The equivalent function of g(f(x)) for the given function is 2x³ - 3.
Function composition is an operation × that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x.
We have been given that
f(x) = x3 – 1
g(x) = 2x - 1
and find out g(f(x)) =?
The notation for function composition is h = f • g or h(x) = (f • g)(x) and is read as 'f of g of x'. The procedure is called composition because the new function is composed of the two given functions f and g, where one function is substituted into the other.
g(f(x)) = 2(f(x))- 1
Put the value of f(x) in the equation
g(f(x)) = 2( x³ - 1) -1
g(f(x)) = 2 x³ - 2 -1
g(f(x)) = 2 x³ - 3
Hence , For the given function, 2x3 - 3 serves as the corresponding function of g(f(x)).
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y = bx(x - a)(x-a)(x + b)(x - b)
In the equation above, a and b are positive
constants and a ≠ b. How many distinct x-intercepts
does the graph of the equation in the xy-plane have?
The x-intercepts of an equation are simply the zeros of the equation
The equation [tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex] has 4 distinct x-intercepts
The equation is given as:
[tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex]
Set the equation to 0; i.e. calculate the zeros
[tex]\mathbf{bx(x - a)(x -a)(x + b)(x - b) = 0}[/tex]
Divide both sides by constant b
[tex]\mathbf{x(x - a)(x -a)(x + b)(x - b) = 0}[/tex]
Split the above equation, as follows
[tex]\mathbf{x= 0\ or\ x - a = 0\ or\ x -a = 0\ or\ x + b = 0\ or\ x - b = 0}[/tex]
Solve for x in each of the equation
[tex]\mathbf{x= 0\ or\ x = a\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]
Remove repeated solutions
[tex]\mathbf{x= 0\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]
The count of solutions above is 4
Hence, the equation has 4 distinct x-intercepts
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Need help with 5-8 with working out will be marking brainliest
Answer:
hope to have helped you:)
Help please! Only answer if you know for sure.
Answer:
c I am 100% sure
Step-by-step explanation:
a= 18 in.
C = 82 in.
What is the length of b?
Answer:
B should equal 80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Use Pythagorean theorem so 18^2 +b^2 =82^2 which is 324 +b^2=6724 then subtract 324 on both sides then square root which is 80
Select all the true statements. Group of answer choices The ratio of triangles to squares is 2 to 4. The ratio of squares to smiley faces is 6:4. The ratio of smiley faces to triangles is 6 to 4. There are two squares for every triangle. There are two triangles for every smiley face. There are three smiley faces for every triangle.
Answer:
The ratio of triangles to squares is 2 to 4
There are two squares for every triangle.
There are three smiley faces for every triangle.
Step-by-step explanation:
The number of triangles, smiley and squares are shown in the diagram attached.
From the diagram, there are 6 smiley faces, 2 triangles and 4 squares.
A ratio compare two or more values, thereby showing how many times one number contains the other.
A) Correct. The ratio of triangles to squares = number of triangle / number of square = 2 / 4 = 2 to 4
B) Incorrect. The ratio of squares to smiley faces = number of square / number of smiley face = 4 / 6 = 4 to 6
C) Incorrect. The ratio of smiley faces to triangles = number of smiley faces / number of triangles = 6 / 2 = 6 to 2
D) Correct. Since the ratio of squares to triangles = number of squares / number of triangle = 4 / 2 = 2 / 1 = 2 to 1, hence there are two squares for every triangle
E) Incorrect. Since the ratio of triangles to smiley faces = number of triangle / number of smiley faces = 2 / 6 = 1 / 3 = 1 to 3, hence there is one triangle for every 3 smiley faces
F) Correct. Since the ratio of smiley faces to triangles = number of smiley faces / number of triangles = 6 / 2 = 3 / 1 = 3 to 1, hence there is 3 smiley faces for every one triangle
How many gallons of water are in a 2 gallon pitcher that is 3/4 full?
Answer:
1.5 gallons
Step-by-step explanation:
2 x 0.75
1.5 gallons
Brainliest appreciated!
Answer:
1.5 gallons
Step-by-step explanation:
1/4 of container would be 0.5 gallons, so 3/4 of the container is 1.5 gallons. Multiply 0.5 times 3.
Determine which product has the lower unit price a 16- ounce bag of chocolate for $1.99 or B an 18- ounce bag of chocolates for $2.29
Step-by-step explanation:
Just divide 16 and 1.99 and 18 and 2.29 and choose the one with less value
Plz answer it’s timed
Answer:
1,5
Step-by-step explanation:
cuz it's part of the green
Help!
Which solution(s) are correct?
Answer: D. Matthew’s, Rhoda’s, and Ming’s
Step-by-step explanation:
√0.89 ≈ 0.94
Anyah is incorrect because both of her decimals are smaller than √0.89.
Matthew is correct because 0 is less than 0.89 but 1 is still greater than 0.89.
Rhoda is correct because 0.9² is 0.81 is less than 0.89 but 1.0² is 1 which is still greater than 0.89.
Ming is correct because 0.93² is about 0.87 which is less than 0.89 but 0.95² is about 0.9 which is still greater than 0.89.
I hope this helps!
I don't understand this at all. Can you help me solve this please :)
Answer:
y = -1/2x +3
Step-by-step explanation:
basically all you have to do is change the y intercept, but keep the slope the same and you create a parallel line
What is the equation of the line described below written in slope-intercept form? the line passing through point (2,4), parallel to the line whose equation is y = x
A. y=x + 2
B. y = -x + 2
C. y=-X
Answer:
y = x + 2
Step-by-step explanation:
Questions 1-5. Bryan invests $500 in an account earning 4% interest that compounds annually. If he makes no additional deposits or withdrawals, how much will be in the account:
After 15 years?
(round to the hundredths place
Answer:
608.33
Step-by-step explanation:
Geometry homework!
Hiii I’m having a really hard time with my homework, by any chance do you know the right answer?
Thank you!
Answer:
D
Step-by-step explanation:
The numbers between the < , > show the change from the preimage to the image. So, <-2,3> would be the x - 2 and the y + 3.
So, A(5,6) -> A'(3,9)
B(6,-3) -> B'(4,0)
C(7,2) -> C'(5,5)
The average fun size Snickers bar has the mass of 20.1 grams with a standard deviation of 0.7 grams What percent of Snickers bars have a mass more than 21.5 grams?
Step-by-step explanation:
The “fun size” of a Snickers bar is supposed to weigh 20 grams. Because the penalty for selling Snickers candy bars that weigh less than 20 grams is so severe, the manufacturer calibrates the machine so that the mean weight is 20.2 grams. The quality control manager at the candy company is concerned that the candy produced does not weigh 20.2 grams. She obtains a random sample of 64 candy bars and weighs them. She finds that the mean weight of this sample is 20.05 grams with standard deviation 0.72. By answering the following questions, test the claim that the Snickers bars have a mean weight less than 20.2 grams at the level of α = 0.01.
1. Select from the following list all the requirements that are met in this problem scenario for this test: (circle your choice(s))
a. The population is approximately normal.
b. The population standard deviation is known.
c. The sample taken is a random sample.
d. The population standard deviation is unknown. e
. The degrees of freedom is 0.01.
f. The sample size is greater than 30.
2. Which of the following statements is correct?
a) Parameters describe sample characteristics.
b) Statistics describe population characteristics.
c) We use statistics to estimate the value of parameters.
d) We use parameters to estimate the value of statistics
Expert Answer
The percent of Snickers bars which have a mass more than 21.5 grams is equal to 2.28%.
To find the percentage of Snickers bars with a mass more than 21.5 grams,
use the concept of standard normal distribution.
Calculate the z-score for 21.5 grams.
The z-score is a measure of how many standard deviations a particular value is away from the mean. It can be calculated using the formula:
z = (x - μ) / σ
where x is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.
Here
x = 21.5 grams
μ = 20.1 grams (mean)
σ = 0.7 grams (standard deviation)
z = (21.5 - 20.1) / 0.7
z = 1.4 / 0.7
z = 2
The percentage of values greater than the z-score in the standard normal distribution calculator.
The percentage of values greater than 2 standard deviations from the mean is approximately 2.28%.
Therefore, approximately 2.28 percent of Snickers bars have a mass more than 21.5 grams.
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The phone company charges a flat rate of $25 per month. In addition they charge $0.05 for each minute of service Which equation can be used to determine c, the monthly charge based upon the number of minutes (m) of service each month. C = 25m + 0.05 c = 25m + 0.05 c = 0.05m + 20 c = 0.05m + 20 c = 25m + 0.05 c = 25m + 0.05 m = 0.05c + 30
Answer:
c= 25+0.05m
Step-by-step explanation:
Given that,
The phone company charges a flat rate of $25 per month. In addition they charge $0.05 for each minute of service.
$25 is fixed here and charge $0.05 for each minute of service.
We need to find the equation that can be used to find the monthly charge based upon the number of minutes (m) of service each month.
c= 25+0.05m
Hence, this is the required equation.
Geometry Question: Image is provided below.
Please show all work and your steps.
25 points
Answer:
x=7
y=10
Step-by-step explanation:
8x and 11y+14 are same side interior angles so they add to 180 degrees
11y+14 and 10x+54 are vertical angles so they are equal
8x + 11y+14 = 180
11y+ 14 = 10x+54
Substitute 10x+54 for 11y+14 in the first equation
8x +10x+54 = 180
Combine like terms
18x+54 =180
Subtract 54
18x+54-54=180-54
18x =126
Divide by 18
18x/18 = 126/18
x=7
Now we can find y
11y+ 14 = 10x+54
11y + 14 = 10*7+54
11y+14 = 70+54
11y+14 =124
Subtract 14 from each side
11y = 124-14
11y =110
Divide by 11
11y/11=110/11
y =10
7
Pls answer I’m to tired for this
What is the midpoint
between (-2, -3) and
(1, 2)?
a) (-1,-)
b) (-:-)
c) (-1,-)
d) (-3,-)
Answer:
I think it's B
...........
Answer:
d
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (- 2, - 3) and (x₂, y₂ ) = (1, [tex]\frac{1}{2}[/tex] ), thus
midpoint = ( [tex]\frac{-2+1}{2}[/tex], [tex]\frac{-3+\frac{1}{2} }{2}[/tex] ) = ( [tex]\frac{-1}{2}[/tex], [tex]\frac{-3+\frac{1}{2} }{2}[/tex] ) = ( - [tex]\frac{1}{2}[/tex], [tex]\frac{-\frac{5}{2} }{2}[/tex] ) = ( - [tex]\frac{1}{2}[/tex], - [tex]\frac{5}{4}[/tex] ) → d
A submarine dives below the surface, heading downward in four moves. If each move downward was 235
feet, where is the submarine after it is finished diving?
The submarine would be
feet below sea level, or
feet.
Answer:
Step-by-step explanation:
It drops 235 feet per move.
235 * 4 = 1140 feet below sea level.
-1140 is also possible.
will you guys help me with anything i need?
(don't listen about the subject for now i just need to know)
Answer:
Ummm yeah , i'm literally a nice person and a good listener .
Step-by-step explanation:
Can i pls have brainly ? <3
Answer:
yes
Step-by-step explanation:
hjoyybhfddsjjsjajajdhvdbenwkwq
What are two different ways of saying "find the
solution"?
Answer:
find the difference. find the sum
Step-by-step explanation:
I cannot figure out how to solve this, we did not cover it in class today and it is on tonights homework.
Answer:
x = 32.5
y = 65
Step-by-step explanation:
y = 65 degrees
65 and y are the base angles in an isosceles triangle ( single lines) so they are equal
y+z = 180 since they form a straight line
65+z = 180
z = 180-65
z = 115
The second triangle is also an isosceles triangle so the base angles are the same as shown by x
180 = x+x+z
180 =2x+ 115
65 = 2x
Divide by 2
x = 32.5
In which quadrant does the terminal side of your angle lie if sec theta < o and cot theta < o ?
Answer:
The endpoint of an angle
x
lies in the 4th quadrant. Here is why.
First of all, let's recall a few definitions.
Recall the definition of a trigonometric function
sec
(
x
)
:
sec
(
x
)
=
(by definition)
=
1
cos
(
x
)
Recall the definition of a trigonometric function
cot
(
x
)
:
cot
(
x
)
=
(by definition)
=
cos
(
x
)
sin
(
x
)
Step-by-step explanation:
jhyjyujtyuyju
solve for x
(3/x-c)=(4/x-d)
9514 1404 393
Answer:
x = 4c-3d
Step-by-step explanation:
Cross multiply, separate variables terms and constant terms.
[tex]3(x-d)=4(x-c)\\\\3x-3d=4x-4c\\\\4c-3d=x\qquad\text{add $4c-3x$}\\\\\boxed{x=4c-3d}[/tex]
what a number named as a googolplexian might be ?
Answer:
A 1 with a hundred 0's following it
Step-by-step explanation:
5- ܫ ܐx
.9
Use square roots
A certain test is scored by adding 1 point for
each correct answer and subtracting 1/4 of a
point for each incorrect answer. If Jan answered
31 questions correctly and 9 questions incor-
rectly, what was her score?
a. 28 3/4
b. 28 1/4
c. 26
d. 22 1/4
Answer:
A
Step-by-step explanation:
31 correcct answers gives her 31 points, then you subtract 9/4 for the 9 incorrect answers to get twenty eight and 3/4
The parallelogram shown below has an area of 140
Simplify the expression using the variable replacements.
2a² – 4bifa= 2andb = 1
Answer:
= 4
Step-by-step explanation:
2a^2-4b
=2(2)^2-4(1)
=2×4-4
= 8-4
=4
If John drove 210 miles in 3 hours, how far will he have
driven in 4.5 hours?
Answer:
3hours and 15 mins
Step-by-step explanation:
210 divied by 3=70
70=per hour
4 hours=280
70 divied by 2= 35
.5=35
280+35=315
315 miles in 4.5 hours
What is a good problem to use for an inequality equation? using ax + b > c. Including the solution.
Answer:
A "solution'' of an inequality is a number which when substituted for the variable makes the inequality a true statement. When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality.Step-by-step explanation:
Answer:
the person above me is correct
Shark boi U~U