the width of the lake on the scale drawing will be 12.5 cm.
Tom's telephone company charges a flat fee of $33.00 a month, plus $0.10 a minute for all long-distance calls made during the month. Tom's bill for the month of June was $53.00 before taxes . Which equation can be used to deternine how many long distance minutes ,x, Tom used during the month of June?
A.33=0.10x+53
B.33=53x+0.10
C.53=0.10x+33
D.53=33x+0.10
Answers
Answer:
D.
Step-by-step explanation:
What transformations produce the graph of g(x)=5^-x+2 from the graph of the parent function f(x)=5^x? Select all that apply.
Answers
Solution
For this case we have the following function:
\(g(x)=5^{-x+2}\)And we want to find the steps to obtain the above function from this one:
\(f(x)=5^x^{}\)So we can do the following:
Reflection over the x axis
horizontal shift to the left 2 units
What is the function of rational root theorem?
Answers
A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.
A polynomial expression is given and after solving them we get the two values known as the roots of the function.
These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .
We should use the rational root theorem only when the value of coefficients are small.
The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,
p is an integer factor of the constant term a0, and
q is an integer factor of the leading coefficient an.
Read more on rational root theorem
brainly.com/question/10937559
#SPJ4
Spencer has a retirement account through his employer. His monthly contributions to the account are taken out of his check before payroll taxes are calculated.
The fact that his employer sponsors his benefit package, and the contributions are (tax deferred, tax exempt), indicates that Spencer’s retirement account is a (traditional IRA, Roth IRA, traditional 401k, or a roth 401k.
Answers
This question requires a long answer to fully explain the possible options for Spencer's retirement account. Based on the information provided, it is clear that Spencer's employer sponsors his benefit package and his contributions are taken out of his check before payroll taxes are calculated. This indicates that his retirement account is either a traditional IRA, traditional 401k, Roth IRA, or Roth 401k.
A traditional IRA or 401k is funded with pre-tax dollars, meaning the contributions are deducted from the employee's taxable income, reducing the amount of income subject to taxes. The earnings on the account are also tax-deferred, meaning taxes are not paid until the funds are withdrawn during retirement.
A Roth IRA or 401k, on the other hand, is funded with after-tax dollars, meaning the contributions are made with money that has already been taxed. However, the earnings on the account are tax-exempt, meaning they are not subject to taxes when the funds are withdrawn during retirement.
Based on the information provided, it is most likely that Spencer's retirement account is a traditional 401k, as this type of account is commonly offered by employers and allows for pre-tax contributions. However, it is important to note that without further information about Spencer's specific retirement account, it is impossible to know for certain which type of account he has.
Spencer's retirement account is a traditional 401(k). This is because his contributions are made before payroll taxes are calculated, which indicates that the contributions are tax-deferred. Additionally, his employer sponsors the benefit package, which aligns with a 401(k) rather than an IRA.
To know more about Spencer's retirement visit:-
https://brainly.com/question/16816345
#SPJ11
Find the GCF using any method:
36, 84, and 90
Answers
Answer:
6
Step-by-step explanation:
Big brain
Please help I’m a bit stuck!!
Answers
Step-by-step explanation:
From n=1, to n=4, plug this in the sigma notation
The first four terms of this series are
-4,-8/3,-16/9,-32/27
b. Since -1<r<1, the series diverge
c. The sum of an infinite geometric series is equal to
\( \frac{a}{1 - r} \)
Where a is the initial value and r is the rate
a=-4
r =2/3
\( \frac{ - 4}{1 - \frac{2}{3} } = \frac{ - 4}{ \frac{1}{3} } = - 12\)
X
Frequency
50
3
60
8
70
15
80
30
90
29
100
15
Distribution Type 1: Normal distribution with mean = 75 and std.
dev = 25
Distribution Type 2: Uniform Distribution U[50,100]
Distribution
Answers
The second is a Uniform distribution with a minimum value of 50 and a maximum value of 100, where all values have equal frequencies.
Frequency distribution is a statistical representation of the number of occurrences of each value in a set of data. Let's consider the given set of values and describe two types of distributions for it.
Distribution Type 1: Normal Distribution with mean = 75 and standard deviation = 25.
This distribution follows a bell-shaped curve that is symmetric around the mean value of 75. The standard deviation of 25 indicates that the data is spread out with a moderate amount of variability. The highest frequency occurs at the mean value of 75, and as we move away from the mean in either direction, the frequency gradually decreases. The distribution provides information about how the values are distributed around the mean.
Distribution Type 2: Uniform Distribution U[50, 100].
This distribution is characterized by a rectangular shape, where all values have the same frequency. In this case, the minimum value is 50, and the maximum value is 100, resulting in a range of 50. The frequencies are uniform throughout the distribution, meaning that each value has the same frequency. In this case, since there are seven values in the set, each value has a frequency of 1/7.
To summarize, the given set of values can be represented by two different distributions. The first is a Normal distribution with a mean of 75 and a standard deviation of 25, which shows the overall pattern and spread of the data.
Learn more about standard deviation
https://brainly.com/question/29115611
#SPJ11
Please give the code word and the method as to how you did it
Answers
Answer:
1. true 2. true 3. false 4. false 5. false
15 + 15 + 10 + 10 + 10 = 60/5 = 12 ( CODE WORD)
Step-by-step explanation:
1. There are different forms of linear equations. Slope intercept has it's equation y = mx + b
2. A proportional relationship has a constant rate of change.
ex: y =2x +5, then the rate of change is 2 and it only ever rises by 2.
3. A proportional relationship must pass through the origin in order to be a proportional relationship.
4. The variable M in slope-intercept form represents the slope. B represents the Y-intercept.
5. Standard form for a linear equation is Ax+By=C. Y = MX+B is slope-intercept form.
CODE WORD: 12 or Twelve is correct because 12 is the mean of all 5 answers.
Find f(4) for the function f(x) = 3x2 + x - 6
Answers
Answer:
f(4) = 46
Step-by-step explanation:
\(f(x)=3x^2+x-6\\f(4)=3(4)^2+4-6\\f(4)=3(16)+4-6\\f(4)=48+4-6\\f(4)=52-6\\f(4)=46\)
A political scientist received a grant to fund a research project on voting trends. The budget includes $3,200 for conducting door-to-door interviews on the day before an election. Undergraduate students, graduate students, and faculty members will be hired to conduct the interviews. Each undergraduate student will conduct 18 interviews for$100. Each graduate student will conduct 25 interviews for $150. Each faculty member will conduct 30 interviews for$200. Due to limited transportation facilities, no more than 20 interviewers can be hired. How many undergraduate students, graduate students, and faculty members should be hired in order to maximize the number of interviews? What is the maximum number of interviews?
Answers
To maximize the number of interviews, 12 undergraduate students, 4 graduate students, and 4 faculty members should be hired. The maximum number of interviews that can be conducted is 684.
Let x, y, and z be the number of undergraduate students, graduate students, and faculty members hired, respectively. The objective is to maximize the number of interviews, which is given by the function
N = 18x + 25y + 30z.
The total cost of hiring interviewers is given by the function
C = 100x + 150y + 200z.
The constraints are x + y + z ≤ 20 (due to transportation limitations), and C ≤ 3200 (the budget constraint). Using linear programming techniques, we can solve for the optimal values of x, y, and z, which are 12, 4, and 4, respectively.
The maximum number of interviews is 18(12) + 25(4) + 30(4) = 684.
Learn more about Simple Maths:
https://brainly.com/question/30198551
#SPJ4
find the limit if is exists. if it exists, enter the value of the limit. if it does not exist enter dne. y sin(x-y)
Answers
The limit of the given function is π/2.
What is a limit?
A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.
Here, we have
Given: \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)
We have to find the limit of the given function.
= \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)
Now, we substitute the value of each variable.
x = π and y = π/2
= y sin(x-y)
= π/2sin(π-π/2)
= π/2sinπ/2
= π/2sin(90°) (∴sin90° = 1)
= π/2×1
= π/2
Hence, the limit of the given function is π/2.
To learn more about the limit from the given link
https://brainly.com/question/29013259
#SPJ4
May I have help?
True or False: The graph represents a function.
Answers
Answer:
Step-by-step explanation:
It's gonna be true in just trust me when i say that im that guy
Answer:
true
Step-by-step explanation:
Y + 43 > 30 then m could be
Answers
Answer:
M could be 15!
Step-by-step explanation:
As long as Y is greater than M, it should be Y + 43 > 30 + M.
Hope this helps.
Verify the identity shown below.
tan∅+cot∅=sec∅×csc∅
Answers
Answer:5
That is exactly correct! Just two things: First, tan,sin,cos, etc hold no meaning on their own, they need an argument. So just be sure to write tanx, cosx etc rather than just tan or cos.
Finally, you could save time on your proof by noticing on the fourth step that
1cosxsinx=1cosx1sinx=secxcscx
Share
Cite
Follow
Step-by-step explanation:
9-7v-1.1-8v simplified
Answers
Answer:
7.9−15v
Step-by-step explanation:
Answer:
poop
Step-by-step explanation:
poop
What is the value of x in the equation below?1+2e^x+1=9a). x=log4-1b) x=log4c). x=Ln4-1d). x=ln4
Answers
The -1 part is not inside the natural log.
==============================================
Work Shown:
1 + 2*e^(x+1) = 9
2*e^(x+1) = 9-1
2*e^(x+1) = 8
e^(x+1) = 8/2
e^(x+1) = 4
x+1 = Ln(4)
x = Ln(4) - 1
HELP NOW PLEASE ASAP!!
Answers
Answer:
The answer is D, your welcome
Answer:
The 2nd answer is correct.
Step-by-step explanation:
Between x = - 4 and x = - 1 the function is represented by a straight line (and is therefore lineair). Moreover, the value of y increases when moving to the right (and therefore the function is increasing).
Help please!!! ASAP!!! Currently failing!! ✌️
Answers
Answer:
1. x = 21°
2. x = 30°
3. x = 7°
5 x = 3
Step-by-step explanation:
Solving for x
1. 15+ 5x + 60° = 180°
75 + 5x = 180°
5x = 180 - 75
5x = 105
x = 105/5
x = 21°
2. These angle are vertical angles
Hence:
13x - 5 = 125°
13x = 125° + 5
13x = 130
x = 130/3
x = 30°
3. 8x - 1 = 55°
8x = 55 + 1
8x = 56
x = 56/8
x = 7°
5. These angles are angles in a straight line
17x - 1 + 130° = 180°
17x + 129° = 180°
17x = 180° - 129°
17x = 51
x = 51/17
x = 3°
Please Solve. First answer with explanation gets Most Brainliest and Points. TYSM
Answers
Answer:
2x+10+x+5=180
3x+15=180
3x=165
x=55
hope this helps
have a good day :)
Step-by-step explanation:
how many ways can the coach select with seven players will be in the batting order on an 11 person team?
Answers
There are 330 ways the coach can select a batting order of seven players from an 11 person team.
To determine the number of ways the coach can select a batting order of seven players from an 11 person team, we can use the combination formula, which is given by:
nCr = n! / r!(n-r)!
where n is the total number of players on the team, and r is the number of players in the batting order. In this case, n = 11 and r = 7.
So, the number of ways the coach can select a batting order of seven players from an 11 person team can be calculated as follows:
11C₇ = 11! / (7!(11-7)!)
= (11 x 10 x 9 x 8) / (4 x 3 x 2 x 1)
= 330
To learn more about combination click on,
https://brainly.com/question/17196495
#SPJ4
Factor this polynomial completely. And can you please really go into detail
6x^4-30x^3-84x^2
Answers
Answer:
6x²(x -7)(x +2)
Step-by-step explanation:
The first step is to look at what you are given. Here, we notice that the greatest common factor of all terms is 6x², so that can be factored out right away.
= 6x²(x² -5x -14)
To factor the quadratic, you look for factors of -14 that have a sum of -5.
-14 = (-14)(1) = (-7)(2) . . . . the only integer factor pairs with a negative sum
The sums of these factor pairs are -13 and -5, so we're interested in the latter. You can use these factors directly in the binomial factors of the quadratic:
= 6x²(x -7)(x +2)
_____
Additional comments
It is useful to start with the polynomial in standard form (decreasing powers of x), as it is here. That way, if there are any factors of x at the right end of the expression, they will be able to be factored from all terms. Here, the right term is a multiple of x², so x² can be factored from all terms.
Your knowledge of multiplication tables tells you 30 is a multiple of 6. Your knowledge of divisibility rules tells you 84 is even and a multiple of 3 (8+4=12 is a multiple of 3). That means 2·3 = 6 is also a factor of 84. (Most folks learn multiplication tables to 10×10, or maybe 12×12. If the latter, you know 84=7×12, so will be a multiple of 6.) The point here is that you can recognize all of the coefficients as being multiples of 6. Now you know that 6x² is a factor of every term, so is a factor of the expression.
using point Q as the center of dilation.
Point Q is the center of dilation. Line segment A B is dilated to create line segment A prime B prime. The length of Q A is 1.25 and the length of A A prime is 1.25.
What is the scale factor?
1
1.25
2
2.5
Answers
Answer:
(c) 2
Step-by-step explanation:
The dilation scale factor multiplies the distance from the center of dilation.
Distance from QWe are given that QA = 1.25, and that AA' = 1.25. By the segment sum theorem, we have ...
QA' = QA +AA'
QA' = 1.25 +1.25 = 2.50
Scale factorThe scale factor multiplies the original distance:
QA' = k·QA . . . . . . . . . . where k is the dilation scale factor
2.50 = k·1.25 . . . . . . . . using the known lengths
2.50/1.25 = k = 2 . . . . divide by the coefficient of k
The scale factor is 2.
PLSSS HELPPP
Scott and his family went on a backpacking trip. They started hiking at 3:00 P.M. It took 1 hour and 55 minutes to reach their campsite. After they arrived, it took 1 hour and 10 minutes to set up the campsite. What time was it when Scott and his family finished setting up their campsite?
Answers
Answer:
6:05PM
Step-by-step explanation:
did the math , three hours and 5 minutes
Answer:
3:00 pm + 1 hr 55 min = 4:55 pm
4:55 pm + 1hr 10 min= 6:05 pm
Scott and his family finished setting up their campsite at 6:05 pm.
Factor by grouping (sometimes called the ac-method).3x²+x-10First, choose a form with appropriate signs.Then, fill in the blanks with numbers to be used for grouping.Finally, show the factorization.Form:Х?23x+x ++ 0x--1023x+X1023xx ++ 0x102X03xX10Factorization:0
Answers
Given the expression:
3x² + x - 10
We can rewrite it as:
3x² + 6x - 5x - 10
Which can be factoriced as:
3x(x + 2) - 5(x + 2) =
(x + 2)(3x - 5)