How do the graphs of the functions f(x) = (Three-halves)x and g(x) = (Two-thirds)x compare?
Answers
Answer:
The answer to this question can be defined as follows:
Step-by-step explanation:
Given:
[tex]\bold{f(x)= (\frac{3}{2})^x}\\\\\bold{g(x)= (\frac{2}{3})^x}\\[/tex]
Following are the graph attachment to this question:
The second function, that is [tex]g(x)= (\frac{2}{3})^x[/tex] is not even a function.
Remember that g(x) function is the inverted f(x) function. And when you see this pattern, a reflection on the Y-axis expects you.
Reflection in the axis.
In x-axis:
Increase the function performance by -1 to represent an exponential curve around the x-axis.
In y-axis:
Increase the input of the function by -1 to represent the exponential function around the y-axis.
We want to compare the graphs of the two given functions. We will see that the graph of g(x) is the graph of f(x) reflected across the line y = x.
The given functions are:
f(x) = (3/2)*x
g(x) = (2/3)*x
Note that each point on the line f(x) is written as:
(x, (3/2)*x)
And each point on the line g(x) is written as:
(x, (2/3)*x)
Now, if we multiply both sides of the above point by (3/2) we will get:
((3/2)*x, x)
Now, remember that for a general point (x, y), if we apply reflection across the line y = x, we get.
(y, x)
So the order of the values changes, exactly as we can see for f(x) and g(x).
Then we can conclude that g(x) is obtained by reflection f(x) across the line y = x.
Then the graph of g(x) is the graph of f(x) reflected across the line y = x.
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Related Questions
18
What is the value of y?
10
2y + 4
10 + 2x
5
Answers
Step-by-step explanation:
8
ahhdhdvab ah a. b b b n n bk.
A physics test is normally distributed. The class average was 79.3, and the standard deviation was 7.5. What percent of students scored between a 68 and 86.8?
Answers
Answer:97.275% or 97.5%
Step-by-step explanation:
The box plots show Devonte’s scores in Spanish and in French. Spanish 2 box plots. The number line goes from 50 to 100. For Spanish, the whiskers range from 55 to 95, and the box ranges from 60 to 85. A line divides the box at 70. For French, the whiskers range from 55 to 90, and the box ranges from 65 to 80. A line divides the box at 75. French Devonte inferred that his French scores have less variability than his Spanish scores. Which explains whether Devonte’s inference is correct? Devonte is correct because the range is greater for French. Devonte is correct because the interquartile range is less for French. Devonte is not correct because his highest grade is in Spanish. Devonte is not correct because the interquartile range is less for Spanish.
Answers
Answer:it's D i took the test.
Answer:
B
Step-by-step explanation:
i took the test
can someone help me on these 2 questions?
Answers
7. x=20
8. x=19
Step-by-step explanation:
7. The shape is a parallelogram and the angles that are labeled are opposite from each other, meaning that they are congruent. So, 4x-40=2x (and solve)
8. Same case as last time (parallelogram), and the angles labeled are congruent. So, 2x+19=3x (and solve)
Joshua has a rectangular vegetable garden with the dimensions shown below. If he doubles the length and width of the garden, how will the area of the new garden compare to the area of the original garden?
Answers
A taxi service charges a flat fee pen $1.25 and $0.75 per mile. If Henry has $14.00 which of the following shows the number of miles he can afford to ride in the taxi?
Answers
Answer:
A. M less than or equal to 17
Step-by-step explanation:
A line passes through the point (–7, 5) and has a slope of One-half. Which is another point that the line passes through?
A. (–13, 9)
B. (–9, 13)
C. (9, 13)
D. (13, 9)
Answers
Answer:
C. (9, 13)
Step-by-step explanation:
y = mx + b
y = (1/2)x + b
(-7, 5)
5 = (1/2)*(-7) + b
5 = - 7/2 + b
b = 5+ 7/2 = 10/2 + 7/2 = 17/2
y = (1/2)x + 17/2
C. (9, 13)
13 = (1/2)*9 + 17/2
13 = 26/2
13=13 True
Answer:
It is C (9,13)
Step-by-step explanation:
took the test on edge
Find the first five terms of the geometric sequence a1=0.3,an=10an-1
Answers
Answer:
{0.3, 3, 30, 300, 3000}
Step-by-step explanation:
Here a(1) = 0.3, and
a(2) = 3, and
a(3) = 30, and
a(4) = 300, and
a(5) = 3000
The first term (given) is 0.3, and the common ratio is 10.
is it possible to make a quadrilateral with any four dots as corners?
Answers
Answer:
Yes it is possible, given with 4 dots, lets say were set anywhere within a page or anywhere upon a circumference of a circle even. We can draw 4 straight lines to meet each corner and call this a quadrilateral.
Step-by-step explanation:
Squares, Rectangles and Rhombuses are all Parallelograms and squares and rectangles are regular quadrilaterals!
So any other 4 sided shape that is quadrilateral could be made.
The picture below shows all branches of quadrilaterals.
Answer:
No
Step-by-step explanation:
No.
For example, if all 4 dots are on a line, then the 4 dots do not make a quadrilateral.
Answer: No
Select the correct answer from each drop-down menu.
Shape I is similar to shape II.
Answers
Answer:
Translation (moving the figure) will map figure 1 onto figure 2 and then after this , dilation by a scale factor of "2"
Answer:
The first one is Translation 3 units down and8 units left, then a dialationby a scale factor of 2
Step-by-step explanation:
Write the set of real numbers x less than 6 in set builder notation
Answers
Answer:
{x ∈ R: x<6}
Step-by-step explanation:
Given
x is a real numberx is less than 6Required
Write the set using set builder notation
The very first thing to do is to list out the range of x, using inequalities;
x is less than 6 implies that -infiniti < x < 6
The next step is to translate this to set builder. This is done as follows
x ∈ R - > This means that x is a real number
x < 6 -> where x is less than 6.
Bringing these two together, it gives:
{x ∈ R: x<6}
Hence, the set of real numbers x less than 6 is equivalent to {x ∈ R: x<6} using set builder notation
will mark bianleast
Find the mean of the data in this set.
9.4
6
8.5
8
Answers
Answer:
The mean is 7.975.
Step-by-step explanation:
Answer:
The correct answer is 9.4, Hope this helps!
Step-by-step explanation:
I took the test and this was the correct answer!
Which of these triangle pairs can be mapped to each other using a reflection and a translation?
OL
A
R
K
K
Q
A
P
R
Answers
Answer: The first one
Step-by-step explanation:
It is being reflected over the x axis and It is translated
Given a = 4, b= -2 and c= 8, evaluate a - b - C.
-14
-6
0-2
Answers
Answer:
[tex]( - 2)[/tex]
Step-by-step explanation:
Given that
[tex]a = 4 \\ b = - 2 \\ c = 8[/tex]
Let's solve now
[tex]a - b - c[/tex]
[tex]4 - ( - 2) - 8 \\ 4 + 2 - 8 \\ 6 - 8 \\ - 2[/tex]
Given
a = 4b= -2 c= 8To find out:
Find the value of a - b - c ?
Solution:
a - b - c
Putting the value in the above
4 - ( - 2 ) - 8
4 + 2 - 8 [ - - = + ]
6 - 8
-2
Which is the graph of y?
Answers
Replace x with a number and solve for y. Plot the points out on a graph.
See the attached picture.
Rotate the image.
help me plz asap ill mark u brainliest
Answers
Answer:
b
Step-by-step explanation:
this is because 1 3/4 is equal to 7/4 which we can round to 2. so it says she rode back and forth to school so that would be 2 + 2 and she did that 5 times
this means that the final answer 5 * ( 2 + 2 )
Penny received an unexpected $5,000.00 gift from a distant relative. She invests it
in a mutual fund that increases the value of the original investment by 8% each year.
You must show all calculations to earn credit.
How much will her original investment be worth in 10 years?
Answers
Answer:
$9,000.00 is her original investment worth in 10 yrs.
5000 x 1.08 ^10 = 10794.6249864
Then subtract -500000 = 5794.62498636
Step-by-step explanation:
Why, because the first year is proved 5000 x 0.08 = 400
= 400 year 1 but cna keep only if stays in investment for 10 years
400 x 10 = 4000 interest on investment
5000+ 4000 = $9,000.00 SI
+ 1,794.62 Interest on interest if applies (this is called CI) and makes $10794.62
Help idk how to do it
Answers
Answer:
55
Step-by-step explanation:
The base angles of an isosceles triangle have the same measure
3x+40 = x+50
Subtract x from each side
3x+40-x = x+50-x
2x+40 = 50
Subtract 40 from each side
2x+40-40 = 50-40
2x = 10
Divide each side by 2
2x/2 = 10/2
x = 5
We want angle A
3x+40
3*5 +40
15+40
55
The price of gasoline increased 25% from July to August. If c = cost of gasoline in July, write two expressions that represent the price of gas in August. If you know the cost of gas in July, which expression do you think would be easier to use to calculate the cost of gas in August and why?
Answers
Answer:
Wrote it in the explanation :)
Step-by-step explanation:
Expression One: c + 25% = price of gas in august
Expression Two: c + 0.25 = price of gas in august
Expression Two would be easier to use if we knew "c" because the numbers are already in decimal form. If it were in percentage form, it would cause us an extra step to convert it into a decimal.
Please tell me if you have any further questions...
Hope this helped!!
How many triangles???
Answers
Answer:
4
Step-by-step explanation:
The triangle itself
Also the 3 at the top
They are the only ones with 3 sides
Answer:
9 triangles
Step-by-step explanation:
explain the triangle angle sum property
Answers
Explanation: The triangle sum property states that a triangle’s angles always add up to 180 degrees. Whether or not the triangle is acute, obtuse, or right, all of its three angles always add up to 180 degrees.
Answer:
The Triangle Sum Theorem states that the three interior angles of any triangle add up to 180 degrees.
Step-by-step explanation:
The radius of the semicircle in the following composite figure is 8.5 millimeters. What is the total area of the composite figure rounded to the nearest hundredth?
Answers
Answer:
13.35 millimeter. (About)
Step-by-step explanation:
To find the area or circumference of any circle, you need to use pi. So, if we are trying to fine the area of a semicircle, you use the the formula:
πr²/2
So, if the radius is 8.5,
8.5 · 3.14 = 26.69
Now we divide it by 2.
26.69 = 13.345
Since the question is asking to round to the hundredths, the answer will be 13.35 millimeters.
Answer:
185.43 mm 2
Step-by-step explanation:
,.
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What is the solution of 3square root x+8 = -4?
• x=-72
• x=-66
• x=58
• no solution
Answers
Answer:
No solution
Step-by-step explanation:
I'd suggest you try to solve this first: 3√(x + 8) = 4. First, square both sides; this results in 9(x + 8) = 16, or x + 72 = 16/9, or x = -632/9. We cannot let x = -632/9 in √(x + 8) because -632/9 is not in the domain of the square root function. No solution.
If we now write 3√(x + 8) = -4 (note the negative sign), similar efforts at solution result in 9(x + 8) = -4, or x + 8 = -4/9, or x = -8 - 4/9. If we now substitute this result for (x + 8) in 3√(x + 8) = -4 (above), we get 3√(-8 + 8 - 4/9), which has no solution; -4/9 is not in the domain of the square root function.
The solution for the given equation is 16.
The given equation is 3√x+8=-4.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The solution for the given equation can be determined as follows:
Now, 3√x+8=-4
⇒ 3√x=-4-8
⇒ 3√x=-12
⇒ √x=-12/3
⇒ √x=-4
Squaring both the sides, we get
x=16
Therefore, the solution for the given equation is 16.
To learn more about an equation visit:
https://brainly.com/question/14686792.
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What is the value of m+(6n-1) when m=3 and n=1?
Answers
Answer:
8
Step-by-step explanation:
you do the brackets first so (6n-1) would be 6-1 which equals 5
now we have m=5, m is 3 so 3+5=8
Verify the identity cosx cos(-x) - sinx sin(-x) =1
Answers
Answer:
(identity has been verified)
Step-by-step explanation:
Verify the following identity:
cos(x) cos(-x) - sin(x) sin(-x) = 1
Hint: | Cosine is an even function.
Use the identity cos(-x) = cos(x):
cos(x) cos(x) - sin(-x) sin(x) = ^?1
Hint: | Sine is an odd function.
Use the identity sin(-x) = -sin(x):
cos(x) cos(x) - -sin(x) sin(x) = ^?1
Hint: | Evaluate cos(x) cos(x).
cos(x) cos(x) = cos(x)^2:
cos(x)^2 - ( - sin(x) sin(x)) = ^?1
Hint: | Evaluate -(-sin(x)) sin(x).
-(-sin(x)) sin(x) = sin(x)^2:
cos(x)^2 + sin(x)^2 = ^?1
Hint: | Use the Pythagorean identity on cos(x)^2 + sin(x)^2.
Substitute cos(x)^2 + sin(x)^2 = 1:
1 = ^?1
Hint: | Come to a conclusion.
The left hand side and right hand side are identical:
Answer: (identity has been verified)
Which ordered pair lies on the function f(x) = x^2 + 3?
Question 7 options:
A)
(–1,–4)
B)
(1,–4)
C)
(–1,4)
D)
(–4,–1)
Answers
Answer:
c
Step-by-step explanation:
The sum of three numbers is 16. The sum of twice the first number, 5 times the second number, and 6 times the third number is 85. The difference between 4 times the first number and the second number is negative 3. Find the three numbers.
Answers
Answer:
1, 7, 8Step-by-step explanation:
x, y, z - numbers to find
The difference between 4 times the first number and the second number is negative 3:
4x - y = -3
- y = -3 - 4x
y = 3 + 4x
The sum of three numbers is 16:
x + y + z = 16
x + 4x + 3 + z = 16
5x + z = 13
z = 13 - 5x
The sum of twice the first number, 5 times the second number, and 6 times the third number is 85:
2x + 5y + 6z = 85
2x + 5(3 + 4x) + 6(13-5x) = 85
2x + 15 + 20x + 78 - 30x = 85
-8x + 93 = 85
-8x = -8
x = 1
y = 3 + 4•1 = 7
z = 13 - 5•1 = 8
Veryfying:
1 + 7 + 8 = 16
2•1 + 5•7 + 6•8 = 2 + 35 + 48 = 85
Which statement about this figure is true?
a. it has rotational symmetry with an angle of rotation of 90°
b. it has no reflectional symmetry
c. it has reflectional symmetry with two lines of symmetry
d. it does not have symmetry point
Answers
Answer:
a. it has rotational symmetry with an angle of rotation of 90°
Step-by-step explanation:
For this graph, Mark the statements that are true.
Answers
A worker needs to create a 4-character password. The worker can use alphabet as well
as number(0-9) and 4 special characters. How many outcomes are possible?
Answers
Answer: 2560000
Step-by-step explanation:
Given, A worker needs to create a 4-character password.
Worker can use :
Alphabets, numbers and 4 special characters
Total alphabets = 26
Total digits = 10
So, total characters he can use = 26(alphabets) + 10 (digits) +4 (special characters)
= 26+10+4 = 40
Since, there is no pattern or condition is provided to choose them.
So, the total possible outcomes to create a 4-character password. = [tex](\text{Total characters})^4=40^4=2560000[/tex]
Hence, the total possible outcomes = 2560000