Answers
The consequence of the two functions f(x) = (1 / 6) · ∛x and g(x) = 6 · x³ by composition is f[g (x)] = (1 / 6) · ∛3 · x and g[f (x)] = (1 / 6) · x³, respectively.
How to use composition between two functions
In this question we must use the definition of composition between two functions f and g, where the independent variable of the function f is substituted by function g. That is to say:
f ° g (x) = f [g(x)]
If we know that f(x) = (1 / 6) · ∛x and g(x) = 6 · x³, then the result of each composition is:
f [g (x)] = (1 / 6) · ∛(6 · x³)
f[g (x)] = (1 / 6) · ∛3 · x
g[f (x)] = 6 · [(1 / 6) · ∛(6 · x³)]³
g[f (x)] = 6 · (1 / 216) · (6 · x³)
g[f (x)] = (1 / 6) · x³
The results of the compositions of the two functions f(x) = (1 / 6) · ∛x and g(x) = 6 · x³ are f[g (x)] = (1 / 6) · ∛3 · x and g[f (x)] = (1 / 6) · x³, respectively.
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Related Questions
A car wash makes $7 profit p per car, resulting in the equation of the total T; T = 7p. If the car wash made $147, how many cars were washed?
Answers
T= $147
x * car = T
x * 7 = 147
x = 147/7
x = 21
There were 21 cars washed.
Solve the system of equations using elimination:
-5x + 8y = -6.
-
- 5y = -9 and
Answers
Answer:
x=102/25 y=9/5
Step-by-step explanation:
Monica has $50 to spend at the video arcade. If each game costs $0.25, which of these graphs shows how much
money she will have after x games?
Answers
Answer:
A
Step-by-step explanation:
If Monica has $50 dollars to spend on the video arcade, and each game costs $0.25 then we can use an equation that looks something like this:
total = amount of money × cost of one game
50 × 0.25 = 200
Now look at the graphs.
The graph that best matches this equation is A.
what time will it be in 2 hours 30 minutes . if I went to work at 11:30 am and I clock out in 2 hours 30 minutes but what time will it be in 2 hours 30 minutes
Answers
Answer:
I'm pretty sure it would be 3:00
Step-by-step explanation:
I could be wrong tho-
Please help me!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation: One denominator in the question is 4/5 and another is 1/2. A common denominator would be /10 because it applies to /5 and /2.
The total height of a building, b, and the antenna tower on top of it, t, is 425 feet. The difference in heights of the building and the antenna tower is 324 feet. The following system of equations represents the situation.
b + t = 425 b- t = 324
a. Solve the system of equations using elimination. Explain your process in your own words.
b. What is the height of the antenna tower?
Answers
Answer:
It A
Step-by-step explanation:
To prove that the triangles are similar by the SAS
similarity theorem, it needs to be shown that
Ozcazc
OC 2G
O AC-H
BC
O AC-BE
HI
Answers
It needs to be shown that <W = <H by the SAS congruent theorem
How to determine the additional information?The question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Triangles = IWO, and IHOGiven theorem = SASThe SSS congruent theorem implies that the corresponding sides of the triangles in question and the angles between them are congruent
From the question, we can see that the following corresponding sides on the triangles have the same mark
W O and H O
AO and AO
This implies that these sides are congruent sides
For the triangle to be congruent by SAS, the following sides must also be congruent
Angle W must be congruent to Angle H
Hence, the additional info is <W = <H
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Complete question
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that____
Help me out!! Giving Brainly to whoever helps!
Answers
Answer: 325 adult tickets
Step-by-step explanation:
721 = (a+71) + a
721 = 2a + 71
2a = 650
a = 325
Min receives an average score of 7 after completing 5 math tests. If she has another test coming up, find what mark she must gain to raise her average to 75.
Answers
Min needs to gain 80 marks to raise her average to 75.
What is Average number?Average number is got from sum of all numbers divided by the number of values.
Why we use average value?Average value is used to compare among different quantities of same terms.
given, Min receives an average score 70 from 5 math test.
let she needs to gain X in her 6th test to obtain an average of 75 from the total six test.
she gained average 70 from 5 test
if average is 75 then
75 = (X+ 70)/2
X=80
hence, in the 6th test she needs to gain 80 marks.
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Two perpendicular lines intersect at K(-2,-5). One line has equation y = -5/3x-25/3. what is the equation of the other line?
Answers
Answer:
It is y = 3/5x - 19/5
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes. Thus, the slope is 3/5x. Plug in -2 as x and solve for the intercept. It ii -19/5.
PLEASE HELP I REALY NEED THIS NOW How much simple interest is earned on an investment of $800 with a rate of 6.1% over 7 years?
A. $341.60
B. $410.87
C. $3,416.00
D. $4,108.70
Answers
The amount of simple interest is (a) $341.60
How to determine the amount of simple interest?From the question, we have the following parameters that can be used in our computation:
Principal, P = $800
Rate, r = 6.1 %
Time = 7 years
The simple interest on the investment is calculated as
I = PRT
Substitute the known values in the above equation, so, we have the following representation
I = 800 * 6.1% * 7
Express 6.1% as decimal
So, we have the following representation
I = 800 * 0.061 * 7
Evaluate the products
I = 341.6
Hence, the amount is (a) $341.6
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find a equation line perpendicular to y-8=-2x that passes through the point (8,-5)
Answers
Answer:
Step-by-step explanation:
y = -2x + 8
perp.: 1/2
y + 5 = 1/2(x - 8)
y + 5 = 1/2x - 4
y = 1/2x - 9
Suppoe that the concentration of a bacterial ample i 100,000 bacteria per millimeter. If the concentration double every three hour how long will it take for the concentration to reach 350,000 material per millimeter?
Answers
The time t = 3.4209 will it take for the concentration to reach 350,000 material per millimeter.
How do you calculate hours and minutes?In an hour, there are 60 minutes. Divide the number of minutes by 60 to convert it to hours. For instance, 120/60=2 means that 2 hours are equal to 120 minutes.
What is millimeter?The millimeter, abbreviated mm in the International System of Units (SI), or millimeter, abbreviated mm in the American spelling, is a unit of length that is one thousandth of a metre long, the SI base unit of length. As a result, a metre is made up of 1000 millimeters.
We are going to use formula
y = a * e ^ (b * t)
a and b are constants and t is for time.
Initially there are 100,000 bacteria, so;
100000 = a * e ^ (b * 0)
100000 = a * 1
a = 100000
given condition is that the concentration doubles every 3 hours so
300000 = a * e ^ (b * 3)
As a equals to 100,000
e ^ (b * 3) = 3
b * 3 = ln 3
b = (ln 3) / 3
b = 0.3662
now we have to find value of the time when concentration of bacteria reaches to 350,000:
350000 = 100000 * (e ^ 0.3662 * t)
3.5 = e ^ 0.3662* t
ln 3.5 = 0.3662* t
t = 1.2527 / 0.3662
t = 3.4209
That is the required value of time
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If the simple interest on $2,000 for 10 years is $1,400, what is the interest rate?
Answers
Answer: I = $ 200.00
Step-by-step explanation:
I = Prt
Convert R (percent) to r (decimal)
r = R/100 = 1%/100 = 0.01 per year
I = 2000 × 0.01 × 10 = 200
I = $ 200.00
hope this helps!
Can anyone help me understand this please? I am mainly just confused about how to graph the first equation the second I can do
Answers
A graph of the given system of equations f(x) = 2x² - 8x + 3 and g(x) = -2x + 3 is shown in the image attached below.
The points that make both equations true is (0, 3)
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
What is a quadratic function?In Mathematics, the graph of every quadratic equations (functions) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic equation (function) would always form a parabolic curve.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each, which is the ordered pair (0, 3);
f(x) = 2x² - 8x + 3
3 = 2(0)² - 8(0) + 3
3 = 3 (True).
g(x) = -2x + 3
3 = -2(0) + 3
3 = 3 (True).
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The diagram shows a sector of a circle radius 10 cm.
Find the area of the sector, giving your answer correct to 1 decimal place.
Answers
Answer:
[tex]117.8cm ^{2} [/tex]
Step-by-step explanation:
[tex]a = {r}^{2} \theta \: \div 2 \\ = 100 \times 135 \div 2 \\ = 117.8 \: {cm}^{2} [/tex]
PLS HELP ME IN THIS ASAP
Answers
Answer:
0.004
Step-by-step explanation:
Hope it helps!
through (4,-9) perpendicular to 8y=x-16
Answers
Answer:
y = -8x + 23
Step-by-step explanation:
8y=x-16
we need to turn this into slope-intercept form by dividing 8 on both sides
y = x/8 - 2
to make a line perpendicular from another, we must make sure the slope is the negative reciprocal of the original line.
Right now, it's the same as the original. To make it a negative reciprocal, switch the places of the denominator and numerator and flip the signs
-8x is the negative reciprocal of x/8
Does it go through (4,-9)? No.
To make sure it goes through 4,-9, we change it's y-intercept.
Plug in the coordinate given (4,-9) in the y = -8x + b ( we removed -2 since it's not the right answer.
y = -8x + b
(-9) = -8(4) + b
-9 = -32 + b
-9 +32= -32 + b +32
23 = b
plug in b and we get our answer
y = -8x + 23
which is more likely rolling a total of 8 when two dice are rolled or rolling a total of 8 when thre dices are roled
Answers
Answer: Two dice
Step-by-step explanation:
For the two dice, there are 5 possible: (6, 2);(5, 3);(4, 4);(3, 5);(2, 6)
So two dice, the probability is 5/36 = 30/216
For three dice, the number of favorable cases is 21
The probability is 21/216
So the two dice are more likely
Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales. Last week, she sold $843 worth of goods. How much was she paid?
Answers
The amount that Josephine will be paid is $644.30.
How much was Josephine paid?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this situation, Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales and she sold $843 worth of goods.
The amount she'll be paid will be:
= $560 + (10% × $843)
= $560 + $84.3
= $644.30
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A regular polygon has its interior angles all equal to 171 Find the number of sides of the polygon.
Answers
The measure of the interior angles of a polygon is determined by the formula ((n - 2)180)/n = interior angle
measure
what is 6 plues 9 i need it plesae.
Answers
6️⃣9️⃣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Write an equation in standard form of the line that passes through the given point and has the given slope (I need an answer ASAP please)
1. (4, -1); m = 3
2. (-8, 0); m = -4
3. (-6, -10); m = 1/6
Answers
The equation of the lines is,
1. (4, -1); m = 3 : - y = 3x - 13
2. (-8, 0); m = -4 :- y = -4x - 24
3. (-6, -10); m = 1/6 :- y = -1/6x - 9
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The equation of the lines will be,
y = mx + c
y = 3x + c
-1 = 4 x 3 + c
c = -13
y = 3x - 13
y = mx + c
y = -4x + c
0 = -4 x -8 + c
c = -24
y = -x -24
y = mx + c
y = 1/6x + c
-10 = -1 + c
c = -9
y = -1/6x - 9
Therefore, the equation of the lines is,y = 3x - 13 y = -4x - 24 and y = -1/6x - 9.
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The number of different hands possible in the game of bridge is about 635 billion. Write this number in scientific notation
Answers
6.35 × 10^11
#9 -5=9+(c divide by 4) *
O A. c = -56
O B. c = 56
O C. c = -16
OD. c = 16
Answers
After solving the given equation for c, we know that the value of c is (A) -56.
What are equations?Equivalent systems refer to sets of equations with the same solution.
We can create an analogous system from a system of two equations by replacing one equation with the total of the two equations or by replacing an equation with a multiple of itself.
So, we have the equation:
-5 = 9+(c/4)
Now, solve for the subject c as follows:
-5 = 9+(c/4)
-5 -9 = (c/4)
-14 = c/4
c = -14*4
c = -56
Therefore, after solving the given equation for c, we know that the value of c is (A) -56.
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mark has 100$in his savings account. He earns 25$ a week mowing lawns. If mark puts all of his earnings from mowing lawns into a savings account, how many weeks will it take for him to have 500$?
Answers
400+ 100 = 500
Therefore the answer is 16
Point QQ is located at (3,-1)(3,−1) on the coordinate plane. Point QQ is reflected over the yy-axis to create point Q'Q ′ . What ordered pair describes the location of Q'?Q ′ ?
Answers
The ordered pair that describes the location of Q' is (-3, -1)
How to determine the ordered pair that describes the location of Q?From the question, we have the following parameters that can be used in our computation:
Point Q = (3, -1)
This point can be represented as
(x, y) = (3, -1)
Also, from the question, we have the transformation to be:
Point Q is reflected over the y-axis
Mathematically, this can be expressed as
(x, y) = (-x, y)
So, we have the following representation
Point Q' = (-3, -1)
Hence, the image is (-3, -1)
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Out of 400 plants sold daily at a nursery, 90% of them have flowers. How many of the plants have flowers?
Answers
Answer: 360 plants
Step-by-step explanation:
90% is equivalent to 0.90.
You multiply 0.90 and get your answer of 360.
The function rule for this graph is
Answers
Answer:
Step-by-step explanation:
(0, 2) (4, 0)
(0 - 2)/(4 - 0) = -2/4 = -1/2
y - 2 = -1/2(x - 0)
y - 2 = -1/2x + 0
y = -1/2x + 2
What is the equation for the graph shown?
Answers
The linear equation on the graph shown is:
y = (2/3)*x + 4
What is the equation on the graph?
We can see that we have a linear equation on the graph, remember that a general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
On the graph, we can see that the line intercepts the y-axis at y = 4, then the y-intercept is b = 4
y = a*x + 4
To find the slope we can use another point on the line, for example, we can see that (-6, 0) is also on the line, replacing these values in the linear equation above we will get:
0 = a*-6 + 4
6a = 4
a = 4/6 = 2/3
Thus, the line is:
y = (2/3)*x + 4
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