The function f(x)=log2x is transformed 4 units down and vertically compressed by a factor of 0.2 to become g(x).
Which function represents the transformation g(x)?
The answer is: g(x)=15log2(x)−4
Answers
Using translation concepts, it is found that function g(x) is given by:
[tex]g(x) = \frac{1}{5}\log_{2}{x} - 4[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is given by:
[tex]f(x) = \log_{2}{x}[/tex]
It was shifted 4 units down, hence:
[tex]g(x) = \log_{2}{x} - 4[/tex]
It was vertically compressed by a factor of 0.2, hence:
[tex]g(x) = \frac{1}{5}\log_{2}{x} - 4[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
Answer:
g(x)=0.2 log[tex]_{2}[/tex] (x)−4
Step-by-step explanation:
Related Questions
Explain how you would find 2/3 x 12 mentally. (help lol)
Answers
Answer: 8
You just need to multiply the numerator (top number) by the 12
2x12=24
so now its 24/3
24/3 simplified is 8
About 50 cane toads were introduced into Australia in 1935 to try to control the population of beetles that destroy sugar cane plants. By 2005, there were an estimated 100,000,000 cane toads in Australia. An exponential function that models the number of female cane toads in Australia t years after 1935 is given by f(t)=50(1.23)t .
a. Write a linear function p that models the number of cane toads in Australia t years after 1935. p(t)=_____
b. Describe the parameters in the exponential function, , in terms of the context of the problem. ____
c. Describe the parameters in the linear function, p , in terms of the context of the problem. ____
Question 4 d. Which model do you think is more appropriate to model the female cane toad population? Use the parameters of the functions to justify your reasoning. Linear or exponential?
Predict the population of female cane toads in Australia in 2000 based on each function. The linear function predicts that there would be ___ female cane toads in 2000. The exponential function predicts that there would be ___ female cane toads in 2000.
Answers
The linear function predicts that there would be 92857146 female cane toads in 2000 while the exponential function predicts that there would be 34898137 female cane toads in 2000.
Part A: The linear model of the number of cane toadsFrom the question, we have the following points
(t, f(t)) = (0,50) and (70, 100000000)
The linear function is then calculated as:
f(t) = [f(t2) - f(t1)]/[t2 - t1](t - t1) + f(t1)
This gives
f(t) = [100000000 - 50]/[70 - 0](t - 0) + 50
Evaluate
f(t) = 1428570.71t + 50
Hence, the linear function is f(t) = 1428570.71t + 50
Part B: The parameters in the exponential functionThe exponential function is given as:
f(t) = 50(1.23)^t
So, the parameters are:
50 represents the initial value1.23 represents the ratet represents the number of years from 1935f(t) represents the number of cane toad in year tPart C: The parameters in the linear functionThe exponential function is calculated as:
f(t) = 1428570.71t + 50
So, the parameters are:
50 represents the initial value1428570.71 represents the ratet represents the number of years from 1935f(t) represents the number of cane toad in year tPart D: The appropriate modelWhen the population of an entity is being model, it is best to use the exponential model, because the populations would grow exponentially for some time, and then stop growing at some point
Hence, the more appropriate model is the exponential model.
Part E: The number of female cane toads in 2000
The year 2000 is 65 years from 1935.
So, we have:
t = 65
For the exponential model, we have:
f(t) = 50(1.23)^t
The equation becomes
f(65) = 50(1.23)^65
Evaluate
f(65) = 34898137
For the linear function, we have:
f(t) = 1428570.71t + 50
The equation becomes
f(65) = 1428570.71 * 65 + 50
Evaluate
f(65) = 92857146
This means that. there would be 34898137 female cane toads in 2000 according to the exponential function.
Read more about linear and exponential functions at:
https://brainly.com/question/725335
Please help me find the angles marked in the above diagrams The first figure is 8cm,5cm
2. 8m,15m
3. 8.4m,6.3m
4. 105m,123m
Answers
10. A museum gift shop sells hats with embroidered logos of the museum.
The hats are available in small, medium, and large sizes. They are available
in the colors red and green.
Make a tree diagram or a table to represent all possible varieties of hats sold at
the museum.
Answers
Due yesterday
Even if ur sure its correct j send it, ill turn in anything
Answers
Answer:
A)8000
B) 1296a^4
C) 9x^2
D)100000000
E)0.00097656
F)x^⁶
G)y^11
Step-by-step explanation:
What is 26.375% written as a decimal number?
Answers
Answer: 263.75
Step-by-step explanation:
because i know
The decimal form of 26.375% is 0.26375.
How to convert percentage into decimal ?
Let, x be a number.
Now, if we want to convert x% to decimal, then we have to divide x by 100.
How to find decimal form of 26.375% ?To convert the given percentage into decimal, we have to divide the given percentage by 100.
∴ 26.375% = [tex]\frac{26.375}{100}[/tex] = 0.26375
Hence, 26.375% = 0.26375
Learn more about percentage here :
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Solve:
5 = p/4
SOMEONE PLEASE HELP IM SO CONFUSED AND THEIR IS 90 QUESTIONS AND IM ONLY ON 50 AND ITS DUE THIS FRIDAY
Answers
Answer:
p = 20
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other.
Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtraction
~
Isolate the variable, p, by multiplying 4 to both sides of the equation:
[tex]5 = \frac{p}{4}\\ 5 (* 4) = \frac{p}{4} (* 4)\\ 5 * 4 = p\\p = 20[/tex]
p = 20 is your answer.
~
You have to put unknowns (p) on 1 side and knowns on other side.
To get p alone you have to move the 4. Since p divides 4, you have to multiple by 4 to cancel it out. BUT Remember if you have to change one side, you have to change other side by same amount too, so the equality stays true. So multiply BOTH sides by 4
4* 5 = (p/4)*4
the 4s on the right side cancel each other because 4/4=1
So,
20 = p
if the equation of a circle is x^2+y^2-3x-y-13/2=0, find the length of the diameter of the circle
Answers
Answer:
x² + y² - 3x - y - 13/2 = 0
Step-by-step explanation:
I think thats the answer if it is right pls mark me as brainliest and learn well
I’ll give brainiest
Answers
Answer:
If you taKE the pentagon and the hexagon she is wrong.
Step-by-step explanation:
hope this helped.
Answer:
nothing
Step-by-step explanation:
she is crazy, it fits perfectly, lol
help pls
I'm not good with this stuff lol
Answers
40 square feet
Steps:
Formula for the area of a triangle.
A = B*H/2
Formula for the area of a rectangle.
A = L*W
1. Break up the shape into 1 triangle and 1 rectangle.
2. The length of the rectangle is 8 ft and the width is 3 ft. Plug-in these values into the formula for the area of a rectangle.
A = 8 * 3
A = 24
3. The base of the triangle is 8 ft and the height is 4 ft. Plug-in these values into the formula for the area of a triangle.
A = (8 * 4) / 2
A = 32 / 2
A = 16
4. Now add the two areas together to find the amount of carpet needed.
24 + 16 = 40
Answer:
38 ft²Step-by-step explanation:
You can take it as combination of two figures, a trapezoid and a triangle.
Trapezoid has bases 12 ft and 8 ft and height 3 ft
Its area is
A = 1/2(8 + 12)(3) = 30 ft²Triangle has height 4 ft and base 4 ft,
Its area is
A = 1/2(4*4) = 8 ft²Total area is
30 + 8 = 38 ft²find the lateral area and surface area of each prism. please show your work.
Answers
[tex]\stackrel{\textit{\Large Lateral Area}}{\stackrel{\textit{area of the 6 sides}}{6(12)(15)}\implies 1080} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ p=\stackrel{6\times 12}{72}\\ a=10.39 \end{cases}\implies A=\cfrac{1}{2}(10.39)(72)\implies 374.04 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{lateral}{1080}~~ + ~~\stackrel{two~hexagons}{2(374.04)}}\implies 1828.08\qquad \leftarrow \textit{total surface area}[/tex]
Some of the dimensions of a square pyramid are shown in the diagram. The height of the pyramid is 7.5 meters.
square pyramid
What is the volume of the square pyramid in cubic meters?
Question 8 options:
40 m3
120 m3
360 m3
60 m3
DIGRAM BELOW
Answers
Answer:
40 m^3.
Step-by-step explanation:
Volume = 1/3 * 4^2 * 7.5
= 40 m^3.
Jeff drinks 2/3 of a glass of juice write A fraction that is equivalent to 2/3
Answers
Answer:
4/6 , 8/12, etc
Step-by-step explanation:
A fraction that can be equivalent to 2/3 is 4/6 or 8/12
This is because if you were to multiply 2/3 by 2/2 you multiplied by the same amount and also the product of that can be simplified to 2/3s.
I GOT THIS WRONG!! So what is the answer??
BOTS=BAN/REPORT
TROLL=BAN/REPORT
Answers
Use one of the sets and divide them to find the proportional relationship.
3 / 43.5 = 0.06896
Now since it's not in the answer choices, you round it.
0.06896 rounded to the nearest tenths is 0.7
Aliya lined up the interior angles of the triangle along line p below
When the measure of angle A increases in the triangle, what happens to angle A on line p?
It also increases.
Olt decreases
It stays the same.
It may increase, or it may stay the same.
Answers
Answer:
it also increases
Step-by-step explanation:
HELP ASAP
The table shows how the number of sit-ups marla does each day has changed over time. At this rate, how many sit-ups will she do on day 12? Explain your steps in solving this problem
Day 1 - 12
Day 2 - 21
Day 3 - 25
Day 4 - 29
Day 5 - 33
Answers
Answer:
177
Step-by-step explanation:
just answered this for someone else but the number of sit-ups is going up in 4s so just add four to 33 7 times since thats how many days she has left til 12th day
What is the value of x?
Answers
Answer:
Step-by-step explanation:
Sum of all angles of triangle = 180°
15x + 3 + 3x - 1 + 52 = 180
15x + 3x + 3 - 1 + 52= 180
Combine like terms.
18x + 54 = 180
To find the vlaue of x, we have to islolate x
Step1: Subtract 54 from both sides
18x = 180 - 54
18x = 126
Step2: Divide both sides by 18
x = 126/18
x = 7
Answer:
x = 7 degrees
Step-by-step explanation:
See attached image.
Which statement is true?
A. |-2.5| >|-3|
B. |-2.5| <|-3|
C. |-2.5| = |-3|
Answers
Answer:
A. |-2.5| >|-3|
Step-by-step explanation:
In January 2015, the Pew Research Center reported results from one of their surveys. "Asked about whether vaccines for childhood diseases such as measles, mumps, rubella (MMR) and polio should be required or left up to parental choice, 68% of adults say such vaccines should be required while 30% say that parents should be able to decide whether or not to vaccinate their children. "
The following is an excerpt from the press release:
The survey of the general public was conducted using a probability-based sample of the adult population by landline and cellular telephone Aug. 15-25, 2014, with a representative sample of 2,002 adults nationwide. The margin of sampling error for results based on all adults is plus or minus 3. 1 percentage points. What is 95% confidence interval for these findings
Answers
Considering the margin of error, it is found that the 95% confidence interval for the percentage of adults who say vaccines should be required is (64.9%, 71.1%).
What is a confidence interval?
It is given by the sample statistic plus/minus the margin of error.
In this problem, 68% of adults say such vaccines should be required, with a margin of error of 3.1%, hence:
68% - 3.1% = 64.9%.
68% + 3.1% = 71.1%.
The 95% confidence interval for the percentage of adults who say vaccines should be required is (64.9%, 71.1%).
More can be learned about confidence intervals at https://brainly.com/question/25890103
Name a diameter.
8
G
E
A
FG
С
CE
B.
AB
D
BO
Answers
Answer:
FG
Step-by-step explanation:
FG is the only line which goes straight across the circle through the centre
Matt wants to start zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint? Use specific numbers from the situation to justify or refute whether Matt’s design meets the slope constraint
Answers
There is no difference in height that is not sufficient to meet the slope constraint if Matt wants to start a zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
We know the slope can be evaluated using:
[tex]\rm Slope = \frac{Change \ in \ y \ axis}{Change \ in \ x \ axis}[/tex]
Change in y-axis = difference in height
Change in y-axis = 16 - 10
= 10 feet
Change in x-axis = distance between tress
Since the data is not given.
So, the height difference is insufficient to keep the slope constraint.
Thus, there is no difference in height that is not sufficient to meet the slope constraint if Matt wants to start a zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint.
Learn more about the slope here:
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A quadrilateral has two angles that measure 222° and 81°. The other two angles are in a ratio of 6:13. What are the measures of those two angles?
Answers
[tex]\sf\huge\underline{\star Solution:-}[/tex]
[tex]\rightarrow[/tex] Ratio of two angles are 6:13.
So, let the one angle be [tex]\sf{6x}[/tex] and another be [tex]\sf{13x.}[/tex]
As we know that,
Sum of all interior angles of a quadrilateral = [tex]\sf\pink{360°.}[/tex]
So let's sum up the given angles,
[tex]\rightarrow[/tex] [tex]\sf{222°+81°+6x+13x \:=\: 360°}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{303+19x \:=\: 360°}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{19x \:=\: 360-303}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{19x \:=\: 57}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{x \:=\: \frac{19}{57}}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{x \:=\: 3}[/tex]
Hence, [tex]\sf{x \:=\: 3}[/tex]
So, First angle [tex]\sf{= \:6x\: = \:6×3 \:=}[/tex] [tex]\sf\purple{18°.}[/tex]
Second angle [tex]\sf{= \:13x\: = \:13×3 \:=}[/tex] [tex]\sf\purple{39°.}[/tex]
_________________________________
Hope it helps you:)
Help! Khan academy geometry practice
Answers
V = 4/3πr³ = 4/3π2³= 33.5 (rounded)
i dont know this and i think its going to be in our FSA please help THANK YOU.....
Answers
Answer:
You never put a screenshot
Step-by-step explanation:
Pls put screenshot :)
round 256.709 to the nearest tenth place
Answers
Answer: 256.7
Step-by-step explanation: the tenth place, (7) is rounded to 7 because when you round the number after the tenth place (7) the number has to be at 5 or greater inorder to change values.
Solve using the Elimination Method
5x + y = 4
6x - y = 7
Answers
Answer:
x=1,y=-1
Step-by-step explanation:
To use the elimination method, we make the coefficient of y the same:
But they are already the same just with different signs.
So we add the 2 equations to make equation 3:
5x + y = 4
+ + = +
6x - y = 7
11x = 11
Solve for x:
x = 1
Substitute the value of x into either equation 1 or 2 to find y:
I chose 1:
5(1)+y=4
5+y=4
y=4-5
y=-1
Our answer is x=1,y=-1
Substituting these values into equation 2 verifies our answer
if the prisms below are similar what is the ratio of the surface area of the smaller prism to the surface area of the larger prism
v=24
v=375
Answers
The ratio between the surfaces areas of the two prisms is equal to 6.25.
How to get the ratio of the surface areas?
The ratio between the volumes of the prisms is:
[tex]R_v = \frac{375 in^3}{24 in^3} = 15.625[/tex]
This number is equal to the cube of the scale of dilation applied to the dimensions of the smaller prism, so the scale factor is:
[tex]\sqrt[3]{15.625} = 2.5[/tex]
And the ratio between the areas should be the square of the scale factor, then we will have that the ratio between the surface areas of the two prisms is:
[tex]2.5^2 = 6.25[/tex]
If you want to learn more about scale factors, you can read:
https://brainly.com/question/3457976
Use the portion of the exponential graph below to answer questions 7-8.
What is the domain?
What is the range?
Answers
Answer:
See below ~
Step-by-step explanation:
Domain = range of x values
Lowest value = -1Highest value = 3Domain ⇒ -1 ≤ x ≤ 3Range = range of y-values
Lowest value = 6Highest value = 27Range ⇒ 6 ≤ y ≤ 27» Look at this scatter plot.
60
54
48
42
36
.
30
24
18
12
6
х
6
6
12
.
18
24
30
36
42
48
54
60
)) Which equation could represent the line of best fit for this data?
II
y = -3x + 42
-X
+ 18
y = kx +
+ 24
y = 3x + 30
y = -x + 36
y
y = x + 12
Answers
Answer:
The mean for the data in the dot plot is 5. What is the
absolute deviation for the data point at 7?
2
Step-by-step explanation:
Which is a larger volume, a candle with a height of 6. 3 inches and a radius of 3. 1 inches, or a candle with both a height and a radius of 3. 9 inches?
Answers
Step-by-step explanation:
such candles are cylinders.
the volume of a cylinder is
pi×r²×height
the volume of candle 1 is
pi×3.1²×6.3 in³ = pi × 60.543 in³
the volume of candle 2 is
pi×3.9²×3.9 in³ = pi × 59.319 in³
so, candle 1 has the larger volume.