Lin's family has completed approximately 86.15% of the total Distance to her grandmother's house.
The percentage of the distance Lin's family has completed, the ratio of the distance they have traveled to the total distance.
The distance traveled is 325 miles, and the total distance to Lin's grandmother's house is 377 miles.
To calculate the percentage, we can use the following formula:
Percentage = (Distance Traveled / Total Distance) * 100
Plugging in the values, we have:
Percentage = (325 / 377) * 100
= 0.8615 * 100
= 86.15
Therefore, Lin's family has completed approximately 86.15% of the total distance to her grandmother's house.
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Which transformations are needed to transform the graph of f(x) = 4^x to the
graph of g(x) = (4)(x+³) — 2
-
Select 2 correct answer(s)
Horizontal translation 2 units right
Vertical translation 2 units up
Vertical translation 3 units up
Vertical translation 2 units down
Horizontal translation 3 units right
Horizontal translation 3 units left
Answer:
Horizontal translation 3 units left
Vertical translation 2 units down
Step-by-step explanation:
Inside the parent function is horizontal.
Outside the parent function is vertical.
using properties of the type of triangle you have identified (isosceles) (QR and RS are equal), set up a problem and solve for x
Q: 8x-17
R: 19x+4
S: 5x+1
The required required value of angles are 31, 118, 31.
Explain isosceles triangle.An Isosceles triangle is a triangle that has two equal sides. Also, the two angles opposite the two equal sides are equal. In other words, we can say that “An isosceles triangle is a triangle which has two congruent sides“.
According to question:We have,
∠Q = 8x-17, ∠R = 19x+4, ∠S = 5x+1
So,
∠Q + ∠R + ∠S = 180
= 8x-17 + 19x+4 + 5x+1
= 32x - 12 = 180
= 32x = 192
x = 6
Angles are;
∠Q = 8x-17 = 8(6)-17 = 31
∠R = 19x+4 = 19(6)+4 = 118
∠S = 5x+1 = 5(6)+1 = 31
Thus, required value of angles are 31, 118, 31.
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Anyone able to assist with the last question
The graph of the equation x^2-x-2=3 is a parabola which opens downward.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of two expressions separated by an equals sign (=). Equations are used to express relationships between unknowns, knowns, and constants. Equations are used to solve problems and describe the behavior of systems.
The graph intersects the x-axis at two points, x=1 and x=3.
Therefore, the solutions to the equation are x=1 and x=3.
To find an estimate of the solution, we can draw a straight line from the x-axis to the point of intersection on the parabola.
The line intersects the x-axis at a point slightly higher than x=1, so the estimated solution is x=1.5.
This is an approximate solution and is only an estimate. To find the exact solution, the quadratic formula must be used.
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1 Gavin's mother poured 1 cups of milk in his
3
5
glass. If Gavin drinks cup of the milk, what
fraction of the milk will remain in the glass?
A
11
20
B
7
20
C
9
20
D
13
20 which should I choose
Answer:
choice B ( 7/20) is the right answer.
Step-by-step explanation:
If Gavin's mother poured 1 cup of milk in the glass and Gavin drinks 1/5 of the milk, the fraction of the milk that will remain in the glass is (4/5) of 1 cup.
So, B ( 7/20) is the right answer.
Ten thousand draws are made at random with replacement from a box with ninety-nine tickets marked "0" and one ticket marked "1." True or false, and explain:
a) The sum will be around 100, give or take 10 or so.
b) There is about a 68% chance that the sum will be in the range 90 to 110.
a) The sum will be around 100, give or take 10 or so. - True
b) There is about a 68% chance that the sum will be in the range of 90 to 110. - True
a) True. The expected value of a single draw is (0.990)+(0.011)=0.01, and the expected value of 10,000 draws is 0.0110,000=100. The standard deviation of a single draw is the square root of (0.990^2)+(0.011^2)=0.01. So, the standard deviation of 10,000 draws is sqrt(10,0000.01)=10. This means that the sum of 10,000 draws will be around 100, give or take 10 or so.
b) True. The sum of 10,000 draws follows a normal distribution with a mean of 100 and a standard deviation of 10. Using the 68-95-99.7 rule, 68% of the data falls within one standard deviation of the mean. So, the chance that the sum will be in the range of 90 to 110 is 68%.
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In Exercises 5-8, use the graph which shows the right-hand and left-hand behavior of a polynomial function f.
The other information required while using the intermediate value theorem to show the existence of zero for the polynomial function plotted is
f(x₁) < 0 and f(x₂) > 0
What is intermediate value theorem?The intermediate value theorem says that if "f" is a continuous function across a closed interval [a, b] with values f(a) and f(b) at its endpoints, then the function takes any value at a point inside the interval that is between the values of f(a) and f(b).
The root of a polynomial is the value of y when x is zero. hence to show that there is a zero between the points x₁ and x₂ there is a need to show there was a change of sign in the output value
Using the graph
f(x₁) is less than 0 which shows negative values f(x₂) is greater than 0 which shows positive valuesAt the point of change of sign is the required zero
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The graph of two functions is shown
AY
If x=3 is a solution to f(x)=x²-x and g(x)=2x, why is it also a solution to f(x) = g(x)
(1 point)
O It is a solution to f(x) = g(x) because it is the x-intercept of the two graphs
O it is a solution to f(x) = g(x) because it is the y-intercept of the two graphs.
O It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect
O it is a solution to f(x) = g(x) because both graphs are positive at x = 3.
The correct option regarding the solution to the system of equations is given as follows:
It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect.
How to obtain the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
The point of intersection in this problem has a x-coordinate of 3, hence the third option is the correct option.
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parallelograms are ___ rectangles
Parallelograms are all rectangles because a rectangle has two sets of parallel sides and two pairs of opposite sides that are equal.
What is parallelogram?Parallelogram can be defined as a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
There are five important properties of parallelograms such as:
Opposite sides are congruent (AB = DC)Opposite angels are congruent (D = B)Consecutive angles are supplementary (A + D = 180°)If one angle is right, then all angles are rightThe diagonals of a parallelogram bisect each otherTherefore all rectangles are parallelograms because a rectangle has two sets of parallel sides and two pairs of opposite sides that are equal. It abides by all the properties of a parallelogram.
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Is -3/5 greater than or less than -2/3
Answer:
Step-by-step explanation:
So, to compare fractions, we need them to have the same denominators because for example, 4/1 = 4 and 4/2 = 2 is totally different.
(in that case, we could have looked at the denominators, and the fraction with the smallest denominator would be the greater one since the numerators are the same, but it was just an example)
To do that, we look at them : we see -3/5 and -2/3
3 is not a multiple of 5, neither 5 is a multiple of 3, so we use 3*5 =15
(if it was 3 and 6, we could have used 6/2 = 3 or 3*2 = 6)
Next move, we put the fractions on 15 : [tex]\frac{-2}{3} =\frac{-2*5}{3*5} =\frac{-10}{15}[/tex] and [tex]\frac{-3}{5} =\frac{-3*3}{5*3} =\frac{-9}{15}[/tex]
Now, we look at the numerators : -10 < -9
(don't forget they're negative numbers )
And to conclude :
[tex]\frac{-10}{15} < \frac{-9}{15\\}\\\frac{-2}{3} < \frac{-3}{5}[/tex] hope it helps :)
PLEASE HELP!!!!!
Isa's family uses sap to make maple syrup. The table shows the temperature of the sap as it heats up. Find the slope and y-intercept then write the equation in slope intercept form. Interpret the meaning of this equation.
Time (h)
Temp (°F)
Chart:
0 1 2 3 4
38 83 128 173 218
Write a system of linear equations in two variables that has a solution of (4.2, -2.5)
The system of linear equations y = x - 6.7 and y = - x + 1.7 have solution at point (x, y) = (4.2, - 2.5).
How to derive a system of two linear equations
In this problem we need to construct a system of two linear equations whose solution is point (x, y) = (4.2, - 2.5). Linear equations are algebraic equations of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableThe procedure is shown below. First, obtain the intercept of the first equation:
b = y - m · x
(x = 4.2, y = - 2.5, m = 1)
b = - 2.5 - 4.2
b = - 6.7
Second, write the first linear equation:
y = x - 6.7
Third, find the intercept of the second equation:
b = y - m · x
(x = 4.2, y = - 2.5, m = - 1)
b = - 2.5 - (- 1) · (4.2)
b = - 2.5 + 4.2
b = 1.7
Fourth, write the second linear equation:
y = - x + 1.7
Please see the image attached below for a representation of the system of linear equations.
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Can someone help me with this
Answer: D
Step-by-step explanation:
If the simple interest on 7,000 for 10 years is 3,500, then what is the interest rate?
The interest rate on 7,000 for 10 years with a simple interest of 3500 is 5.
What is the rate of a simple interestSimple interest is the amount paid on a principal amount of money that is borrowed or loaned to someone. It is calculated using the formula: SI = (P × R × T) / 100. Interest Rate (R) is a percent of the principal earned or paid.
From the question;
P = 7,000
T = 10
SI = 3500
we shall evaluate for the rate R as follows:
3500 = (7,000 × R × 10)/ 100
3500 = 70R
divide through by 70
3500/70 = 70R/70
R = 35/7
R = 5
Therefore, the rate for the amount 7,000 that will give a simple interest of 3500 for 10 years is 5
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The result of adding the numbers in the given data set
489
527
758
Assuming that 13.2% of pennies in circulation are pre-1982 copper pennies, is it surprising to randomly select 50 pennies for which 11/50 = 22% or greater? Justify your answer.
It is surprising to some extent when the probability of getting pre-1982 copper pennies is 6.6 and you get 11 pre-1982 copper pennies.
What is probability?As with "point" and "time," which we can't exactly define, the concept of "the probability of something" is one of those concepts that is still useful. The ideas in the paragraphs that follow should help you grasp the idea.
Typically, events are the "somethings" for which we consider the probabilities. We might discuss the likelihood that someone in a particular group will develop a specific disease within the next five years, the probability that the number on a die we rolled is 5, the likelihood that it will rain tomorrow, etc.
The pre-1982 copper pennies are 13.2%
That is for every 100 pennies randomly selected there will 13.2 pre-1982 copper pennies,
And for 50 pennies there will be 13.2/2 pre-1982 copper pennies
= 6.6
So the probability of getting a pre-1982 copper pennies from random 50 pennies are 6.6.
Therefore, it is surprising to some extent when the probability of getting pre-1982 copper pennies is 6.6 and you get 11 pre-1982 copper pennies.
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If the ratio of A2 to A1 was 100, what force would be required to lift a 10,000 N car?
Therefore ,As a result, the answer to the provided problem of force is (-26.46i-52.92k) Nm.
What is a force?It is capable of both pulling and pushing. Unbalanced forces are what lead to acceleration. A force is represented by the Newton (abbreviation is N). One Newton of force is required to change a weight of one kilogram's mobility by one meters per seconds (m/s) per sec. It goes like this: 1 N = 1 kg m/s2 (kg metre / second squared)
Here,
Given: There is a force F occurring at a size of F = 165 N along the parallelepiped's diagonal in this situation.
In order to calculate the force moment F around point A.
MA=rBXF
={(-600) (-88.2i+132.3j+44.1k)}
=(-52920k - 26460i) Nm
=(-26.46i-52.92k) Nm
Therefore , the solution to the given problem of force comes out to be (-26.46i-52.92k) Nm.
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three hundred fifty - two thousand five hundred seventy-six
The value of expression after subtraction is, 2,226.
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
We have to given that;
The expression is,
⇒ three hundred fifty - two thousand five hundred seventy-six
Now, We can write the expression as;
⇒ three hundred fifty - two thousand five hundred seventy-six
⇒ 350 - 2,576
After subtraction we get;
⇒ - 2,226
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Graph the solution or the following inequality on the number line
(X+3)(x-4)<0
_
Treat the,, >, or sign as a = sign when graphing an inequality.
How do you graph the solution of an inequality on a number line?Draw a circle over the number to begin plotting an inequality on a number line, such as x>3 (e.g., 3). The circle should be filled in if the sign also includes equal to (or). Leave the circle blank if the sign doesn't contain the equal to symbol (> or ).
By treating the,, >, or sign as a = sign, the inequality can be shown graphically. Make a dotted line graph of the equation if the inequality is either or. Make a solid line out of the equation if the inequality is either or.
Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers. The value is not included, as indicated by the open circle. The value is included, as indicated by the closed circle.
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Solve for b.
7+b=a
I need this for a quiz review
Answer:
b = a - 7
Step-by-step explanation:
subtract 7 from both sides of the equation
2. Determine the lateral and total surface area of the pyramid. 6.9 cm 8 cm Lateral Surface Area Total Surface Area
Answer:
Step-by-step explanation:
Step 1: Calculate the slant height of the pyramid.
Slant Height = √(6.9^2 + 8^2) = 10.1 cm
Step 2: Calculate the lateral surface area of the pyramid.
Lateral Surface Area = 4 * (1/2 * 6.9 * 10.1) = 176.5 cm^2
Step 3: Calculate the total surface area of the pyramid.
Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area = 176.5 cm^2 + (1/2 * 6.9 * 8) = 227.7 cm^2
find the y intercept of y=x^2-6x+8
The y-intercept of the expression y=x^2-6x+8 is y(0,8).
What are intercepts?
The term "intercept" refers to the location where a line or curve crosses a graph's axis. The x-intercept is the point at which the x-axis is crossed. The y-intercept is the point at which the y-axis is crossed.
The given expression is -
y = x²-6x+8
To find the y-intercept, substitute the value of x with 0.
y = x²-6x+8
y = (0)²-6(0)+8
y = 8
Therefore, the y-intercept is (0,8).
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What’s 1x+6y=8 graphed?
Answer: y = -1/6x + 1 1/3
Step-by-step explanation:
A person charges $100 to a credit card with a 24% nominal annual interest rate.
Assuming no other charges or payments are made, what is the balance on the card, in dollars, after 1 year if interest is calculated:
1. Annually: $
2. Every 6 months: $
3. Every 3 months: $
The balance (future value) on the card after 1 year if interest is calculated:
1. Annually: $124.00
2. Every 6 months: $125.44
3. Every 3 months: $126.25.
What is the future value?The future value represents the present value compounded at an interest rate into the future, using the principle of the time value of money.
The future value can be computed using an online finance calculator.
1. Interest Calculation Annually:
N (# of periods) = 1 year
I/Y (Interest per year) = 24%
PV (Present Value) = $100
PMT (Periodic Payment) = $0
Results:
FV (Account Balance) = $124.00
Total Interest = $24.00
2. Interest Calculation Every 6 months:
N (# of periods) = 2 semi periods (1 year x 2)
I/Y (Interest per year) = 24%
PV (Present Value) = $100
PMT (Periodic Payment) = $0
Results:
FV (Account Balance) = $125.44
Total Interest = $25.44
3. Interest Calculation Every 3 months:
N (# of periods) = 4 quarters (1 year x 4)
I/Y (Interest per year) = 24%
PV (Present Value) = $100
PMT (Periodic Payment) = $0
Results:
FV (Account Balance) = $126.25
Total Interest = $26.25
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A zebra can run at a constant speed of 0.6 miles per minute. How far can a zebra run in 30 minutes? Choose the equation that could be used to answer this question.
Responses
d=(0.6)(0.5) d is equal to 0 point 6 times 0 point 5
30=0.6t 30 is equal to 0 point 6 t
d=(0.6)(30) d is equal to 0 point 6 times 30
0.6=30r
The equation that can be used to answer this question concerning speed would be = d=(0.6)(30). That is option C.
What is constant speed?Constant speed is defined as the quantity that expresses the an object which travels the same distance in the same period of time.
The constant speed of the zebra = 0.6 miles per minute
Therefore, if 0.6 miles = 1 minute
d miles = 30 minutes
d miles = 30 × 0.6/1
d miles = 18 miles
Therefore the expression that can be used to answer this question would be = d=(0.6)(30).
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Simple interest easy pleas ehelp due please pls
Answer:
Part A - Option B $382.50
Part B - 11 years
Step-by-step explanation:
The formula for simple interest is
[tex]A=P(1+rt)[/tex]
[tex]A[/tex] is the final amount
[tex]P[/tex] is the initial amount
[tex]r[/tex] is the interest rate as a decimal
[tex]t[/tex] is the time
We are given
[tex]P=3000\\r=0.0425[/tex]
Part A
To evaluate the amount of interest we need to use this equation
[tex]I=Prt[/tex]
[tex]I=3000*0.0425*3[/tex]
[tex]I=382.5[/tex]
Part B
We can start with this equation, but we need to solve for [tex]t[/tex].
[tex]A=P(1+rt)[/tex]
Lets solve for [tex]t[/tex].
Divide both sides of the equation by [tex]P[/tex].
[tex]\frac{A}{P} =1+rt[/tex]
Subtract 1 from both sides of the equation.
[tex]\frac{A}{P}-1 =rt[/tex]
Divide both sides of the equation by [tex]r[/tex].
[tex]\frac{\frac{A}{P}}{r}-\frac{1}{r}=t[/tex]
Simplify the first term by multiplying the numerator by the reciprocal of the denominator.
[tex]\frac{A}{Pr} -\frac{1}{r}=t[/tex]
[tex]t=\frac{A}{Pr} -\frac{1}{r}[/tex]
Now we have an equation for time.
Substituting our values into the equation gives us
[tex]t=\frac{4402.50}{3000*0.0425} -\frac{1}{0.0425}[/tex]
[tex]t=11[/tex]
Justina surveyed students to find how many sports they play Which graph is the most appropriate to illustrate the results?
A circle graph
B venn diagram
C stem-and-leaf plot
D double line graph
Answer:
A. Circle Graph, also known as a pie chart, is the most appropriate to illustrate the results of Justina's survey.
Step-by-step explanation:
A circle graph, also known as a pie chart, is the most appropriate to illustrate the results of Justina's survey.
A circle graph is used to display the proportion of different categories of data. In the case of Justina's survey, the categories would be the different sports that the students play, and the proportion of students who play each sport would be represented by the size of the corresponding wedge in the circle graph. The circle graph allows for a clear and easy-to-understand comparison of the relative popularity of different sports among the surveyed students.
A Venn diagram is used to show the relationships between different sets of data. It's not appropriate in this case as the students are not being asked to pick two or more sports they play, but the number of sports they play.
A stem-and-leaf plot is used to display the distribution of numerical data, it's not appropriate for this case because it does not show the proportion of students playing each sport.
A double line graph is used to compare two sets of data over time. It's not appropriate for this case because it doesn't show the proportion of students playing each sport.
is it inversely proportional
A given information is inversely proportional when one value decreases at the same rate that the other increases. It should be noted that an example is speed and travel time
What is an inverse relationship?Only when two variables are directly proportional to one another's reciprocal can two variables be said to be inversely proportional. Alternately, we can state that when two variables or quantities are in inverse proportion, their product has a constant value.
One kind of proportionality relationship is inverse proportion. If two quantities are inversely related, one will increase while the other will decrease.
Note that your information is incomplete and a overview was given.
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#6
Write an equation in slope-intercept form of the line that passes through the given points.
The line y=—x-2 can be seen on the right-hand graph. the expression for m=273. A slope intercept form is one that offers both a gradient and an intercept.
What exactly is a slope-intercept form?The slope intercept format can be used once you are aware that Y = mx + b. The point-slope form is a way to express an equation for a line by utilizing just a specific point just on line and its slope. You can use the slope intercept equation, y = mx + b, to get the slope, which is defined as the rise over run and represented by the point form (x,y) (0, b). The point-slope form is a way to expression an equation for a line by utilizing just a specific point on the linear and its slope.
Here,
Given:
The line y = 3x - 1 undergoes dilation with such a scale factor of 2.
The lines y = 3x is enlarged and centered by a factor of two (scaling factor).
The chart on the right displays the equation m=273 and the line y=—x-2.
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helppp pleaseeeee im stuck on this
The closing balance of the accumulated depreciation account, obtained from the values in the table is; $3,000
What is the depreciation of an asset?Depreciation is the cost of an asset during the indicated useful life of the asset
The closing balance of the accumulated depreciation account can be found as follows;
The accumulated depreciation is the sum of the depreciation charged on an asset up to the current date.
The formula for calculating the accumulated depreciation can be presented as follows;
Accumulated depreciation = [tex]\frac{(Cost \ of\ asset - Salvage\ Value)}{Life\ of\ Asset}[/tex] × Indicated Period
The indicated period is the number of years of use for the asset
The specified table is the accumulated depreciation account which is a contra asset (that reduces the value of the asset) account, therefore, the amounts stated indicates the depreciation during a specified period
The balance b/f on January 1, 2012, (beginning of the year) is the depreciation balance brought forward, which in the table is $1,000
The depreciation on Dec 31, 2012, (the end of the year) which is the depreciation during the year is; $2000
The accumulated depreciation is therefore; $1,000 + $2,000 = $3,000
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Find the solution set of the system of linear equations represented by the augmented matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set
x4 = t
and solve for x1, x2, and x3 in terms of t.)
1 2 0 1 3
0 1 2 1 3
0 0 1 2 1
0 0 0 1 4
(x1, x2, x3, x4) =
The solution set of the system of linear equations represented by the augmented matrix is (x1, x2, x3, x4) = (2, 4, 2, -1)
How do we determine the values?To determine the values, first express the system of linear equation as represented by the augmented matrix.
The system of linear equations represented by the augmented matrix is:
1x1 + 2x2 + 0x3 + x4 = 3
0x1 + 1x2 + 2x3 + x4 = 3
0x1 + 0x2 + 1x3 + 2x4 = 1
0x1 + 0x2 + 0x3 + 1x4 = 4
By applying row operations to the matrix we can find the solution set
R2 - R1
0 -1 2 0 0
0 0 1 2 1
0 0 0 1 4
R3 - 2R1
0 -1 2 0 0
0 0 1 2 1
0 0 0 -3 2
R4 - 4R1
0 -1 2 0 0
0 0 1 2 1
0 0 0 -7 8
R3 - R2
0 -1 2 0 0
0 0 0 -1 3
0 0 0 -7 8
R4 - 7R2
0 -1 2 0 0
0 0 0 -1 3
0 0 0 0 -1
R4/ -1
0 -1 2 0 0
0 0 0 -1 3
0 0 0 1 -1
x4 = -1
x3 = 3x4 + 1 = 2
x2 = 2x3 = 4
x1 = 3 - 2x2 - x4 = 2
Therefore, the solution set is (x1, x2, x3, x4) = (2, 4, 2, -1)
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