State the possible number of positive real zeros,negative real zeros, and imaginary zeros forf(x) = 3x4 – 2x3 – 5x2 + 6x - 2.
Answers
Okay, here we have this:
Considering the provided equation, we will identify if its roots are negative, positive or imaginary, so we obtain the following:
\(f(x)=3x^4-2x^3-5x^2+6x-2\)According to the rule of the signs of Descartes, we can identify that since in f(x) there are three changes of signs then there will be 1 or 3 positive roots.
Now, let's find p(-x) to see how many possible negative roots there are:
\(\begin{gathered} f(-x)=3\mleft(-x\mright)^4-2\mleft(-x\mright)^3-5\mleft(-x\mright)^2+6\mleft(-x\mright)-2 \\ f(-x)=3x^4+2x^3-5x^2-6x-2 \end{gathered}\)Since there is only one sign change, then there is only one negative root.
Now, finally we will factor it to see how many positive roots we can get:
\(\begin{gathered} 3x^4-2x^3-5x^2+6x-2=0 \\ \mleft(x-1\mright)\mleft(3x^3+x^2-4x+2\mright)=0 \end{gathered}\)
As it cannot be simplified further, we finally obtain that f (x) has a positive root, a negative root and two imaginary ones.
Related Questions
A boat is being towed such that the tow line is at an angle of 30° with respect to the surface of the ocean. If the boat is towed with a force of 50 Newtons for 7,000 meters, approximately how much work is done?
A. 152,000 Joules
B. 175,000 Joules
C. 303,000 Joules
D. 350,000 Joules
Answers
Answer:
C. 303,000 Joules
Step-by-step explanation:
1. use abcos(theta)
a=50
b=7000
theta=30 degrees
2. (50)(7000)cos(30)=303,000
Answer:
C: 303,000 Joules
Step-by-step explanation:
Edge 2020
2 816 436 What is the sum of the value of the digit 8 in the number and 8?
Answers
The value of the digit 8 in the number is eight hundred thousand
The sum is 800,008.
I want to know the coefficient of each expression and all it’s potential roots
Answers
We are given the following polynomial
\(3x^5-7x^4-5x^3+18x^2-5\)The constant term is -5
The factors of the constant term are ±1 and ±5
The leading coefficient is 3
The factors of the leading coefficient are ±1 and ±3
We can use the factors of the constant term and the leading coefficient to find the potential roots
\(potential\; roots=\frac{p}{q}\)Where p represents the factors of the constant term and q represents factors of the leading coefficient.
\(\begin{gathered} \frac{p}{q}=\frac{\pm1,\pm5}{\pm1,\pm3} \\ \frac{p}{q}=\frac{\pm1}{\pm1},\frac{\pm1}{\pm3},\frac{\pm5}{\pm1},\frac{\pm5}{\pm3} \\ \frac{p}{q}=\pm1,\pm\frac{1}{3},\pm5,\pm\frac{5}{3} \end{gathered}\)Therefore, the potential roots of the given polynomial are
\(\pm1,\pm\frac{1}{3},\pm5,\pm\frac{5}{3}\)Exit Ticket
A student number for a high school requires that student identification number consist of 6
characters. The first 4 characters can be any number without restriction. The last 2 characters are
letters and can- not repeat. How many student ID's are possible?
Answers
Answer:
There are 6,500,000 possible student IDs
Step-by-step explanation:
Berry, we want to calculate the number of possible student ID’s
The numbers to choose from are;
0 1 2 3 4 5 6 7 8 9 - Ten numbers
and 26 alphabets
For the first digit - there are 10 choices
Second digits - 10 choices
Third digit - 10 choices
Fourth digit - 10 choices
1st Alphabet - 26 choices
2nd Alphabet- we can choose all other alphabets aside the one chosen at first and that leaves us with 25 choices
So, the number of possible student ID will be;
10 * 10 * 10 * 10 * 25 * 26 = 6,500,000
9. IN A GROUP OF 60 STUDENTS, 31 SPEAK FRENCH, 23 SPEAK SPANISH AND 14 SPEAK NEITHER FRENCH NOR SPANISH DETERMINE THE NUMBER STUDENTS WHO SPEAK- (a) BOTH FRENCH AND SPANISH (FRENCH ONLY (SPANISH ONLY (FUS) = ?
Answers
The number of students that speak both French and Spanish are 7 students, 24 students speak French only, and 16 students speaks Spanish only.
How to determine the number of students that speaks the different languagesTo solve this problem, we can use the formula for the size of a union of two sets:
|A ∪ B| = |A| + |B| - |A ∩ B|,
where |A| represents the number of elements in set A.
Let F be the set of students who speak French, S be the set of students who speak Spanish, and N be the set of students who speak neither language. Then, we have:
|F| = 31,
|S| = 23,
|N| = 14.
We want to find the number of students who speak both French and Spanish, as well as the number who speak French only and the number who speak Spanish only. Let B be the set of students who speak both French and Spanish, F-only be the set of students who speak French only, and S-only be the set of students who speak Spanish only. Then:
|B| = (unknown),
|F-only| = (unknown),
|S-only| = (unknown).
We know that the total number of students is 60, so:
|F ∪ S ∪ N| = 60.
Using the formula for the size of a union, we get:
|F ∪ S ∪ N| = |F| + |S| + |N| - |F ∩ S| - |(F ∩ N) ∪ (S ∩ N)|.
We can simplify this expression using the fact that |N| = |(F ∩ N) ∪ (S ∩ N)|, since the sets (F ∩ N) and (S ∩ N) are disjoint:
60 = 31 + 23 + 14 - |B| - |N|.
|N| = 14.
Substituting |N| = 14, we get:
|B| = |F ∩ S| - 9.
So, to find |B|, we need to determine |F ∩ S|. We can use the formula for the size of an intersection:
|F ∩ S| = |F| + |S| - |F ∪ S|.
Substituting the known values, we get:
|F ∩ S| = 31 + 23 - |F ∪ S|.
|F ∪ S| = 31 + 23 - |F ∩ S|.
|F ∪ S| = 54 - |B|.
Substituting this into the expression for |F ∪ S ∪ N|, we get:
60 = 31 + 23 + 14 - |B| - 14 - |B|.
2|B| = 54 - 31 - 23 + 14 = 14.
|B| = 7.
So there are 7 students who speak both French and Spanish.
To find |F-only| and |S-only|, we can use the following formulas:
|F-only| = |F| - |B|,
|S-only| = |S| - |B|.
Substituting the known values, we get:
|F-only| = 31 - 7 = 24,
|S-only| = 23 - 7 = 16.
Therefore, there are 7 students who speak both French and Spanish, 24 students who speak French only, and 16 students who speak Spanish only.
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According to the fundamental theorem of algebra, which polynomial function has exactly 6 roots? f (x) = 5 x superscript 4 baseline 10 x squared 2 f (x) = 5 x superscript 5 baseline 3 x superscript 4 baseline 12 x cubed 7 x squared minus 2 x 15 f (x) = 6 x superscript 5 baseline x cubed minus 4 x squared x minus 5 f (x) = 7 x superscript 6 baseline 3 x cubed 12
Answers
The polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12. Then the correct option is D.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
According to the fundamental theorem of algebra.
The polynomial function has only exactly 6 roots.
The roots are the value of the variables in the polynomial at which the value of the polynomial is zero.
If the degree of the variable is n then the number of the roots will be n or less than n.
If the number of the roots are 6, then the degree of the variable will be 6 in the polynomial.
Then the polynomial function has exactly 6 roots is f(x) = 7x⁶ + 3x³ + 12.
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Y=2(x-2)^2+7\(y=2(x-2)^2+7\)
Answers
We have a circular plate of radius a
. The temperature distribution, u(rho,ϕ)
, has boundary conditions u(a,ϕ)=T1
when 0<ϕ<π
and T2
when π<ϕ<2π
. The steady state temperature distribution satisfies the Laplace equation.
I have used separation of variables to reduce the equation to two ODE's which I solved to find the general solution to be u(rho,ϕ)=∑Cλexp(λϕ)ϕλ
The question then asks us to find the Fourier series for u(a,ϕ)
. I did this by finding the series for the two boundary conditions which resulted in: u(a,ϕ)=(T1−T2)2+∑((−1m)−1)(T2−T1)sin(mϕ)πm
(Noted that I am not 100% sure this is correct)
The final part of the question, and the source of my problem, asks us to find an expression for u(rho,ϕ)
as an infinite series using the previous answer. I do not understand how to form a general solution using this - I cannot see how the Fourier series is of any relevance to a general solution as it doesnt appear to help us find Cλ
or λ
itself. Any help would be much appreciated!
Answers
the Fourier series solution is not directly used to find the general solution but is used as a part of it, along with the radial solution. The Fourier series solution helps in finding the solution to the given boundary value problem, which, when combined with the radial solution, gives the complete solution to the Laplace equation.
The Fourier series approach that you have used helps in finding the solution to the boundary value problem, i.e., finding u(a,ϕ) for the given boundary conditions. However, to find a general solution to the Laplace equation, we need to use the superposition principle, which states that the sum of any two solutions to the Laplace equation is also a solution.
Therefore, we can use the previously obtained Fourier series solution for u(a,ϕ) as a building block to construct the general solution. We know that the Laplace equation has radial symmetry, which means that the temperature distribution is only a function of radius (rho) and not of angle (ϕ). Hence, we can write the general solution as:
u(rho,ϕ) = f(rho) + u(a,ϕ)
where f(rho) is the radial component of the solution and u(a,ϕ) is the previously obtained Fourier series solution.
To find f(rho), we need to solve the radial ODE using the boundary conditions at rho=0 and rho=a. Once we have obtained f(rho), we can add it to u(a,ϕ) to get the general solution.
Therefore, the Fourier series solution is not directly used to find the general solution but is used as a part of it, along with the radial solution. The Fourier series solution helps in finding the solution to the given boundary value problem, which, when combined with the radial solution, gives the complete solution to the Laplace equation.
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Calcular los 3/5 de los 2/3 de las 3/4 de 560
Answers
For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.
How to solve fractions?To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:
Step 1: Calculate 3/4 of 560:
3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420
Step 2: Calculate 2/3 of the result from Step 1:
2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280
Step 3: Calculate 3/5 of the result from Step 2:
3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168
Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.
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Choose the phrases below that will make the sentence true.
In the figure, the length of any line segment in the image is _________________ the length of the corresponding line segment in the preimage. The scale factor of the dilation is _________.
A
shorter than; 2
B
longer than; 2
C
longer than; 1
D
the same length as; 2
Answers
In the figure, the length of any line segment in the image is longer the length of the corresponding line segment in the preimage. The scale factor of the dilation is 2
What is the scale factor of dilation?The scale factor of dilation is defined as the change in size of a figure. Thus, a scale factor that is greater than 1 is referred to as an enlargement while a scale factor that is greater than 0 but less than 1 is referred to as a reduction.
Now, we are told that ΔABC has been dilated from center D to form ΔRST, This means that the lengths in ΔRST are longer than the lengths in ΔABC.
Secondly, by close inspection we can see that it was dilated by a scale factor of 2.
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p[(-3)+n]=p x ____ + ______ x _____
Answers
Answer:
241234567890-234567890-dfgyuiop[iuhgv bnklokjbv bnmklm
Bound
Figure 2.
Jenny would like to buy a new air conditioner for his home. As seen in Figure 2 above he has
3 types of brands that he can consider. The cash price for Daewoo is RM1,899, Daikin at a
price of RM1,699 and last choice is Mitsubishi at a price of RM1.999. He plans to make 18
monthly instalments, if he pays RM300 as a down payment for the air conditioner that he would
like to buy, find the interest charge for each brand if the interest rate is 4% based on originall
balance if he chooses to buy from Daikin, find the monthly instalment price and instalment
price that he needs to pay.
Answers
if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
How to determine the monthly instalment price and instalment price that Daikin needs to pay.Calculating the loan amount for each brand by subtracting the down payment from the cash price:
Loan amount for Daewoo = RM1,899 - RM300 = RM1,599
Loan amount for Daikin = RM1,699 - RM300 = RM1,399
Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699
Calculating the interest charge for each brand:
Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96
Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96
Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96
To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:
Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22
Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89
Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72
Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).
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What is a in this question
Answers
The value of the segment a for the similar triangles is equal to 6.
How to calculate for a for the similar trianglesThe triangles MNO and YXO are similar, this implies that the length OX of the smaller triangle is similar to the length ON of the larger triangle
and the length OY of the smaller triangle is similar to the length OM of the larger triangle
so;
a/(a + 18) = 4/(4 + 12)
16a = 4(a + 18) {cross multiplication}
16a = 4a + 72
16a - 4a = 72 {collect like terms}
12a = 72
a = 72/12 {divide through by 12}
a = 6.
Therefore, the value of the segment a for the similar triangles is equal to 6.
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What is the value of g(1⁄2) when g(x) = 2x2? What is the input? What is the output?
Answers
Answer:
\(g(\frac{1}{2}) = 0.5\)
The input is \(x = \frac{1}{2}\) and the output is \(g(x) = g(\frac{1}{2}) = 0.5\)
Step-by-step explanation:
Suppose we have a function g(x) = a. The input is the value of x and the output is the value of g.
In this question:
\(g(x) = 2x^{2}\)
We want g(1/2) = g(0.5). So
\(g(0.5) = 2*(0.5)^{2} = 2*0.25 = 0.5\)
\(g(\frac{1}{2}) = 0.5\)
The input is \(x = \frac{1}{2}\) and the output is \(g(x) = g(\frac{1}{2}) = 0.5\)
help me fast rapidly is of khan academy:
Answers
Answer:
0 hundreds
0 tens
7 ones
.
4 tenths
0 hundredths
8 thousandths
Standard form=7.408
Step-by-step explanation:
Lets first solve (7x1)+(4x1/10)+(8x1/1000)
7+0.4+0.008
Simplify:
7.408
PLEASE MARK AS BRAINLIESTDetermine whether Salvador's answers and work are correct. If ether answer is incorrect,
provide the correct answer. Use words or mathematics to justify your answers
Enter Your answers and your justifications in the space provided. You may use the driwing
tool to add a drawing to help explain and/or support your answer.
Answers
Answer:
His first answer is wrong.
Step-by-step explanation:
The bar should only be over the 6 since it is the only number repeating.
less than227equal to14.637greater than
Answers
Answer:
\(\sqrt[]{227}\text{ is greater than 14.637}\)Alternative C.
Explanation:
Using a calculator, we find that √227 = 15.0665.
If we compare 15.0665 and 14.637, we know that 15.0665 is greater than 14.637.
So,
√227 is greater than 14.637.
Alternative C.
During the 2012 London Olympics, athletes from the United States won more medals in swimming than any other country. The number of medals earned in swimming by United States athletes are shown in the table below.
Answers
Answer: 22.5
Step-by-step explanation:
math
90x=120y What is the ratio of x : y?
Answers
Answer:
3:4
Step-by-step explanation:
find the GCD of both numbers (30) and divide both sides to get 3:4
Answer:
3:4
Step-by-step explanation:
90x : 120y
Simplify the ratio.
90x/30 : 120y/30
3x : 4y
Determine if the following point is a solution to the system of equations:
(3,4)
x+y=7
y = 2x - 2
Answers
Answer:
Yes it is
Step-by-step explanation:
3 + 4 =7
4 = 2(3) - 2
4 = 6 - 2
4 = 4
Solve for x
Assume the equation has a solution for x.
ax + 3x = bx + 5
Answers
Answer:
x= 5/a+3-b
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Judith made 3/5 of a liter of hot chocolate. Each mug holds 1/5 of a liter. How many mugs
will Judith be able to fill?
Answers
in triangle QRS, the measure of angle RSQ is 48.2 degrees, and the SQR is 75 degrees. what is the QRS?
Answers
The measure of angle QRS in triangle QRS is 56.8 degrees.
To find the measure of angle QRS in triangle QRS, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.
We know that:
- The measure of angle RSQ is 48.2 degrees
- The measure of angle SQR is 75 degrees
Let x be the measure of angle QRS. Then, we can write:
RSQ + SQR + QRS = 180
Substituting the known values, we get:
48.2 + 75 + x = 180
Simplifying and solving for x, we get:
x = 180 - 48.2 - 75x = 56.8
Therefore, the measure of angle QRS in triangle QRS is 56.8 degrees.
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Which relation is a function?
Answers
The only graph that represents a function is: Graph D
How to identify a function?A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
From the graphs, we can see that:
Graph A has 2 outputs at x = -2
Graph B has 2 outputs at x = 0
Graph C has two outputs at x = -1
Graph D has a unique output for every input and as such it is a function
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What is the maximum of f(x)=sin(x)
Answers
Answer:
1
Step-by-step explanation:
The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2. If you look at a graph of
y = sin(x) you can see this.
Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.
Step-by-step explanation:
Property of Sine function:
Sin(x)=0 when x=90°,180°,360°The maximum and Minimum value of Sin(x) is 1 and -1 respectively, when and x=270° respectively.The range of values of sin(x) is -1 to 1.Read more on the Sine function:
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It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end. How long will it take you to read 6.25 pages and also take the test?
Answers
The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end.
The number of minutes to read 6.25 pages will be given as,
⇒ 6.25 x 0.8
⇒ 5 minutes
The number of minutes to take the test will be given as,
⇒ 5.5 - 5
⇒ 0.50 minute
⇒ 0.50 x 60
⇒ 30 seconds
The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.
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helpppp ASAP.
1. What is the height of the cone? Explain how you found the height. (4 points)
2. Now that you have the height of the cone, how can you solve for the slant height, s? (3 points)
3. How far does the ant crawl to get from the base of the cone to the top of the hill? Show your work. (3 points)
Answers
1. The height of the cone is, 22.18 mm.
2. The slant height is, 28.14 mm.
3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
The volume of cone V = (1/3)πr²h
Given that,
The volume = 8792 mm³
1. by using the formula to solve for h,
we get h = (3V)/(πr²).
Plugging in the values given,
we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.
Therefore, the height of the cone is approximately 22.18 mm.
2. it is known that, from the Pythagoras theorem
s² = h² + r²,
where s is the slant height, h is the height, and r is the radius.
Plugging in the values we found in part 1,
we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².
Taking the square root of both sides, we get s ≈ 28.14 mm.
Therefore, the slant height is approximately 28.14 mm.
3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.
Using the value we found in part 2,
the length of the slant height is approximately 28.14 mm.
Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.
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A bag contains 3 blue marbles, 10 green marbles, 4 yellow marbles, and 8 red marbles. A marble is chosen at random, not replaced, then another marble is chosen. What is the probability that it is a red marble, then a blue marble? Write your answer as a fraction in simplest form.
Answers
Answer:
There are a total of 25 marbles in the bag.
The probability of choosing a red marble first is 8/25 since there are 8 red marbles out of 25 marbles in the bag.
Since a marble is not replaced after the first selection, there are now 24 marbles in the bag. There are still 3 blue marbles in the bag.
The probability of choosing a blue marble second, after a red marble has already been selected, is 3/24 or 1/8 since there are 3 blue marbles left out of 24 marbles in the bag.
To find the probability of both events occurring together, we multiply their individual probabilities:
8/25 x 1/8 = 1/25
Therefore, the probability that a red marble is chosen first, followed by a blue marble, is 1/25.
the bouncy toy company is creating a new rubber bouncing balls for spring toy line they need to know how much rubber each of the spherical balls will hold each ball has diameter of 3.5 in find the volume of rubber that each ball can hold in cubic inches show all your work
Answers
The volume that each spherical ball can hold in cubic inches is 67.3 inches³.
How to find the volume of a spherical ball?The bouncy toy company is creating a new rubber bouncing balls for spring toy line they need to know how much rubber each of the spherical balls will hold each ball has diameter of 3.5 inches.
The volume that each ball can hold in cubic inches can be calculated as follows:
The ball is spherical.
Therefore,
volume of the spherical ball = 4πr³
r = 3.5 / 2 = 1.75 inches
Hence,
volume of the spherical ball = 4 × π × 1.75³
volume of the spherical ball = 4 × π × 5.359375
volume of the spherical ball = 21.4375 × 3.14
volume of the spherical ball = 67.31375 inches³
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Questions 16. Santhosh and Co. Chennai, opened a branch at Trichy on 1.1.2018. The following Information relate to the branch for the year 2018.
40,000
36,000
9,000
7200
3,600
30,000
16,200
300
3,000
Prepare branch account to find out the profit or loss of branch. Santosh & Co, Chennai opened its branch in Trichy on 1.1.2018. The action for 2018 is as follows
Credit sales at branch
Office expenses by Head office
Cash remittance to branch for petty cash Stock 31.12.2018
Goods sent to Branch
Salaries paid by head office
Debtors 31.12.2018
Petty cash on 31.12.2018
Cash sales at branch
of
Answers
The preparation of the branch's income statement for Santosh & Co. Chennai is as follows:
Branch of Santosh & Co. Chennai
Income StatementFor the year ended December 31, 2018
Sales revenue $40,300
Cost of goods sold 4,200
Gross profit $36,100
Expenses:
Office expenses $36,000
Salaries 3,600
Total expenses $39,600
Loss $3,500
What is an income statement?An income statement is a financial statement prepared at the end of an accounting period to determine the profit or loss generated by a business or branch.
The profit or loss is the difference between the total revenue and the total expenses for the accounting period.
Credit sales at branch 40,000
Office expenses by Head office 36,000
Cash remittance to branch for petty cash 9,000
Goods sent to Branch 7,200
Salaries paid by head office 3,600
Debtors 31.12.2018 30,000
Petty cash on 31.12.2018 16,200
Cash sales at branch 300
Stock of 31.12.2018 3,000
Sales revenue $40,300 ($40,000 + $300)
Cost of goods sold $4,200 ($7,200 - $3,000)
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