The picture below shows a pole and its shadow:
What is the height of the pole?
121 centimeters
220 centimeters
225 centimeters
231 centimeters
Answers
The height of the pole according to the attached image and parameters given is; 220 cm.
What is the height of the pole as required in the task content?It follows from the task content that the height of the pole is to be determined from the parameters given.
From observation, the triangle formed by the situation is a right triangle.
Hence, the height of the pole can be determined by Pythagoras theorem; where, c² = a² + b².
Therefore, we have;
221² = 21² + p²
p² = 48,841 - 21²
p² = 48,400
p = √48,400
p = 220.
On this note, the height of the pole is; 220 cm.
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Related Questions
HELP ASAP MATH PRE CALC
Answers
The values for the dimensions of the open box are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
The cube as a three dimensional shapes.A cube is 3- dimensional shape with 6 equal sides, 6 faces, and 6 vertices. Each face of a cube is a square. In there dimension, the cube's sides are; the L = length, W = width, and H = height.
From question, squares of equal sides x are cut out of each corner of the metal sheet, hence the dimension for the height of the box is equal to x.
So; H = (x) inches,
L = (30 - x)inches, and
W = (30 - x)inches.
Therefore, the dimensions of the box that can maximize the volume of the metal sheet of 30inches by 30inches are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
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Which values are solutions to the inequality below? Check all that applySqrt x>=9Choices are:-2, 82, 32, 180, 99, 63
Answers
We notice the following:
[tex]\begin{gathered} \sqrt[]{x}\ge9\ge0 \\ \Rightarrow \\ x\ge81 \end{gathered}[/tex]Then, possible solutions of the inequality are all real numbers greater or equal than 81. From the given set of solution, those numbers that fullfill that requirement are:
[tex]82,\text{ 180 and 99}[/tex]true or false16. The y-intercept of the equation, = −7^2 + 11 − 12 is 12
Answers
For us to be able to determine if it is true or false, let's evaluate the given equation:
[tex]\text{ y = -7x}^2\text{ + 11x - 12}[/tex]In order to find the y-intercept of a function, we substitute x equals to 0. A y-intercept always has an x-coordinate of 0.
Thus, we get,
[tex]\text{ y = -7x}^2\text{ + 11x - 12}[/tex][tex]\text{ y = -7(0)}^2\text{ + 11(0) - 12}[/tex][tex]\text{ y = -7(0)}^{}\text{ + 0 - 12 = 0 + 0 - 12}[/tex][tex]\text{ y = -12}[/tex]The y-intercept of the given equation is -12.
Therefore, the answer is FALSE.
Please help me I don’t know how to do this
Answers
We have a point (4,-9) it moves to (9,-14)
(4+x = 9, -9+y= -14)
x = 9-4
x = 5
y = -14 +9
y = -5
We are moving to the right 5 and down 5
We want to move the point (-9,-8) exactly the same way
(-9+5, -8-5)
(-4, -13)
(-4, -13)
Maria used a hundred chart to find a sum. She started at 57 then she moved down 3 rows and back 2 spaces which number did she land on
Answers
She landed on the number 25 on the hundred chart.
What is an 100 chart?
It consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows.
We are given that she was on 57th number
Then she moved down 3 rows
Each row contains 10 elements Hence we subtract 30 for 3 rows
57-30=27
Then also she took 2 steps back
Hence we again subtract 2 from 27
We get 27-2=25
Hence she is at 25th number
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Determine the value of k for which f(x) is continuous.
Answers
These are the conditions of the continuity in a function:
First, the value of x must have an image.
Second, the lateral limits must be equal:
[tex]\lim_{x\to a^+}f(x)=\lim_{x\to a^-}f(x)[/tex]Finally, the value of the limit must be equal to the image of x. This means that:
[tex]f(a)=\lim_{x\to a^}f(x)[/tex]In this case, we must find a value of k that can make the two lateral limits equal in x =3:
[tex]\lim_{x\to3^+}x^2+k=\lim_{x\to3^-}kx+5[/tex]We can solve these two limits easily by replacing the x with the value of 3
[tex]3^2+k=3k+5[/tex][tex]\begin{gathered} 9+k=3k+5 \\ 4=2k \\ k=2 \end{gathered}[/tex]Finally, we can see that the answer is k=2.
what are the three terms and 4x - 2y + 3
Answers
Solution
We have the following expression:
[tex]4x-2y+3[/tex]Here we have 3 terms:
[tex]4x,\text{ -2y and 3}[/tex]Variable terms:
[tex]4x,-2y[/tex]Constant term
[tex]3[/tex]If TW =6, WV =2, and UV =25, find XV to the nearest hundredth.
Answers
TW = 6
WV = 2
UV = 25
XV = ?
XV/UV = WV/TV
XV/25 = 2 /(6 + 2)
XV = 2(25)/7
XV = 50/7
XV = 7.1428
Rounded to the nearest hundredth
XV = 7.14
10. A $152,000 home has an assessment rate of 52% and a tax rateof $48 per $1,000. Use the effective tax method to calculate theproperty tax .Hint: When you determine the effective tax rate, round the rateto three places.
Answers
Given
$152,000
52% assessment rate
$48 per $1,000
Procedure
First, let's calculate the assessment rate.
[tex]152000\cdot0.52=79040.0[/tex]Now let's calculate the taxes
[tex]79040.0\cdot\frac{48}{1000}=3793.92[/tex]Property taxes are equal to $3,793.92.
The first three terms of an arithmetic sequence are as follows.3, -1, -5
Answers
We will take a look at how we go about with arithmatic progressions.
Arithmmetic sequences are caetgorized by the following two parameters:
[tex]\begin{gathered} a\text{ = First term} \\ d\text{ = common difference} \end{gathered}[/tex]Where,
[tex]\begin{gathered} \text{The value of the first term is called ( a )} \\ \text{The common difference between each and every successive value in a sequence is called ( d )} \end{gathered}[/tex]We are given the following arithmetic sequence:
[tex]3\text{ , -1 , -5 , }\ldots[/tex]Now we will try to determine the values of the two parameters ( a and d ) from the given sequence as follows:
[tex]\begin{gathered} a\text{ = 3 }(\text{ first term value )} \\ d\text{ = (-1 ) - ( 3 ) = (-5 ) - ( -1 ) = -4 ( common difference )} \end{gathered}[/tex]Now to determine the value of any term number ( n ) in an arithmetic sequence we use the following formula:
[tex]a_n\text{ = a + ( n - 1 )}\cdot d[/tex]Where,
[tex]n\text{ is the term number}[/tex]So if we plug in the values of arithmetic sequence parameters into the general equation above we get:
[tex]\textcolor{#FF7968}{a_n}\text{\textcolor{#FF7968}{ = 3 + ( n - 1 ) }}\textcolor{#FF7968}{\cdot}\text{\textcolor{#FF7968}{ ( -4 )}}[/tex]Now we are to determine the values of term numbers ( n = 4 ) and ( n = 5 ). We will evaluate the ( an ) for each term number as follows:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{For n = 4}} \\ a_4\text{ = 3 + ( 4 - 1 )}\cdot(-4\text{ )} \\ a_4\text{ = 3 - 12} \\ \textcolor{#FF7968}{a_4}\text{\textcolor{#FF7968}{ = -9}} \\ \\ \text{\textcolor{#FF7968}{For n = 5}} \\ a_5\text{ = 3 + ( 5 - 1 )}\cdot(-4\text{ )} \\ a_5\text{ = 3 - 1}6 \\ \textcolor{#FF7968}{a_5}\text{\textcolor{#FF7968}{ = -}}\textcolor{#FF7968}{13} \end{gathered}[/tex]Hence, the next two consecutive numbers in the arithmetic sequence would be:
[tex]3\text{ , -1 , -5 ,}\text{\textcolor{#FF7968}{ -9}}\text{ , }\text{\textcolor{#FF7968}{-13}}[/tex]in a dog show there are 31 dogs competing in the terror group the top three dogs with we'll all wind crash price of $500 and moved on to complete for a place in the larger Best in Show competition how many ways can the top three dogs be determined if they are finishing position is not important
Answers
The selection of three dogs out of 31 dogs can be done in
[tex]31C3\text{ ways}[/tex]i.e.
[tex]\begin{gathered} =\frac{31!}{(31-3)!\times3!} \\ =\frac{31\times29\times28!}{28!\times3!} \\ =\frac{31\times29}{6} \\ =149.8 \\ \cong\text{ 150} \end{gathered}[/tex]f(x) = x2 + 1 g(x) = 5 – x
(f + g)(x) =
x to the power of 2 – x + 6
then (f – g)(x) =??
Answers
The function operation ( f - g )( x ) in the functions f(x) = x² + 1 and g(x) = 5 - x is x² + x - 4.
What is the function operation ( f - g )( x ) in the given functions?A function is simply a relationship that maps one input to one output. Each x-value can only have one y-value.
Given the data in the question;
f(x) = x² + 1g(x) = 5 - x( f - g )( x ) = ?To find ( f - g )( x ), replace the function designators in ( f - g ) with the actual functions.
( f - g )( x ) = f( x ) - g( x )
( f - g )( x ) = ( x² + 1 ) - ( 5 - x )
Remove the parenthesis using distributive property
( f - g )( x ) = ( x² + 1 ) - ( 5 - x )
( f - g )( x ) = x² + 1 - 5 + x
Collect and add like terms
( f - g )( x ) = x² + x + 1 - 5
( f - g )( x ) = x² + x - 4
Therefore, the function operation ( f - g )( x ) is x² + x - 4.
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The required function would be (f – g)(x) = x² + x - 4.
What is the function?A mathematical expression that defines the connection between two variables is considered a function.
The given functions following as
f(x) = x² + 1 and g(x) = 5 - x
We have to determine the function (f – g)(x).
(f – g)(x) = f(x) - g(x)
Substitute the values of functions f(x) = x² + 1 and g(x) = 5 - x in the function (f - g).
(f – g)(x) = (x² + 1) - (5 - x)
Open the parenthesis and apply the arithmetic operation,
(f – g)(x) = x² + 1 - 5 + x
Rearrange the terms likewise and combine them,
(f – g)(x) = x² + x + 1 - 5
Apply the subtraction operation to get
(f – g)(x) = x² + x - 4
Therefore, the required function would be (f – g)(x) = x² + x - 4.
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Which equation represents a line which is perpendicular to the line y=-5/4x-4?A. 4y−5x=−4B. 5x+4y=−8C. 4x−5y=15D.4x+5y=40
Answers
The slope of a line, m, comes in the equation as the coefficient of x.
In the given equation, m= -5/4. Two perpendicular lines have slopes that are the negative reciprocals of each other.
So, the slope of the perpendicular line will be +4/5.
Between the given options, letter c will be:
4x-5y=15
-5y=15-4x (divided by -5)
y=4/5x-3
Letter C
Find the measurement of each subject. Assume that each figure is not drawn to scale.
Answers
To obtain the measure of segment AD, add the measurement of segment AC and segment CD.
[tex]AD=AC+CD=2\frac{3}{8}+1\frac{1}{4}[/tex]Rewrite the fraction part as similar fractions. Multiply the numerator and teh denominator of the second fraction by 2 to obtain 8 in the denominator.
[tex]\begin{gathered} AC+CD=2\frac{3}{8}+1\frac{1\cdot2}{4\cdot2} \\ =2\frac{3}{8}+1\frac{2}{8} \end{gathered}[/tex]Add the whole numbers, 2 and 1. Add the numerators, 3 and 2, and then copy the common denominator, which is 8.
[tex]\begin{gathered} AD=2\frac{3}{8}+1\frac{2}{8} \\ =3\frac{5}{8}_{} \end{gathered}[/tex]Therefore, the correct answer is the third option, 3 5/8 in.
What is the opposite of the number −12?
A(-1/12
B(1/12
C(0
D(12
Answers
Answer: D(12)
Step-by-step explanation: To find the opposite it the number you would do -12= -12 x -1 = 12
Solve for a: a = 10.
a = , ,
Answers
Answer:
a=10 and a=-10
Step-by-step explanation: its absolute value
QuestionGiven that cot(0)- 1 and 0 is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.Provide your answer below:sin (O)=
Answers
Given:
The trigonometric ratio is given as,
[tex]\cot \theta=-\frac{1}{2}[/tex]The value of θ lies in the second quadrant.
The objective is to find the value of sinθ.
Explanation:
The formula of cotθ is,
[tex]\cot \theta=\frac{\text{adjacent}}{\text{opposite}}=-\frac{1}{2}[/tex]Since, the value of θ lies in second quadrant, the triangle formed for cotθ will be,
Then, the value of x can be calculated as,
[tex]\begin{gathered} x^2=2^2+(-1)^2 \\ x=\sqrt[]{4+1} \\ x=\sqrt[]{5} \end{gathered}[/tex]To find the value of sinθ:
The value of sinθ can be calculated as,
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin \theta=\frac{2}{\sqrt[]{5}} \\ \sin \theta=\frac{2}{\sqrt[]{5}}\times\frac{\sqrt[]{5}}{\sqrt[]{5}} \\ \sin \theta=\frac{2\sqrt[]{5}}{5} \end{gathered}[/tex]Hence, the value of sinθ is (2√5)/5.
I need help finding the exact perimeter. Special right triangles.
Answers
Answer:
The exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]Explanation:
Given the square in the attached image.
The length of the diagonal is;
[tex]d=28[/tex]Let l represent the length of the sides;
[tex]\begin{gathered} l^2+l^2=28^2 \\ 2l^2=784 \\ l^2=\frac{784}{2} \\ l^2=392 \\ l=\sqrt[]{392} \\ l=14\sqrt[]{2} \end{gathered}[/tex]The perimeter of a square can be calculated as;
[tex]\begin{gathered} P=4l \\ P=4(14\sqrt[]{2}) \\ P=56\sqrt[]{2} \end{gathered}[/tex]Therefore, the exact perimeter of the square is;
[tex]56\sqrt[]{2}[/tex]Solve for x8x-11=6x-5Simplify your answer as much as possible
Answers
Solve the given equation for x as shown below
[tex]\begin{gathered} 8x-11=6x-5 \\ \Rightarrow8x-11-6x=6x-5-6x \\ \Rightarrow2x-11=-5 \\ \Rightarrow2x-11+11=-5+11 \\ \Rightarrow2x=6 \\ \Rightarrow\frac{2x}{2}=\frac{6}{2} \\ \Rightarrow x=3 \end{gathered}[/tex]Therefore, the solution to 8x-11=6x-5 is x=3.EFG IS dilated with scale factor of 4 to create triangle E’F’G’ the measure of angle F’ is 53 degrees what is the measurement of angle F
Answers
The measurement of ∠ F = 53 °.
Given,
Triangle EFG is dilated with a scale factor of 4 to create Δ E ' F ' G ' .
The measure of ∠ F ' is 53 °.
To find the measurement of angle F.
We know that a dilation creates similar figures i.e. it preserves the measure of angles.
Therefore, if Triangle EFG is dilated to form Δ E ' F ' G ', then the measure of ∠ F' = measure of ∠ F [Corresponding angles remains same]
⇒ The measure of ∠ F' = measure of ∠ F = 53 °
Hence, The measurement of ∠ F = 53 °.
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I NEED CORRECT ANSWER 100 POINTS ONLY ANSWER CORRECTLY
A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answers
Answer:
[tex]y-9=-\dfrac{8}{3}(x-7)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define the given points:
(x₁, y₁) = (7, 9)(x₂, y₂) = (10, 1)Substitute the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{1-9}{10-7}=-\dfrac{8}{3}[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-9=-\dfrac{8}{3}(x-7)[/tex]
to find the height of a tree, a group of students devised the following method. A girl walks toward the tree along it's shadow until the shadow of the top of her head coincide with the shadow of the top of the tree. if the girl is 150 cm tall, her distance to the foot of the tree is 13 meters, and the length of her shadow is 3 m, how tall is the tree?
Answers
Answer: 8m
Explanation:
Given:
To find the height(h) of the tree, we can use ratio since they are similar triangles.
Triangle 1
Triangle 2
So,
[tex]\begin{gathered} \frac{1.5}{3}\text{ = }\frac{h}{16} \\ \text{Simplify and rearrange} \\ h=\text{ }\frac{1.5}{3}(16) \\ \text{Calculate} \\ h=\text{ 8 m} \end{gathered}[/tex]Therefore, the height of the tree is 8m.
What is the APY for money invested at each rate?(A) 14% compounded semiannually(B) 13% compounded continuously
Answers
APY means Annual Percentage Yield
The APY is given by the formula:
[tex]\text{APY}=\lbrack(1+\frac{r}{n}\rbrack^n-1[/tex]where r is the rate (in decimals)
n is the number of times the interest was compounded
A) For the money invested at 14% compounded semiannually
r = 14% = 14/100
r = 0.14
n = 2
Substitute n = 2, r = 0.14
[tex]\begin{gathered} \text{APY = \lbrack{}1+}\frac{0.14}{2}\rbrack^2-1 \\ \text{APY}=\lbrack1+0.07\rbrack^2-1 \\ \text{APY}=\lbrack1.07\rbrack^2-1 \\ \text{APY}=0.1449 \\ \text{APY}=0.1449\times100\text{ \%} \\ \text{APY}=14.49\text{ \%} \end{gathered}[/tex]B) For the money invested at 13% compounded continuously
A group of friends' dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill,
including tax and tip, rounded to the nearest cent?
O $150.57
O $154.29
o $154.67
O $156.43
Answers
Their total dinner bill including sales tax rate is 8% and 18% tip will be $156.43 by using the concept of percentages and addition.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
What is sales tax?A sales tax is a fee that is paid to the government when certain goods and services are sold. Typically, laws permit the seller to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing body.
Here,
$122.75 dollars to be paid without tax and tip,
=8% of $122.75
=$9.82.
=122.75+9.82
=$132.57
=18% of 132.57
=$23.86
=132.57+23.86
=$156.43
Using the addition and percentages concepts, they can calculate their total dinner bill, which is $156.43 after adding the 8% sales tax and 18% gratuity.
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If Danica has $1200 to invest at 8% per year compounded monthly, how long will it be before he has $2400? If the compounding is continuous,how long will it be? (Round your answers to three decimal places.)
Answers
ANSWER
EXPLANATION
a) To find the time it will take before he has $2400, we have to apply the formula for monthly compounded amount:
[tex]undefined[/tex]a person who weighs 145 pounds on Earth would weigh 47.2 pounds on Mercury. How much would a person weigh on Mercury if they weigh 135 pounds on Earth?
Answers
A person weigh on the Mercury if they weigh 135 pounds on Earth is 43.94 pounds.
Weight of person on Earth = 145pounds
145 = mg
Weight of person on Mercury = 47.2pounds
47.2 = ma
145/47.2 = mg/ma
145/47.2 = g/a
a = 47.2g/145 .....1.
If weight of person on earth = 135pounds
135 = mg
m = 135/g .......2.
Then, Weight of person on Mercury = ma
using the above values of a and m we we get
= (135/g)x (47.2g/145 )
= 135 x 47.2 / 145
= 43.94 pounds
A person weigh on the Mercury if they weigh 135 pounds on Earth is 43.94 pounds.
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For her phone service, Mai pays a monthly fee of $19, and she pays an additional $0.04 per minute of use. The least she has been charged in a month is$70.28. What are the possible numbers of minutes she has used her phone in a month?
Answers
We have a phone service fee which can be divided in:
- A fixed fee of $19 per month.
- A variable fee of $0.04 per minute, so that the cost for m minutes is 0.04*m.
We can add the two fees to express the total cost in function of the minutes as:
[tex]C(m)=19+0.04m[/tex]For a month where the cost is C(m) = 70.28, we can calculate the minutes as:
[tex]\begin{gathered} C(m)=70.28 \\ 19+0.04m=70.28 \\ 0.04m=70.28-19 \\ 0.04m=51.28 \\ m=\frac{51.28}{0.04} \\ m=1282 \end{gathered}[/tex]Answer: if she pays at least $70.28, she has talked at least m = 1282 minutes per month.
Calculate the slope (2,-5) and (4,3)
Answers
Answer:
Slope = 4
Step-by-step explanation:
The slope of a line can be calculated using the following formula:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
From the question can put the points as:
(2, -5) as (x1, y1)
and
(4, 3) as (x2, y2)
Therefore, we can put in the values into the formula to solve for the slope.
[tex] \frac{3 - ( - 5)}{4 - 2} \\ = \frac{3 + 5}{2} \\ = \frac{8}{2} \\ = 4[/tex]
Now , using the formula of slope,m = [tex] y_2-y_1/x_2-x_1[/tex]
=> 3-(-5)/4-2
=> 8/2
=> 4
Hence the required slope of given two ordered pairs is 4
Subtract these polynomials.
(3x + 2x + 4) (x + 2x+ 1) =
Answers
=(3x2 + 2x + 4) - (x2 + 2x + 1)
Combine like terms
=(3x2-x2)+(2x-2x)+(4-1)
=2x2+0+3
The 2x terms cancel each other to 0
=2x2+3
C) 2x2+3 is the answer.
Hope this helps!
Answer:
15x^2+17x+4
Step-by-step explanation:
(3x+2x+4)(x+2x+1)
Combine 3x and 2x to get 5x.
(5x+4)(x+2x+1)
Combine x and 2x to get 3x.
(5x+4)(3x+1)
Apply the distributive property by multiplying each term of 5x+4 by each term of 3x+1.
15x ^2+5x+12x+4
Combine 5x and 12x to get 17x.
15x^2+17x+4
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help meeeeeeeeee pleaseee !!!!!
Answers
The solution to the composite function is as follows;
(f + g)(x) = x² + 3x + 5(f - g)(x) = x² - 3x + 5(f. g)(x) = 3x³ + 15x(f / g)(x) = x² + 5 / 3xHow to solve composite function?The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).
If we are given two functions, it is possible to create or generate a “new” function by composing one into the other.
Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore,
f(x) = x² + 5
g(x) = 3x
Hence, the composite function can be solved as follows:
(f + g)(x) = f(x) + g(x) = x² + 5 + 3x = x² + 3x + 5
(f - g)(x) = f(x) - g(x) = x² + 5 - 3x = x² - 3x + 5
(f. g)(x) = f(x) . g(x) = (x² + 5)(3x) = 3x³ + 15x
(f / g)(x) = f(x) / g(x) = x² + 5 / 3x
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