Answer:
$575 after 5 years
Step-by-step explanation
3% of 500= 15
15 × 5= 75
500 + 75= $575
The function f(x) is shown in the graph.
Graph in two parts. Part one is increasing from negative infinity in quadrant three to pass through negative 3 comma negative 2 and negative 1 comma 2 and continues increasing upward in quadrant two. Part two is increasing from negative infinity in quadrant 4 and passes through 1 comma negative 2 and 3 comma 2, then continues increasing upward to the right in quadrant one.
Which type of function describes f(x)?
Exponential
Logarithmic
Rational
Polynomial
The type of function that describes function f(x) is given as follows:
Rational function.
How to identify the type of function?The four types of functions are given as follows:
Exponential function.Logarithmic function.Rational function.Polynomial function.These functions are identified as follows from their graphs:
Exponential function: only an horizontal asymptote.Logarithmic function: only a vertical asymptote, but with a domain of only positive valuesRational function: can have both vertical and horizontal asymptotes.Polynomial function: no asymptotes.From the graph given by the image at the end of the answer, the features are given as follows:
Vertical asymptotes.Domain of all real values.Hence the function is a rational function.
Missing InformationThe graph of the function is given by the image shown at the end of the answer.
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How do I translate a function?
To horizontally translate a function,
1)substitute 'x-h' for 'x' in the function.
2)The value for 'h' controls how much the graph shifts to the left or right
3)In our example, since h = -4, the graph shifts 4 units to the left
4)To vertically translate a function, add 'k' onto the end
5)The value for 'k' controls how much the graph shifts up or down
You can also perform both horizontal and vertical translations on a function at the same time!
Translation
The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input.
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lightning strikes the number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. (these values are typical of much of the united states.) the national lightning detection network (nldn) uses automatic sensors to watch for lightning in a random sample of 10 one-square-kilometer plots of land. (a) what are the mean and standard deviation of x, the sample mean number of strikes per square kilometer? (b) explain why you cannot safely calculate the probability that x 5 based on a sample of size 10. (c) suppose the nldn takes a random sample of n 50 square kilometers instead. explain how the central limit theorem allows us to find the probability that the mean number of lightning strikes per square kilometer is less than
The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016, when open ground in a year has mean 6 and standard deviation 2.4.
Define mean.It imply a quantity that falls somewhere between the values of the extreme members of a set in mathematics. There are different types of means, and how they are calculated relies on the relationship that is known about or is regarded as governing the other members.
Given,
Mean = 6
Standard deviation = 2.4
The value that has been reduced by the population mean and divided by the standard deviation is called the z-value.
z = x - mean/ standard deviation/√n
z = 5 - 6/2.4/√50
z = - 2.95
Using table A, calculate the corresponding probability;
= P(x <5)
= P( z < -2.95)
= 0.0016
The probability that the mean number of lightning strikes per square kilometer is less than 5 is 0.0016.
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consider people with three-letter initials.what are the number of choices for the first-, second-, and third-letter initials, if none of the letters are repeated?
Answer: 15,600 different choices for initials
Step-by-step explanation:
26 choices for the first, 25 for the second, and 24 for the third. When multipled, this is 15600.
6b 4r repreent the total cot of the rice and bean Gabriel bought. If he return 2 bag of bean and 1 bag of rice, the expreion that repreent the total cot after the return i (6b 4r) – (2b r). What i thi expreion after implifying?
The expression after simplifying is 4b + 3r
What is Expression ?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
According to question
The total cost of the rice = 6b
The total cost of the bean = 4r
The total cost of the rice and bean Gabriel bought = 6b + 4r
The total cost after the return = (6b 4r) – (2b + r)
Simplifying
⇒ (6b + 4r) – (2b + r)
⇒ (6b + 4r) – 2b - r
⇒ 6b + 4r – 2b - r
⇒ 6b – 2b + 4r - r
⇒ 4b + 3r
hence, The expression after simplifying is 4b + 3r
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write a polynomial function f of least defgree that has rational coefficients, a leading coefficient of 1, and the given zeros
A polynomial function f is equal to x^3- 11x^2+41x- 51 of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
The degree of this polynomial is 3 and the leading coefficient is 1. Three zeros are 3, 4+i, 4-i bc, and a-bi if a+bi is zero, also known as the conjugate postulate. With this information, we can say that the factors are (x-3)(x-(4+i) )(x-(4-i)).
When we start multiplying, we group like this
(x-3)( (x-4) + i )( (x-4) -i )
Multiply the second two factors first.
(x-4)^2 - (i)^2 [This is the difference of squares (a+b)(a-b)].
We know that
i^2 = -1
= x^2 -4x -4x +16 - (-1)
= x^2-8x+16+1
= x^2 -8x +17
Don't forget (x-3).
Solving complete factors
(x-3)(x2-8x+17)
= x^3 -8x^2 +17x -3x^2 +24x -51
= x^3-11x^2+41x-51
This is the final equation of the polynomial.
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The sum of the 2nd and 3rd terms of an arithmetic sequence is 27 and the sum of the 4th and 5th terms is 77.
The sequence's average difference is 12.5.
According to the given information
The sum of an arithmetic sequence's second and third terms is 27.
The combination of the fourth and fifth terms is 77.
We must ascertain,
Let d represent the sequence's common difference.
The arithmetic series' second term is,
Second term = a + d
The arithmetic series' third term is as follows:
Third term = a + 2d
The second and third terms in the sequence add up to 27, thus.
Second term + third term = 27
a + d + a + 2d = 27
2a + 3d = 27
The arithmetic series' fourth term is,
Fourth term = a + 3d
The fifth term in the mathematical series is as follows:
Fifth term = a + 4d
The sequence's fourth and fifth terms add up to 77
Fourth term + fifth term = 77
a + 3d + a + 4d = 77
2a + 7d = 77
After resolving the two equations,
2a + 3d = 27
2a + 7d = 77
Subtracting both the equations
2a + 3d - ( 2a + 7d ) = 27 - 77
2a + 3d - 2a - 7d = -50
-4d = -50
d = 12.5
The sequence's average difference is 12.5
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Heidi walks 3 miles per hour and chris walks 20,000 feet per hour. About how much faster is Chris walking than Heidi, in feet per minute?
(1 mile=5,280 feet)
Answer:
his gives us that Chris is walking 69 feet per minute faster than Heidi.
Step-by-step explanation:
1 mile is equal to 5,280 feet, we can multiply 3 by 5,280 to find that Heidi is walking 15,840 feet per hour.
Next, we need to convert both speeds to feet per minute. Since there are 60 minutes in an hour, we can divide both speeds by 60 to convert them to feet per minute. This gives us that Heidi is walking 264 feet per minute and Chris is walking 333 feet per minute.
Finally, to find out how much faster Chris is walking than Heidi, we can subtract Heidi's speed in feet per minute from Chris's speed in feet per minute.
Simplify 3(w+1)-1 pls
Answer:
3w + 2
Step-by-step explanation:
3(w + 1) - 1
(3 · w) + (3 · 1) - 1
3w + 3 - 1
3w + 2
twice a number is equal to negative four. which equation could be used to find the number? 2 n - 4 2 n
Twice a number is equal to negative four :
2n = -4
Equation:
An equation is a formula that expresses equality by connecting two expressions with an equal sign '='. Equations and their cousins in other languages may have subtly different meanings. For example, in French an equation is defined as containing one or more variables, but in English any formula in its proper form consisting of two equations joined by an equal sign is an equation.
The equation resembles a weighted scale. When two bowls have the same weight (such as grain), the two weights balance the scale and are said to be equal. If you remove a certain amount of grain from one pan of the scale, you must remove the same amount of grain from the other pan to keep the scale balanced. More generally, the equation remains in equilibrium if the same operation is performed on both sides.
According to the question:
If you wanted to solve your equation:
2x = -4
⇒ 2x/2 = -4/2
Divide both sides by 2
For getting the value of x only:
x = -2
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1.
Calculate the value of a for which the polynomial 2x^3 +7x^2 + ax + 2 has the root x = -2. Also, calculate the other roots of the polynomial.
The other two roots of the polynomial are x = (7 + √33)/4 and x = (7 - √33)/4.
What is polynomial?A polynomial is an expression of one or more algebraic terms, each of which is composed of constants and/or variables raised to non-negative integer powers. A polynomial can be written in the form of an equation, where the coefficients of the terms form a sequence of numbers. Polynomials can also be expressed using a factored form, in which each of the terms is the product of a coefficient and a single variable or factor. Polynomials are commonly used to model real-world phenomena, such as the behavior of a system or process. The degree of a polynomial, which is the highest degree of the terms, determines the number of solutions it has. For example, a polynomial of degree two has two solutions while a polynomial of degree three has three solutions. The solutions of a polynomial are determined by solving the equation formed by the polynomial's terms.
Let us first rewrite the polynomial in a standard form:
2x^3 + 7x^2 + ax + 2 = 0
We can factor this polynomial using the Factor Theorem. The Factor Theorem states that if a is a root of a polynomial, then x-a is a factor of the polynomial.
Since x=-2 is a root of the polynomial, the factor (x+2) must be a factor of the polynomial.
Therefore, we can rewrite the polynomial as:
2x^3 + 7x^2 + ax + 2 = 2(x+2)(x^2 + bx + c)
Now, we can use the coefficients of the polynomial to solve for a, b and c.
Comparing the coefficients of the polynomial on both sides:
2 = 2c
7 = b
a = -2b-4c
Substituting the values of c and b in the equation for a, we get:
a = -2(b) - 4(2)
= -2(7) - 8
= -16
Therefore, the value of a is -16.
To find the other roots of the polynomial, we just need to solve the remaining factor (x^2 + bx + c) = 0.
Substituting the values of b and c, we get:
x^2 + 7x + 2 = 0
We can solve this equation using the Quadratic Formula:
x = [-b ± √(b^2 - 4ac)]/2a
Substituting the values of a, b and c, we get:
x = [-7 ± √(7^2 - 4(2)(2))]/2(-2)
= [-7 ± √(49 - 16)]/-4
= [-7 ± √33]/-4
Therefore, the other two roots of the polynomial are x = (7 + √33)/4 and x = (7 - √33)/4.
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Last week Aiden earned $50 for working 8 hours. At this rate, how
many hours would he have to work to earn $175?
Answer:
x = 28
Step-by-step explanation:
We can write a proportion to solve
50 dollars 175 dollars
--------------- = --------------------
8 hours x hours
Using cross products
50x = 8 * 175
Divide each side by 50
x = 8 * 175 / 50
x = 28
Answer:
[tex]\huge\boxed{\sf 28 \ hours}[/tex]
Step-by-step explanation:
Given that,
$50 = 8 hours
Using unitary method.Divide both sides by 50
$1 = 8/50 hours
$1 = 0.16 hours
Multiply 175 to both sides
$175 = 0.16*175 hours
$175 = 28 hours[tex]\rule[225]{225}{2}[/tex]
solve for 4x+6+2x<-2(3+3y) show your work
The inequality expression given by 4x + 6 + 2x < -2(3 + 3y) can be simplified and written as : x + y < - 2.
What is an Inequality? What is a expression? What is a mathematical equation? An inequality in mathematics compares two expressions, showing if one is less or greater than, or simply not equal to another value.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, of the given problem.We have the following inequality -
4x + 6 + 2x < -2(3 + 3y)
We have -
4x + 6 + 2x < -2(3 + 3y)
4x + 6 + 2x < - 6 - 6y
6x + 6 + 6y + 6 < 0
x + y < - 2
Therefore, the inequality 4x + 6 + 2x < -2(3 + 3y) is equivalent to -
x + y < - 2.
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Which of the following is an odd function?
After solving we can conclude that (c) f(x) = -x is an odd function.
What is an odd function?If -f(x) = f(-x), then a function f is said to be odd for all values of x.
When taking into account additive inverses, the functions even and odd are those that satisfy particular symmetry relations.
They are crucial to understanding power, the Fourier series, and mathematical analysis.
So, (a) f(x) = x³ + 5x² + x:
f(-x) = (-x)³ + 5(-x)² + (-x)
= -x³ + 5x² - x
= -(x³ - 5x² + x)
Neither even nor odd describe the function.
(b) f(x) = x² + x
f(-x) = (-x)² + (-x)
= -(-x² + x)
Neither even nor odd describe the function.
(c) f(x) = -x
f(-x) = -(-x)
= x
= -f(x)
f(-x) = -f(x) makes the function odd.
Therefore, after solving we can conclude that (c) f(x) = -x is an odd function.
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Complete question:
Which of the following is an odd function?
(a) f(x) = x³ + 5x² + x
(b) f(x) = x² + x
(c) f(x) = -x
An economics graduate student in the united states earns an $18,000 stipend per year. the u.s. sees significant inflation. how might the student react?
The student react that to ask for a cost-of-living increase to her stipend when a graduate student studying economics receives an annual stipend of $18,000. U.S. inflation is quite high.
Given that,
In the United States, a graduate student studying economics receives an annual stipend of $18,000. U.S. inflation is quite high.
We have to find how may the pupil respond.
We know that,
The term "inflation" describes an increase in the cost of any goods or services.
A history graduate who was living in the United States at the time was given an allowance of $18,000. However, the United States economy is negatively impacted by significant inflation. As a result, the price of goods and services that are available to the public rises quickly. Nowadays, everyone has to spend more on everything. As a result, the graduate student must request that the cost of living be added to the stipend because they must now spend more on living expenses.
Therefore, The student react that to ask for a cost-of-living increase to her stipend when a graduate student studying economics receives an annual stipend of $18,000. U.S. inflation is quite high.
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Question 2 Multiple Choice Worth 4 points)
(Budgeting LC)
An entry-level civil engineer earns an average bi-weekly net pay of $2,175.25. The engineer has created a monthly budget using the following percentages for expenses:
Percent
Housing
35%
Food/Household 10%
Savings
10%
Transportation
Debt
Entertainment
15%
5%
6%
Medical/Personal Care 5%
5%
4%
5%
Giving
Clothing
Miscellaneous
Which balance sheet correctly represents the engineer's income, expenses, and balance?
The balance sheet that correctly represents the engineer's income, expenses and balance is illustrated below.
How to determine percentages of income?We should know that a balance sheet is a summary of assets and liabilities and income and expenses of a legal person. We are told that the balance sheet shows a bi-weekly net pay.
This implies that a month has two bi-weeks, therefore every income and expense is multiplied by 2 to get the following figures.
Income Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,350.50
Expenses Percent Amount
Housing 35% $1,522.68
Food/Household 10% $435.05
Savings 10% $435.05
Transportation 15% $652.58
Debt 5% $217.53
Entertainment 6% $261.03
Medical/Personal Care 5% $217.53
Giving 5% $217.53
Clothing 4% $174.02
Miscellaneous 5% $217.53
$4,350.50
Balance
Income $4,350.50
Expenses $4,350.50
Balance $0
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Find the zeros of the equation by factoring. x2 + 4x - 32 = 0
factors should have two whole numbers separated by a: + or - . Do not type parenthese and no spaces. Examples: x+5 x-4
Answer should have a comma between the two numbers. never use a + sign for positive numbers. Do not use any symbols. Use only numbers and a comma with no spaces. Examples: 6,-6 or -8,10. Do not use parenthesis or brackets.
Answer:
I guess this is the answer
Answer:
Step-by-step explanation:
(x+8)(x-4) = 0
x = -8
x = 4
Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
2x + y = 7
-2x + 2y = -5
A. One Solution
B.Infinitely Many Solutions
C. No Solutions
Answer:
A. One Solution
Step-by-step explanation:
To determine if a system of equations has no solutions, infinitely many solutions, or exactly one solution, we can solve the system by any method, such as elimination or substitution.
In this case, we can solve the system by elimination. Multiplying the first equation by -2 and adding it to the second equation, we get:
0x + 4y = -3
This equation tells us that y must be equal to -3/4, but we still need to check if this value of y satisfies the original equations. Substituting -3/4 for y in the first equation, we get:
2x + (-3/4) = 7
Solving this equation for x, we get x = 5/4. Substituting this value of x and -3/4 for y in the second equation, we get:
-2(5/4) + 2(-3/4) = -5
which simplifies to:
-5/2 + (-3/2) = -5
This equation is true, so the solution of the system is x = 5/4 and y = -3/4. Since the system has a unique solution, the answer is (A) One Solution.
What is the area of a figure?
Answer:
Area is calculated by multiplying the length of a shape by its width.
Step-by-step explanation:
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area.
What is 12 x 12 x 12 x 66
Answer:
Step-by-step explanation:
114048
Answer:
114048
Step-by-step explanation:
Show all work to identify the asymptotes and state the end behavior of the function f(x)=[tex]\frac{4x}{x-16}[/tex]
ILL MARK BRAINLIEST!! <3
Answer:
To find the asymptotes and the end behavior of the function f(x) = 4x / (x-16), we can first divide both the numerator and denominator by the highest common factor of 4x and (x-16). This gives us:
f(x) = (4x / 4x) / ((x-16) / 4x)
= 1 / ((x-16) / 4x)
Next, we can find the horizontal asymptotes by looking at the values of the function as x approaches positive and negative infinity. When x approaches positive infinity, the denominator of the function approaches 0, so the function approaches 1 / 0, which is undefined. Therefore, the function does not have a horizontal asymptote as x approaches positive infinity.
When x approaches negative infinity, the denominator of the function approaches -16 / -infinity, which is 0. Therefore, the function approaches 1 / 0, which is undefined. Therefore, the function does not have a horizontal asymptote as x approaches negative infinity.
Next, we can find the vertical asymptotes by setting the denominator of the function equal to 0 and solving for x. In this case, the denominator is (x-16) / 4x, so we can set each factor equal to 0 and solve for x:
x-16 = 0
x = 16
4x = 0
x = 0
Therefore, the function has two vertical asymptotes at x = 0 and x = 16.
Step-by-step explanation:
b. Sketch a graph of G for 0 ≤ t ≤ 12. n
14
12
10
8
6
cost (dollars)
4
2
2
4
6
time (hours)
8
10
12
Plot the Graph with time on X-axis and Cost on Y-axis.
It costs 12$ for 8,10,12 hours.
How to plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables (as a series of one or more points, lines, line segments, curves, or regions). In other words, depending on what you are attempting to prove or establish, values may be represented on a Cartesian coordinate system in a variety of ways. Discrete data would be shown on the graph as single points, such as the average price of vehicles from year to year. Since the calculation is only performed once each year, the data is discrete. The y axis would show the average price of cars for each year, while the x axis would indicate each year.
Plotting:Given;
5$ for first hour;
10$ for up to 2 hours;
12$ for entire day.
G(t) = 5$ up to first hour, 10$ for up to 2 hours and 12$ for more than 2 hours.(So G is a function of t)
So for 0 hours,[tex]\frac{1}{2}[/tex] hours,1 hours it takes 5$;
and 10$ for 1[tex]\frac{3}{4}[/tex]hours, 2 hours
and 12$ for 5h,8h,12h.
Plot the Graph with time on X-axis and Cost on Y-axis.
It costs 12$ for 8,10,12 hours.
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a solid lies between two parallel planes feet apart and has a volume of cubic feet. what is the average area of cross-sections of the solid by planes that lie between the given ones?
Average area of the cross section plane of the solid which lies between the two parallel planes is equal to 197.4square feet.
As given in the question,
Number of parallel planes = 2
Distance between two parallel planes = 22 feet
Volume of the solid is equal to 4343 cubic feet
Let 'x' be the average area of cross section of the solid lies between two parallel planes.
Average area of cross section of the solid lies between two parallel planes = Volume of the solids / Distance between two parallel planes
⇒ x = 4343/22 square feet
⇒ x = 197.4 square feet
Therefore, the average area of the cross section of the solid lies between two parallel plane is equal to 197.4 square feet.
The complete question is:
A solid lies between two parallel planes 22 feet apart and has a volume of 4343 cubic feet. What is the average area of cross-sections of the solid by planes that lie between the given ones?
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Jasmine bought a fidget spinner for $3. She decided to mark up the price by 850% and sell it to her friend Bryan. How much did Jasmine sell the fidget spinner to Bryan for? Do not include the $ sign.
please help:)
Jasmine sold the fidget spinner to Bryan for the cost of $5.55.
To find the cost that Jasmine sold the fidget spinner to Bryan for, we need to first find the amount of the markup by multiplying the original price by the markup percentage.
As per the question, the original price of the fidget spinner is $3, and the markup percentage is 850%, so the markup amount is :
$3 × 850% = $2.55.
Next, we need to add the markup amount to the original price to find the selling price. So, the selling price is :
$3 + $2.55 = $5.55.
Therefore, Bryan paid $5.55 for the fidget spinner that Jasmine had just sold him.
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an agricultural field test compares two varieties of corn, silver queen and country gentlemen. the researches takes 10 plots and divides each of these plots in half. each plot has a similar amount of sun light, shade, quality of soil and irrigation. the variety of corn is randomly chosen for each half of a plot. after the harvest, the yield of corn is measured for each half plot at each location. the yield from silver queen was compared to the yield of country gentlemen. note: differences were taken by taking silver queen - country gentlemen the 95% confidence interval for the mean is (-0.223, 0.988). what can we expect will be the p-value for a two sided test using this data?
The solution to this problem is the p-value must be higher than 0.05.
Confidence interval definition:A confidence interval in frequentist statistics is a range of estimates for an unobserved parameter. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.
Here ,
In this given problem we can see confidence interval has 0 in it.
So,
Since the confidence interval comprises 0, the null hypothesis should be rejected.
When the p-value exceeds the level of significance, the null hypothesis is only rejected.
Since alpha=0.05 in this case, the p-value must be higher than 0.05.
Thus, the p-value must be higher than 0.05.
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at a booth at the school carnival in past years, they've found that 22% of students win a stuffed toy ($3.60), 16% of students win a jump rope ($1.20), and 6% of students win a t-shirt ($7.90). the remaining students do not win a prize. if 150 students play the game at the booth, how much money should the carnival committee expect to pay for prizes for that booth?: * a) $145.80 b) $317.50 c) $218.70 d) $109.35 e) $635.00
The amount of money the carnival committee should expect to pay for prizes for the booth is 218.7 dollars.
Therefore, the answer is option C.
How to find the amount the carnival committee should expect to pay?At a booth at the school carnival in past years, they've found that 22% of students win a stuffed toy ($3.60), 16% of students win a jump rope ($1.20), and 6% of students win a t-shirt ($7.90). The remaining students do not win a prize.
If 150 students play the game at the booth, the amount of money the carnival committee expect to pay for the prizes of the booth is as follows:
total student that partake = 150
number that win stuffed toy = 22% of 150
number that win stuffed toy = 33
number that win jump rope = 16% of 150
number that win jump rope = 24
number that win t-shirt = 6% of 150
number that win t-shirt = 9
Therefore,
prizes for those that win stuffed toy = 33 × 3.60 = 118.8 dollars
prizes for those that win jump rope = 24 × 1.20 = 28.8 dollars
prizes for those that win t-shirt = 9 × 7.90 = 71.1 dollars
Hence,
total amount the committee is expected to pay for prizes = 118.8 + 28.8 + 71.1 = 218.7 dollars
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You and your friends kyra and
Paolo decide to make some money during summer vacation by building and selling birdhouses. To get the business started, Kyra contributes $22, and Paolo contributes $18 to buy equipment and materials. You all agree that each person will earn the same amount of money after Kyra and Paolo get back what they invested. Your business earns a total of $280. How much does each person get at the end of the summer?
The amount of money each person get at the end of the summer is below;
You = $80
Kyra = $102
Paolo = $98
How much does each person earn?Number of friends = 3Kyra contribution = $22Paolo contribution = $18Your contribution = $0Total contribution = $22 + $18 + $0
= $40
Total earnings after investment = $280Amount each person get = (Total earnings after investment - Total contribution) / 3
= ($280 - $40) / 3
= $240/3
= $80
Amount you get = Your contribution + Amount each person get
= 0 + 80
= $80
Amount Kyra get = Kyra contribution + Amount each person get
= $22 + $80
= $102
Amount Paolo get = Paolo contribution + Amount each person get
= $18 + $80
= $98
In conclusion, each person gets an equal amount including their invested money.
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Triangle ABC has angle A = 31 degrees and angle B = 87 degrees. What is the measure of angle C ?
Answer:
All sum of Traingle Angle is 180°
180= 87+31+ Angle C
Angle C = 180 - (31+87)
Angle C = 62
How Do You Solve 3 linear equations with 2 variables?
The steps to solve the 3 linear equations with 2 variables is shown below .
In the question ,
it is asked that how can we find the solution of 3 linear equations that have 2 variables .
Step (1) : Pick any two pair of linear equations ,
Step(2) : Then use addition and subtraction to eliminate the Same Variable from the equations .
Step(3) : In step 2 we will get the value of 1 variable ,
Step(4) : Substituting the value of the variable in Step(2) in the third linear equation ,
we will get the value of other variable also .
Therefore , the value of both the variable can be found by the above steps .
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(2x^3 + 5x^2 - x + 6) divided by (x-3)
We can use polynomial division concept for the given question. The quotient for the polynomial division is (2x^2+11x+32).
How can we do polynomial division?Divide the first term of the dividend by the first term of the divisor to divide polynomials using long division. The quotient's initial term is this. Dividend is calculated by multiplying the new term by the divisor. The new dividend is this difference. A polynomial is divided by another polynomial in an arithmetic operation called division, usually with a lower degree than the dividend. A polynomial may or may not be produced when two polynomials are divided.
CalculationTake Dividend as (2x^3 + 5x^2 - x + 6)
Take Divisor denominator as (x-3)
By using long hand division technique,
(2x^3+5x^2-x+6)/(x-3)
⇒(x-3)(2x^2+11x+32)/(x-3)
∴ The quotient for the given polynomial division is 2x^2+11x+32 and the
Remainder for the polynomial division is 90.
We can use polynomial division concept for the given question. The quotient for the polynomial division is (2x^2+11x+32).
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