What is a NPV net present value ?
The difference between the current value of cash inflows and withdrawals over a period of time is known as net present value (NPV). To evaluate the profitability of a proposed investment or project, NPV is used in capital budgeting and investment planning.
Using the appropriate discount rate, computations are performed to determine the current value of a stream of future payments, or NPV. Projects that have a positive NPV are generally worthwhile pursuing, whereas those that have a negative NPV are not.
The current worth of a stream of payments from a business, project, or investment is determined using net present value (NPV).You must predict the timing and size of future cash flows in order to determine NPV, and you must choose a discount rate that is equal to the least allowable rate of return.Your cost of capital or the rewards offered by substitute investments with equivalent risk may be reflected in the discount rate.Positive NPV indicates that the rate of return on a project or investment will be higher than the discount rate.1.
NPV of project A = [tex]-50+\frac{8}{/(1.10)^1} +\frac{8}{(1.10)^2} \frac{8}{(1.10)^3} +\frac{8}{(1.10)^4} +\frac{8}{(1.10)^5} +\frac{8}{(1.10)^6} +\frac{8}{(1.10)^7} +\frac{8}{(1.10)^8} +\frac{8}{(1.10)^9} +\frac{8}{(1.10)^1^0} +\frac{8}{(1.10)^1^1} +\frac{8}{(1.10)^1^2} +\frac{8}{(1.10)^1^3} +\frac{8}{(1.10)^1^4} +\frac{8}{(1.10)^1^5} +\frac{8}{(1.10)^1^6} +\frac{8}{(1.10)^1^7} +\frac{8}{(1.10)^1^8} +\frac{8}{(1.10)^1^9} +\frac{8}{(1.10)^2^0}[/tex]
=$18.11
2.
NPV of project B = [tex]-15+\frac{3.4}{/(1.10)^1} +\frac{3.4}{(1.10)^2} \frac{3.4}{(1.10)^3} +\frac{3.4}{(1.10)^4} +\frac{3.4}{(1.10)^5} +\frac{3.4}{(1.10)^6} +\frac{3.4}{(1.10)^7} +\frac{3.4}{(1.10)^8} +\frac{3.4}{(1.10)^9} +\frac{3.4}{(1.10)^1^0} +\frac{3.4}{(1.10)^1^1} +\frac{3.4}{(1.10)^1^2} +\frac{3.4}{(1.10)^1^3} +\frac{3.4}{(1.10)^1^4} +\frac{3.4}{(1.10)^1^5} +\frac{3.4}{(1.10)^1^6} +\frac{3.4}{(1.10)^1^7} +\frac{3.4}{(1.10)^1^8} +\frac{3.4}{(1.10)^1^9} +\frac{3.4}{(1.10)^2^0}[/tex]
= $13.95
Use function IRR in excel as = IRR(-50,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8)
= 15.03% is the IRR for A.
Use function IRR in excel as = IRR(-15,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4)
= 22.26% is the IRR for B.
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(c) Select all that describe ST.
Perpendicular bisector of PQ
Angle bisector of ∠ R
Median of ΔP Q R
Altitude of Δ P Q R
None of the above
All of the statements that correctly describe line ST include the following;
A. Perpendicular bisector of PQ.
C. Median of ΔPQR.
D. Altitude of ΔPQR.
What is an isosceles triangle?In Mathematics, an isosceles triangle can be defined as a type of triangle that has two (2) of its sides equal in length and two (2) equal angles. This ultimately implies that, an isosceles triangle comprises two (2) angles and two (2) side lengths that have the same measure or are equal in magnitude.
In every isosceles triangle such as triangle PQR (ΔPQR), both the median and altitude are the same and they will lie on the same line segment when drawn from the top to the base in accordance with the Isosceles Triangle Theorem.
In conclusion, we can logically deduce that the vertex that runs from point T to point S is a perpendicular bisector that bisects line PQ into two (2) equal halves.
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Consider the function f(x) = (x²-x)(x + 5).
1. What are the zeroes of f(x)?
2. Write f(x) in standard polynomial form.
Step-by-step explanation:
[tex]( {x}^{2} - x)(x + 5)[/tex]
[tex]x(x - 1)(x + 5)[/tex]
[tex]x = 0[/tex]
[tex]x - 1 = 0[/tex]
[tex]x = 1[/tex]
[tex]x + 5 = 0[/tex]
[tex]x = - 5[/tex]
So our zeroes are 0,1, and -5
2.
[tex] {x}^{3} + 4 {x}^{2} - 5x[/tex]
through: (-1,-5), parallel to y=-4x+4
The function that is parallel to the graph of y = -4x + 4 is y = -4x - 9
How to determine the parallel line equation?From the question, we have the following parameters that can be used in our computation:
y=-4x+4
To start with, we need to express the equation properly
So, we have the following representation
y = -4x + 4
Also, from the question;
We have the following points
The point is given as
Point = (-1, -5) i.e. (x, y) = (-1, -5)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = -4
This means that the slope is -4
The slopes of parallel lines have the same values
This means that the slope of the other line is -4
The equation of the line is then calculated as
y = m(x - x₁) + y₁
Where
m = -4
(x₁, y₁) = (-1, -5)
So, we have
y = -4(x + 1) - 5
Open the brackets
y = -4x - 4 - 5
Evaluate the like terms
y = -4x - 9
Hence, the line has an equation of y = -4x - 9
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Step-by-step explanation:
function of the organelle in question 4.
Using the diagram and your knowledge of biology, identify the following:
a. Organelle A_____
b. Substance A_____
c. Substance B_____
RT 2: Regents Review!
ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.
scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose
function of the organelle in question 4.
Using the diagram and your knowledge of biology, identify the following:
a. Organelle A_____
b. Substance A_____
c. Substance B_____
RT 2: Regents Review!
ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.
scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose
Airport B is 300 mi from airport A at a bearing N 50° E (see the figure). A pilot wishing to fly from A to B mistakenly flies due east at 250 mi/h for 35 min, when he notices his error.
The pilot is 231 mi from his destination at the time he notices the error.
What is the law of cosines?
The square of a side of a plane triangle is equal to the sum of the squares of the other sides minus twice the product of those sides and the cosine of the angle between them, according to a trigonometry rule.
Here, we have
This line is 300 mi long and makes an angle of 40° from the horizontal (based on N50°E bearing).
From point A draw a horizontal line to point C. This line=(35/60)*250=145.8 mi.
Draw a line connecting point C to point B. You now have a triangle with sides AB = 300 mi and AC = 145.8 mi and their included angle of 40.
Using the Law of cosines to find CB:
(CB)² = (AB)²+(AC)² -2*AB*AC*cos 40°
(CB)² = (300)²+(145.8)²-2*300*145.8*cos 40°
(CB)² = 90000+21257 - 46928 = 64329
CB =√64329 = 253 mi
Hence, the pilot is 231 mi from his destination at the time he notices the error.
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Emily wanted to make cookies.One batch of cookies needed 2/3 cup of milk.How much milk would Emily need to bake three batches of cookies?
A soft drink can has a height of 16cm and a radius of 3cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can). Give your answer rounded DOWN to the nearest cm, to ensure it fits inside the can.
In linear equation, 16.27 is the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).
Describe a linear equation using an example.
An equation in which there is only one variable is known as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.
A linear equation in one variable would be 9x + 78 = 18, for instance.
l² = r² + h²
l² = 3² + 16²
l² = 9 + 256
= 265
l = √265
l = 16.27
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First try was incorrect
Use the graph to answer the questions below.
What is the domain of this function?
The domain of the function are all real numbers between -1 and 0. {x∈R|-1≤x≤0}
What is a function ?
A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
See if any vertical lines that were drawn touch the curve more than once by carefully examining the graph. The graph does not represent a function if there is any such line. The graph does reflect a function if no vertical line can cross the curve more than once.
The domain of function are set of values of x for which the function covers.
For the given function, from the graph the function starts from x =-1 and ends at x = 0.
So, the domain of the function are all real numbers between -1 and 0.
{x∈R|-1≤x≤0}
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Which graph represents the inequality 2.5 is greater than the product of −0.5 and a number?
number line with open circle on point 0.2 and arrow shaded to the left
number line with open circle on point negative 5 and arrow shaded to the left
number line with open circle on point negative 0.2 and arrow shaded to the right
number line with open circle on point negative 5 and arrow shaded to the right
number line with open circle on point negative 5 and arrow shaded to the right is the right description for the graph of the inequality.
what is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
let the number be x
so that 2.5 > -0.5x
dividing through by -0.5 we revert the inequality sign
2.5/-0.5 < x
-5 < x
Taking x to the other side we revert the inequality sign back to greater than
x > -5
In conclusion, number line with open circle on point negative 5 and arrow shaded to the right is the description of the graph
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Answer: D
Step-by-step explanation: I have proof! i got it right on test and i have a picture.
Helpp 8 grade hellppp
With the given coordinates (-3, 1) and (0, 4), the slope is 1.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)
Here,
1) (-3, 1) and (0, 4)
Δy=(4-1)=3 and Δx=(0(-3))=3
So, m= Δy/Δx =3/3 =1
2) (-6, 27) and (2, 3)
Δy=(3-27)=24 and Δx=(2-(-6))=8
So, m= Δy/Δx =24/8 =3
3) (5, 27) and (0, -8)
Δy=(-8-27)=-35 and Δx=(0-5)=-5
So, m= Δy/Δx =(-35)/(-5) =7
4) (1, 0) and (-7, -24)
Δy=(-24-0)=-24 and Δx=(-7-1)=-8
So, m= Δy/Δx =(-24)/(-8) =3
5) (-3, 20) and (-5, 32)
Δy=(32-20)=12 and Δx=(-5-(-3))=-2
So, m= Δy/Δx =12/(-2) =-6
6) (5, -4) and (0, -9)
Δy=(-9-(-4))=-5 and Δx=(0-5)=-5
So, m= Δy/Δx =(-5)/(-5) =1
7) (-8, -2) and (-1, -4.5)
Δy=(-4.5-(-2))=-2.5 and Δx=(-1-(-8))=7
So, m= Δy/Δx = -2.5/7
8) (-7, -2) and (6, 11)
Δy=(11-(-2))=13 and Δx=(6-(-7))=13
So, m= Δy/Δx =13/13 =1
9) (-2, -6.5) and (4, -8)
Δy=(-8-(-6.5))= -1.5 and Δx=(4-(-2))=6
So, m= Δy/Δx = -1.5/6 = -1/4
Therefore, slope of a line with the coordinates (-7, -2) and (6, 11) is 1.
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(Score for Question 1: ___ of 5 points)
Simplify . Show your work.
Answer:
(Score for Question 2: ___ of 5 points)
Solve for x. Show your work.
Answer:
(Score for Question 3: ___ of 5 points)
Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria, how many would be in the petri dish after 24 hours? Show your work.
The bacteria after 24 hours will be equal to 450000.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria.
The number of bacteria will be calculated as,
N = 125×(60×60)
N = 125×3600
N = 450000
Therefore, the bacteria after 24 hours will be equal to 450000.
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A table is on sale for $297, which is 34% less than the regular price. WhAt Is the regular price?
Answer:Above $297 we need to add 34%. Thus the result :
297 X 34/100 =100,98
Result = 297 + 100,98 = 397,98
Step-by-step explanation:Good luck
Assume the supply and demand functions for a manufacturing company are:
Supply: p= 2/3q-250 Demand: p= -4/3q + 750
where p is the price per unit in dollars and q is the quantity in units. Find the equilibrium quantity.
O 1,000
750
O250
O 100
O 500
What is x if 9: 12 = 15:x?
Answer:
Hi, the answer to your question is ×=20
X = 20
when we solve the given equation,
9/12 = 15/x
hence,
X = 15*12/9
X = 20
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Question:
The instructions next to the register state the following: For all purchases less than $400 ask, “Would you like to put this on your Barnes preferred customer card?” What is the most likely reason for these instructions?
A.To build brand recognition with your customers
B.To get customers to join the preferred customer program
C.To keep credit charges from the bank low
D.To receive more credit charges from the bank
Answer:The answer is B
Step-by-step explanation:
The reason that the answer is b is because he wants to keep the prices low from them getting charged by the bank
There are 992 trees in even rows at a tree farm. Each row has 16 trees. How many rows are there?
Answer: 62 rows
992 divided by 16 is 62, so there are 62 rows.
mark as brainliest
Answer:
992÷16=62
Step-by-step explanation:
I hope I helped you
6.3¹
Given conversion factor ¹2 m, what is the above line segment's unit of
measure in inches? Round your answer to the nearest tenth.
Answer here
The line segment's unit of measure is 75.6 inches.
What is the conversion factor?
A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value.
Here, we have
Given
12in/1ft
We have to convert this into inches.
So, we apply here conversion factor and we get
= 6.3ft × 12in ÷1ft
= 75.6 inches
Hence, the line segment's unit of measure is 75.6 inches.
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Helpppppppppppp please due soon!!
Answer:
12
Step-by-step explanation:
pythagoras thereom
a^2 +b^2=c^2
13^2-5^2=144
144 square root = 12
Answer:
12
Step-by-step explanation:
13^2 - 5^2 = 144
square root of 144 = 12
If X + 6 = 7, then X is equal to
X = 1
X + 6 = 7
-6 -6
X = 1
Self check : 1 + 6 = 7
The value of the x in the given equation is 1.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, If X + 6 = 7, then X is equal to
Solving the equation, we get,
x + 6 = 7
Subtracting 6 from both side, we get,
x + 6 - 6 = 7 - 6
x = 1
Hence, The value of the x in the given equation is 1.
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Help me please must use elimination
Answer:
(1,2)
(3, -1)
Step-by-step explanation:
2x + 5y = 12
4x -y = 2 Multiply this through by 5 and then add to the equation above
2ox - 5y = 10
2x + 5y = 12
22x = 22 Divide both sides by 22
x = 1
Substiture in 1 for x in either of the two original equations
2x +5y = 12
2(1) + 5y = 12
2 + 5y = 12 Subtract 2 from both sides
5y = 10 Divide both sides by 5
y = 2
(1,2)
2nd Problem
2x - 5y = 11 Multiply through by 2 4x - 10 y = 22
3x + 2y = 7 Multiply through by 5 15x + 10 y = 35
Add the two bold equation together
4x - 10y = 22
15x +10y = 35
19x = 57 Divide both sides by 19
x = 3
Substitute in 3 for x in one of the original equations to solve for y.
2x - 5y = 11
2(3) - 5y = 11
6 - 5y = 11 Subtract 6 from both sides
-5y = 5 Divide both sides by -5
y = -1
(3,-1)
Drag and drop the correct values for the angles and line segments;
From the diagram, the values of <CAB=60⁰, <ACB=90⁰, <ABC=30⁰,BC=15, DA=32 and BA= 32
How to determine the angles?You should know that an angle is the intersection of two or more straight lines.
Considering the two tringles
ΔACD≡ΔABC
lines DC=BC
<ACD=<ACB=90⁰
Line DA=AB
This implies that 5x+12=8x
Collecting like terms
8x-5x=12
3x=12
Therefore x=4
This means that 5*4+12=32
This implies that BA=AD=32
In triangle ABC;
<ACB=90⁰
<ADC=<ABC=30⁰
This means that
<BAC=90-30=60
Therefore <CAB=60⁰, <ACB=90⁰, <ABC=30⁰,BC=15, DA=32 and BA= 32 respectively
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the population (in millions) of texas from 2001 through 2014 can be approximated by the model , where represents the year, with corresponding to 2001. according to this model, when will the population reach million? (source: u.s. census bureau)
After 23.1 years the population of Texas will reach 32 million.
In this question, we have been given the population P (in millions) of Texas from 2001 through 2014 can be approximated by the exponential function P = 20.913 e^(0.0184t),
where t represents the year, with t = 1 corresponding to 2001.
We need to find the time period t when the population reach 32 million.
For P = 32, we need to find t.
Substitute P = 32 in given exponential function.
32 = 20.913 e^(0.0184t)
32/20.913 = e^(0.0184t)
1.53 = e^(0.0184t)
ln(1.53) = 0.0184 * t
t = 0.4253/0.0184
t = 23.11 years
Therefore, after 23.1 years the population will reach 32 million.
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The complete question is:
The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P = 20.913e0.0184 t, where t represents the year, with t = 1 corresponding to 2001. According to this model, when will the population reach 32 million? (Source: U.S. Census Bureau)
The City Sights tour company had the same ratio of tourists to guides on both days this weekend. On Saturday, there were 120 tourists and 18 guides. On Sunday, there were 40 tourists.
Using ratios we know that the number of guides on Sunday was 6.
What are ratios?In mathematics, a ratio shows how frequently one number appears in another.
For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.
Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.
So, we know that the proportion of tourists to guides was the same on both days of the weekend.
On Saturday, the ratio was:
120:18
120/18
20/3
Ratio: 20:3
So, a number of guides on Sunday will be:
40:x
40/20 = x/3
20x = 40*3
x = 2*3
x = 6
Therefore, using ratios we know that the number of guides on Sunday was 6.
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Complete question:
The City Sights tour company had the same ratio of tourists to guides on both days this weekend. On Saturday, there were 120 tourists and 18 guides. On Sunday, there were 40 tourists. Find number of guides on sunday.
The estimated population of a certain city over time is given in the table below.
Answer the questions below to determine what kind of function would best fit the
data, linear or exponential.
Number of
Years Since
Last Census,
X
Estimated
Population.
f(x)
1
48,391
2
values change
function is approximately
57,332
3
66,237
75,232
function would best fit the data because as x increases, the y
The
of this
A linear function would best fit the data because as x increases, the y values change by an approximate constant. The rate of change of this function is approximately 8950 people a year.
How to classify a function as linear or exponential?To classify a function as linear or exponential, we have to check whether the differences or the quotients between consecutive terms are constant, as follows:
Constant differences -> Linear function.Constant quotient -> Exponential functions.The differences for the consecutive terms in the table are given as follows:
75,232 - 66,237 = 8,995.66,237 - 57,332 = 8,905.57,332 - 48,391 = 8,941.The ratios for the table are given as follows:
77,252/66,237 = 1.166.66,237/57,332 = 1.155.57,332/48,391 = 1.185.The differences have less variation then the ratios, then a linear function best models this data, with an slope of approximately (8995 + 8905 + 8941)/3 = 8947, which is the mean of these differences.
(rounded to 8950).
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complete the following statements. in general, % of the values in a data set lie at or below the 70th percentile. % of the values in a data set lie at or above the 20th percentile.. if a sample consists of 600 test scores, of them would be at or below the 86th percentile. if a sample consists of 600 test scores, of them would be at or above the 62th percentile.
If a sample consists of 600 test scores, 516 of them would be at or below the 86th percentile. If a sample consists of 600 test scores, 228 of them would be at or above the 62th percentile.
What is percentile?A percentile is a score that compares a specific score to the scores of the other members of a group. It displays the proportion of other scores that a given score outperformed. For instance, if you have a test score of 75 and are placed in the 85th percentile, it signifies that your score is greater than those of 85% of other test takers.
Given that,
In general, 70 % of the values in a data set lie at or below the 70th percentile.
20 % of the values in a data set lie at or above the 20th percentile.
Generally percentile defines the percentage of a data set that is below or at a value that is being considered.
Hence the percentage of the values of a data set that lies below or at the 16th percentile is 16%
Also the values of a data set that lies below or at the 24th percentile is 24%
Given a sample of 600 test scores , the number of test scores that will be at or below the 86th percentile is 86% of 600 which is mathematically represented as:
K = [tex]\frac{86}{100}[/tex] × 600
K = 516 test scores
Given a sample of 600 test scores , the number number of test scores that will be above the 62 th percentile is (100 - 62 = 38 )% of 600 which is mathematically represented as:
a = [tex]\frac{38}{100}[/tex] × 600
a = 228 test scores.
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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 19 more than the secondLet and represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles
Provide your answer below:
X=
Y=
Z=
The value of x= 35.5, y= 43.75 and z= 62.75
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the three angles are x, y and z.
x+ y + z = 180............(E3)
The sum of the measures of the second and third angles is three times the measure of the first angle.
So, y+ z = 3x
3x- y- z= 0.............(E1)
and, third angle is 19 more than the second
z= y+ 19
y- z= -19..........(E2)
So, E1+E2, and E3-E2,
3x- 2z= -19
x+ 2z= 161
Now, adding above
4x = 142
x= 35.5
and, y + z = 106.5, y- z = -19
Again, adding
2y= 87.5
y= 43.75
and, z= 62.75
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The following coordinates are each a result of a single transformation. What type of transformation occurred for each image?
A (4,5) --> A (-4,-5)
There is a Rotation of 180 degrees
What is Co-ordinate Geometry?
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
We are given that point A is (4, 5) this means that the point lies in the First Quarter of the Co-ordinate System
and the transformed point lies in the Third Quarter of the Co-ordinate System
So, it can be very well said that there is a Rotation of 180 degrees
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(a) Show that the following polynomials form a basis of P, (the cubic polynomials). Hint: Use the standard basis of P, to prove linear independence. Pe=1 pi=1-1 P₂ = 2-41+1² P. = 6-181 +91- (b) Call the above basis C. Find the coordinate vector (C-name) of polynomial p(/) - 7-81+31° with respect to the C basis.
To prove the given statement we can take into account the matrix produced by the tuples (1,2,0), (1,0,1) and (1,0,1). The three vectors are linearly independent if the matrix's where determinant is nonzero.
det ( -1 2 0
-1 0 1
1 0 1 ) = 4
Now that P2 has a dimension of 3, those three vectors serve as the foundation for P2 by definition.
Therefore, the polynomial forms the basis of P.
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x2+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x2, x, and -12.
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Solve this expression
(8c²) (9c)
The expression 12x + 8 represents the preimeter of a square. Write 12x+ 8 as a product. Then tell what expressions represents one side of the square.
Answer:
(3+2)
Step-by-step explanation:
Perimeter of a square = 4L
L is the length of one side of the square
Given the expression 12 + 8 that represents the perimeter of a square, factoring out 4 from both terms;
12 + 8
= (4*3)+(4*2)
= 4(3+2)
Comparing with 4L
4L = 4(3+2)
Divide both sides by 4
4L/4 = 4(3+2)/4
L = (3+2)
Hence the expression that represents one side of the square is (3+2).
Hope this helps!!! :)
Find how long it takes $2500 to double if it is invested at 6% interest compounded semiannually. Use the formula A=P(1+r/n) to solve the compound interest problem.
It will take approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $2500
Total amount = $5000
Compounded semi -anually,
so formula becomes,
Total amount = amount (1+r/200)^2t
T = [tex]A (1+\frac{r/2}{100})^{2t}[/tex])
5000 = 2500 (1+3/100)^2t
2 = [tex](1+0.03)^{2t}[/tex]
2 = [tex]1.03^{2t}[/tex]
taking log on both sides
log 2 = 2t *log 1.03
0.3/0.012 = 2t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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