if the partial sum with three terms is used to approximate the value of the convergent series ∑n=3[infinity](−1)n 1n2n∑n=3[infinity](−1)n 1n2n, what is the alternating series error b
Answers
The error bound for the approximation is 1/256.
The alternating series error bound for an alternating series of the form ∑n=a∞^(n+1)bn, where bn is a positive decreasing sequence, can be expressed as:
R_N = |b_N+1|
where N is the number of terms used to approximate the series.
In this case, we have:
b_n = 1/(n^2 * 2^n)
To find the alternating series error bound for the partial sum with three terms, we need to find the fourth term of the series and take its absolute value. So, we have:
b_4 = 1/(4^2 * 2^4) = 1/256
Therefore, the alternating series error bound for the partial sum with three terms is:
R_3 = |b_4| = 1/256
So, the error bound for the approximation is 1/256. This means that the absolute error in the approximation of the series is less than or equal to 1/256.
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Related Questions
On a coordinate plane, a circle has a center at (0, 0). Point (0, negative 10) lies on the circle.
A circle centered at the origin contains the point
(0, –9). Does (8, StartRoot 17 EndRoot) also lie on the circle? Explain.
No, the distance from the center to the point
(8, StartRoot 17 EndRoot) is not the same as the radius.
No, the radius of 10 units is different from the distance from the center to the point
(8, StartRoot 17 EndRoot).
Yes, the distance from the origin to the point
(8, StartRoot 17 EndRoot) is 9 units.
Yes, the distance from the point (0, –9) to the point (8, StartRoot 17 EndRoot) is 9 units.
Answers
The distance between point \((8, \sqrt{17})\) and the center (0,0) is of 9 units, which is less than the radius, hence the correct option is:
Yes, the distance from the origin to the point \((8, \sqrt{17})\) is of 9 units.
What is the distance between two points?Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:
\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
In this problem, we have a circle with center at (0,0) and radius 10. Hence, every point that is less than 10 units of distance from point (0,0) will be on the circle.
The distance of \((8, \sqrt{17})\) is:
\(D = \sqrt{(8 - 0)^2+(\sqrt{17} - 0)^2}\)
\(D = \sqrt{81}\)
D = 9 units.
9 < 10, hence the correct option is:
Yes, the distance from the origin to the point \((8, \sqrt{17})\) is of 9 units.
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Rewrite the equation by completing the square X^2 = -8 - 7
Answers
Answer: x= \(\sqrt{x=15i} or \sqrt{x=-5\)
c=5(y-8) solve for y
Answers
Answer:
The steps to do this :
\(c = 5(y - 8)\)
\(c = 5y - 40\)
\(c + 40 = 5y\)
\(y = \frac{c + 40}{5} \)
1. distribute 5 to y and 8 so you get c= 5y-40
2. subtract 40 over (c-40=5y)
3. finally divide by 5, getting you c-8=y :))
in the picture above, ec = 10cm, ae = 4cm, and m∠eab = 45°. find the area of the kite.
Answers
If ec = 10cm, ae = 4cm, and m∠eab = 45°, then the area of the kite is 250/49 square cm. Therefore, the correct option is (b) 250/49.
In the picture above, ec = 10 cm, ae = 4 cm, and m∠eab = 45°. Formula to find the area of a kite is: A = (d1d2)/2
Where,d1 and d2 are the diagonals of the kite. In the given diagram, a kite ABCE is shown. So, we need to find the diagonals of the kite. So, we have to find the length of diagonal AB. Diagonal AB divides the given kite into two triangles ABE and ACE. In triangle ABE,∠BAE = 90°and ∠EAB = 45°
Therefore, ∠ABE = ∠BAE - ∠EAB∠ABE = 90° - 45°∠ABE = 45°
Now, tan ∠ABE = EA/BE4/BE = tan 45°BE = 4 cm As diagonals of kite AC and BD are perpendicular to each other and their lengths are in ratio of 5:2
Diagonal AC = 5x, Diagonal BD = 2x.
Diagonal AC + Diagonal BD = 10 cm (Given ec = 10 cm)5x + 2x = 10 cm7x = 10 cmx = 10/7 cm
Therefore, Diagonal AC = 5x = 5(10/7) = 50/7 cm And, Diagonal BD = 2x = 2(10/7) = 20/7 cm
Now, we have found both the diagonals. So, let's apply the formula of the area of a kite. A = (d1d2)/2A = [(50/7)(20/7)]/2A = 500/98A = 250/49 sq cm.
Area of the kite is 250/49 square cm. Therefore, the correct option is (b) 250/49.
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HELP PLS!! I need help for question 10, answers a, b, and c! (Everything is in the picture)
Answers
Answer:
A. The line on the left
B.not sure
C. 20 dollars
Step-by-step explanation:
8.118 times 12 (I got it wrong multiple times)
Answers
Answer:
97.416Step-by-step explanation:
What is indicated by a Pearson correlation of r= +1.00 between X and Y? a. Each time X increases, there is a perfectly predictable increase in Y b. Every increase in X causes an increase in Y c. All of the other 3 choices occur with a correlation of +1.00. d. Every change in X causes a change in Y
Answers
Each time X increases, there is a perfectly predictable increase in Y is indicated by a Pearson correlation of r= +1.00 between X and Y
A Pearson correlation coefficient of +1.00 indicates a perfect positive linear relationship between the variables X and Y. It means that as X increases, Y increases in a perfectly predictable manner. The correlation coefficient of +1.00 indicates a strong and direct relationship between the two variables, where the values of Y can be precisely determined based on the values of X.
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Volume of cylinder & cone ... Help me please
Answers
Answer:
The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h.
a sign in the elevator of a college library indicates a limit of 16 persons. in addition, there is a weight limit of 2,500 pounds. assume that the average weight of students, faculty, and staff at this college is 155 pounds, that the standard deviation is 29 pounds, and that the distribution of weights of individuals on campus is approximately normal. a random sample of 16 persons from the campus will be selected.
Answers
The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%
Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.
Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.
The total weight of a group of 16 individuals can be estimated as follows:
Total weight = 16 x average weight = 16 x 155 = 2480 pounds
To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:
Standard deviation of total weight = square root of (n x variance)
where n is the sample size (16) and variance is the square of the standard deviation (29 squared).
Standard deviation of total weight = square root of (16 x 29^2) = 232.74
Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:
Z-score = (2,500 - 2,480) / 232.74 = 0.86
Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.
Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.
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The 2017 balance sheet of Kerber's Tennis Shop, Inc., showed long-term debt of $5 million, and the 2018 balance sheet showed long-term debt of $5.2 million. The 2018 income statement showed an interest expense of $165,000. During 2018, the company had a cash flow to stockholders for the year was $70,000. Suppose you also know that the firm’s net capital spending for 2018 was $1,370,000, and that the firm reduced its net working capital investment by $69,000. What was the firm’s 2018 operating cash flow, or OCF?
Griffin's Goat Farm, Inc., has sales of $686,000, costs of $332,000, depreciation expense of $65,000, interest expense of $48,500, and a tax rate of 24 percent. What is the net income for this firm?
Answers
The net income for Griffin's Goat Farm, Inc., was \(\$184,340\).
The operating cash flow (OCF) for Kerber's Tennis Shop, we can use the following formula:
\(OCF = EBIT + Depreciation - Taxes + \triangle Working Capital\)
where EBIT is earnings before interest and taxes.
Calculate EBIT by subtracting interest expense from operating income:
EBIT = Operating Income - Interest Expense
We do not have the information for operating income, but we can use the fact that interest expense was. \(\$165,000\) to calculate EBIT.
EBIT = Interest Expense / (1 - Tax Rate)
= \(\$165,000 / (1 - 0)\)
= \(\$165,000\)
Calculate the change in working capital (Δ Working Capital). We are told that the company reduced its net working capital investment by \(\$69,000\), which means that working capital increased by \(\$69,000\).
Therefore:
\(\triangle Working Capital = \$69,000\)
Now, we can calculate OCF:
OCF = EBIT + Depreciation - Taxes + Δ Working Capital
=\(\$165,000 + 0 - 0 +\ $69,000\)
=\(\$234,000\)
Therefore, the firm’s 2018 operating cash flow (OCF) was \(\$234,000\) .
To calculate the net income for Griffin's Goat Farm, we can use the following formula:
Net Income = EBIT - Interest Expense - Taxes
where EBIT is earnings before interest and taxes. We can calculate EBIT as:
EBIT = Sales - Costs - Depreciation
= \(\$686,000 - \$332,000 - \$65,000\)
=\(\$289,000\)
Next, we need to calculate taxes. We are given a tax rate of 24%, so:
Taxes = Tax Rate x (EBIT - Depreciation)
= \(0.24 \times (\$289,000 - \$65,000)= \$56,160\)
Now, we can calculate net income:
Net Income = EBIT - Interest Expense - Taxes
= \(\$289,000 - \$48,500 - \$56,160= \$184,340\)
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A survey company must contact 136 people via phone calls. How many buttons must be pushed to make the 136 long distance calls
Answers
A survey company must contact 136 people via phone calls. The no.of buttons that must be pushed to make the 136 long-distance calls is
136 ✖ 10 = 1,360 buttons.
A survey is a study approach used for accumulating information from a predefined institution of respondents to benefit records and insights into diverse subjects of the hobby. They can have multiple functions, and researchers can conduct it in lots of approaches relying on the method chosen and have a look at's intention.
A survey can be used to investigate the characteristics, behaviors, or evaluations of a set of human beings. Those research gear may be used to ask questions about demographic information about traits which includes intercourse, faith, ethnicity, and profits.
In studies of human subjects, a survey is a list of questions aimed at extracting precise information from a selected institution of human beings. Surveys may be conducted with the aid of telephone, mail, thru the net, and additionally at road corners or in department stores.
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$10,000 for 5 years at 4% interest
Answers
Simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
As given in the question,
Simple Interest:
The simple interest is an amount that is paid for loan or borrowed money over a certain period at a fixed percentage of borrowed money.
Principal amount:
Principal amount is the money that is taken as loan or borrowed.
Formula of Simple Interest:
Simple interest = Principal amount × Rate × Time
Since,
Principal amount = $10,000
Rate = 4% per year
Time = 5 years
Then,
Simple interest = 10,000 × 4 × 5
Simple interest = $ 12000
Total value after 5 years = $ 12000
Principal amount = $ 10000
Interest Earned = (Total value) - (Principal amount)
Interest Earned = $ 12000 - $ 10000
Interest Earned = $ 2000
Therefore, simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
The complete question is:
Fabian is taking out a loan in the amount of $10,000. His choices for the loan are a 5-year loan at 4% rate of interest .What is the amount of simple interest and interest earned Fabian would have to pay?
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The sum of an integer and seven times next consecutive odd integers -26 find the value of the lesser integer
Answers
Answer:
-5
Step-by-step explanation:
Let n = an integer
Let (n+2) = the next consecutive odd integer
n + 7( n + 2) = -26 Distribute the 7
n + 7n + 7(2) = -26
n + 7n + 14 = -26 Combine like terms
8n +14 = -26 Subtract 14 from both sides
8n + 14 - 14 = -26 -14
8n = -40 Divide both sides by 8
n = -5
The next consecutive odd integer would be -3
Consecutive just means the next number.
Which of the following sets of values has the greatest
variability?
Group of answer choices
A) 1, 4, 7, 9, 11
B) 2, 2, 3, 3, 4
C) 7, 7, 8, 9, 9
D) 2, 3, 5, 7, 8
Answers
Given that g(x) = x°, find each of the following.
a) g(1)
b) g(-2)
c) g(-x)
d) g(3y)
e) g(1 + h)
Answers
present value of $13450.00 due in two years and nine months if interest is 7.8% p.a. semi-annually.
Answers
The present value of $13,450.00 due in two years and nine months, with an interest rate of 7.8% p.a. compounded semi-annually, is approximately $11,539.32.
To calculate the present value, we need to use the formula for compound interest:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = Present Value
FV = Future Value
r = Annual interest rate (in decimal form)
n = Number of compounding periods per year
t = Number of years
Given:
FV = $13,450.00
r = 7.8% p.a. = 0.078 (as a decimal)
n = 2 (compounded semi-annually)
t = 2 years + 9 months = 2.75 years
Substituting the values into the formula:
PV = 13,450 / (1 + 0.078/2)^(2*2.75)
PV = 13,450 / (1 + 0.039)^5.5
PV = 13,450 / (1.039)^5.5
PV ≈ $11,539.32
The present value of $13,450.00 due in two years and nine months, with an interest rate of 7.8% p.a. compounded semi-annually, is approximately $11,539.32. This means that if you were to receive $13,450.00 after two years and nine months, and you have an investment opportunity with a 7.8% interest rate compounded semi-annually, the present value of that future amount would be approximately $11,539.32.
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PLEASE HELP ASAP
During a lab experiment, the temperature of a liquid changes from 6 2/5°F to 10 3/4°F.
What is the percent of increase in the temperature of the liquid?
Enter your answer in the box as a percent rounded to the nearest hundredth.
Answers
Answer: 67.97%
Step-by-step explanation: I took the test. THE ANSWER IS NOT 39.56%.
Answer:
67.97
Step-by-step explanation:
I took the test
What numbers fill the boxes in this equation?
Answers
By algebra properties, the complete algebraic equation is now described:
a · x · (x + 3) + 7 · x · (2 · x + 1) = 5 · x · (a · x + 5), where a = 7 / 2.
How to complete an algebraic equation by comparing the terms
An algebraic equation is shown herein, this expression must completed by filling the blanks. This can be done by clearing a variable through algebra properties:
a · x · (x + 3) + 7 · x · (2 · x + 1) = 5 · x · (a · x + 5)
a · x² + 3 · a + 14 · x² + 7 · x = 5 · a · x² + 25 · x
(a + 14) · x² + 7 · x + 3 · a = 5 · a · x² + 25 · x
Then, by comparing terms:
a + 14 = 5 · a
14 = 4 · a
a = 14 / 4
a = 7 / 2
The complete expression is introduced below:
(7 / 2) · x · (x + 3) + 7 · x · (2 · x + 1) = 5 · x · [(7 / 2) · x + 5]
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What are some benefits of representing data sets using frequency distributions What are some benefits of using graphs of frequency distributions? What are some benefits of representing data sets using frequency distributions?
a. Organizing the data into frequency distribution can make patterns within the data more evident:
b. Organizing the data into frequency distribution makes it possible to graph quantitative data
c. It is easier t0 determine the minimum and maximum values of a data set when has been arranged into a frequency distribution.
What are some benefits of using graphs of frequency distributions?
a. It can be easier to determine the class boundaries by looking at a graph of the frequency distribution_
b. Graphing a frequency distribution makes possible to determine the relative frequencies of each of the classes_
c. It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution_
d. Graphing frequency distribution makes it possible to find the total number of observations.
Answers
Representing data sets using frequency distributions and using graphs of frequency distributions can have several benefits. Here are some of the benefits of representing data sets using frequency distributions:
a) Organizing the data into afrequency distribution can make patterns within the data more evident. By organizing the data into classes or bins and counting the number of observations within each class, you can see how the data is distributed and identify patterns or trends that may not be immediately apparent when looking at the raw data.
b) Organizing the data into a frequency distribution makes it possible to graph quantitative data. Many types of graphs, such as bar graphs and histograms, are based on frequency distributions and can be used to visualize the distribution of data.
c) It is easier to determine the minimum and maximum values of a data set when it has been arranged into a frequency distribution. By organizing the data into classes, you can easily see the range of values within each class and determine the overall range of the data set.
Here are some of the benefits of using graphs of frequency distributions:
a) It can be easier to determine the class boundaries by looking at a graph of the frequency distribution. When you create a graph of a frequency distribution, the class boundaries are often marked along the x-axis, which makes it easy to see where one class ends and the next begins.
b) Graphing a frequency distribution makes it possible to determine the relative frequencies of each of the classes. By looking at the heights of the bars on a bar graph or the heights of the columns on a histogram, you can see how each class compares to the others and determine the overall shape of the distribution.
c) It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution. Graphs are a visual representation of data, and they can help you see patterns or trends that may not be immediately apparent when looking at the data in tabular form.
d) Graphing frequency distributions makes it possible to find the total number of observations. By adding up the frequencies of all the classes, you can determine the total number of observations in the data set.
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Help please. thanks :)
Answers
Answer:
A. x=8 y=21
Step-by-step explanation:
line l and line m are parallel, and both angles that have x in the values are on the same side, so they are equal to each other.
7x+12=12x-28
+28 +28
7x+40=12x
-7x -7x
40=5x
/5 /5
8=x
Since A is the only choice that has x=8, it must be the right answer.
Answer:
x = 8, y = 21
Step-by-step explanation:
parallel means they're equal so..
7x + 12 = 12x - 28
-7x -7x
12 = 5x -28
+28 +28
40 = 5x
8 = x
plug in 8 to 12x - 28
12(8) - 28
96 - 28 = 68
180 - 68 = 112
9y - 77 = 112
+77 +77
9y = 189
y = 21
Please help me immediately
Answers
The exponent is 81.m⁴.n²⁰
Here we have to determine the sign for exponential or radical expression
\((-3mn^5)^4\)
Now using the exponent power rule (aˣ)ⁿ = aˣⁿ =. We get
= 81.m⁴.n²⁰
Therefore the exponent as a product of power is 81.
What is an exponent?The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the phrase "2 to the 3rd" (written as 23) means:
2 x 2 x 2 = 8.
23 and 2 x 3 = 6 are not equivalent.
Keep in mind that any number is itself when raised to the power of 1.
The outcome is always a fraction when the exponent is negative. A numerator and a denominator make up fractions. The numerator in this case is always 1. Assuming the negative exponent is positive, raise the number to that power to determine the denominator
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Part A
Tom's house cost $100000 in the year 2000.
In 2008 he sold his house for $125000. Was the change in price a positive or negative change?
Answer:
Positive
V
Part B
What was the percentage of change in the price of the house?
Answer:
%
Answers
There was a 125% change in the price of the house.
The answer can be deduced to be above 100% because the revised price represented an increase from the initial 100,000.
Tom's house cost $100000 in the year 2000.
In 2008 he sold his house for $125000.
Whatever the case, in order to solve this problem,
you must divide 100,000 by 125,000 to discover the answer. 125,000/100,000=1.25.
Then 1.25 can be converted to 125%.
So, There was a 125% change in the price of the house.
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Given the equation A=
b−c
π
, where b=95.68±0.05 and c=43.28±0.02. What is the absolute uncertainty in A ? Select one: a. 0.05995±0.00007 b. 0.05995±0.00008 c. 05995±0.00006
Answers
The absolute uncertainty in A is approximately 0.022254. Rounding it to the same number of decimal places as A, we express the absolute uncertainty as 0.05995 ± 0.00008.
To calculate the absolute uncertainty in A, we need to determine the maximum and minimum values that A can take based on the uncertainties in b and c. The absolute uncertainty in A can be found by propagating the uncertainties through the equation.
Given:
b = 95.68 ± 0.05
c = 43.28 ± 0.02
To find the absolute uncertainty in A, we can use the formula for the absolute uncertainty in a function of two variables:
ΔA = |∂A/∂b| * Δb + |∂A/∂c| * Δc
First, let's calculate the partial derivatives of A with respect to b and c:
∂A/∂b = 1/π
∂A/∂c = -1/π
Substituting the given values and uncertainties, we have:
ΔA = |1/π| * Δb + |-1/π| * Δc
= (1/π) * 0.05 + (1/π) * 0.02
= 0.07/π
Since the value of π is a constant, we can approximate it to a certain number of decimal places. Let's assume π is known to 5 decimal places, which is commonly used:
π ≈ 3.14159
Substituting this value into the equation, we get:
ΔA ≈ 0.07/3.14159
≈ 0.022254
Therefore, the absolute uncertainty in A is approximately 0.022254.
To express the result in the proper format, we round the uncertainty to the same number of decimal places as the measured value. In this case, A is approximately 0.05995, so the absolute uncertainty in A can be written as:
ΔA = 0.05995 ± 0.00008
Therefore, the correct answer is option b. 0.05995 ± 0.00008.
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Draw a nap of the town to meet the conditions below
Answers
Answer:
Abbey lane is parallel with brittney drive
collin street is perpendicular with brittney drive
Doltan road is parallel with abbey lane
Edward street is perpendicular to doltan road
From the given conditions the map can be constructed in many ways,
we can construct the map as,
algebra test so please don’t answer unless you know you’re right.
Answers
Answer: I found the perimeter of the rectangle I got: 10x+4
Step-by-step explanation:
i need help asap plsss
Answers
justin is driving from riverton to rock springs, a distance of 144 miles. he plans to stop along the way for 15 minutes. how fast must justin drive in order to averafe 64 miles per hour for the whole trip, including the time when he stops
Answers
Justin must drive at least 67.2 miles per hour (rounded to one decimal place) to average 64 miles per hour for the whole trip, including the 15-minute stop
To average 64 miles per hour for the whole trip, Justin must complete the 144-mile distance and the 15-minute stop in a total of 144 minutes (2 hours and 24 minutes) or less.
If we subtract the 15 minutes stop from the total time, Justin will have to cover the 144 miles in 129 minutes (2 hours and 9 minutes) or less.
To determine the required speed, we can use the formula:
\(speed = \frac{distance }{time}\)
So, \(speed = \frac{144 miles}{129 minutes}=1.12 miles per minute\)
To convert this to miles per hour, we can multiply by 60:
1.12 miles per minute x 60 minutes per hour = 67.2 miles per hour
Therefore, Justin must drive at least 67.2 miles per hour (rounded to one decimal place) to average 64 miles per hour for the whole trip, including the 15-minute stop.
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2. explain what is meant by (distribution) transparency and give examples of different types of transparency.
Answers
The phenomena of hiding distribution characteristics in a system from applications and users is known as distribution transparency. Access transparency, location transparency are some examples.
Define the term (distribution) transparency?Distributed databases have the attribute of distribution transparency, which keeps consumers from knowing the internal workings of the distribution.
The DDBMS designer has the option of replicating table fragments, storing them at several locations, and fragmenting tables.There are numerous distribution methods. Systems that need a wide range of management systems to pinpoint the source of resources, a product, or a service delivery process from the end user.Typically, the distributor, seller, or producer is responsible for maintaining transparency to track the many points at which resources, goods, or services are delivered.Accounting supplied by any intermediary company in the product, service, or resource flow is, of course, the usual approach to determine the degrees of value added through distribution management.Thus, access transparency, location transparency are some examples of the (distribution) transparency.
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What is the distance between points (4, 36) and (13, -4) on a coordinate plane?
Answers
The linear equation y = negative 2 x + 4 is represented on the graph below.
On a coordinate plane, a line goes through (0, 4) and (2, 0).
A second linear equation is represented by the data in the table.
x
y
–4
–3
0
–1
2
0
6
2
What is the solution to the system of equations?
(2, 0)
(0, 4)
(0, –1)
(4, –4)
Answers
The solution to the system of equations will be;
⇒ (2, 0)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The first equation is,
y = - 2x + 4
And, A line goes through (0, 4) and (2, 0).
Now,
For the second linear equation;
The coordinates are,
(-4, -3) (0, -1) , (2, 0) , (6, 2)
Hence, The equation of line passes through the points (-4, -3) and (0, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - (-3)) / (0 - (-4))
m = 2 / 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - (-3)= 1/2 (x - (-4))
⇒ y + 3 = 1/2 (x + 4)
⇒ y = 1/2x + 2 - 3
⇒ y = 1/2x - 1
Now, We find the value of system of equations;
y = - 2x + 4
y = 1/2x - 1
Solve both above equation, we get;
1/2x - 1 = - 2x + 4
1/2x + 2x = 4 + 1
5/2x = 5
x = 2
And, y = 1/2 (2) - 1 = 0
Thus, The solution to the system of equations will be;
⇒ (2, 0)
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Answer:
A
Step-by-step explanation: