The value of Isabel's account after three years can be calculated using the future value of the annuity formula.
Isabelle's budget car is:
Choice 2Choice 3Choice 4Reason:
Monthly savings, PMT = $200
Account compound interest, r = 1.7%
t = Account value after 3 years is displayed as increase.
We know that:
[tex]FV =PMT * \frac{[(1+i)^n -1]}{i}[/tex] --------------------- (1)
Where;
i = r/12
⇒ n = 12 × t
From the above equation(1), we get:
[tex]FV =200 * \frac{[(1+\frac{1.7}{2} )^{12*3} -1]}{\frac{1.7}{12} }[/tex]
≈ 7381.4
Therefore,
The budget cars she can buy, those that require a down payment of less than $7,381.4, which are:
The required down payment of choice 02 is $6200.
The required down payment of choice 03 is $5100.
The required down payment of choice 04 is $7250.
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How do you find the missing side of an obtuse triangle?
Answer:
Using the cosines law
Step-by-step explanation:
So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC
On a coordinate plane, a line is drawn from point R to point Q. Point R is at (4, negative 1), and point Q is at (negative 5, 3). What are the coordinates of point P on the directed line segment from R to Q such that P is the length of the line segment from R to Q
The coordinate points of the point P is (-3.5, 2.3).
What is a coordinate plane?
Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line.
The ratio in which the point 'P' divides the line segment RQ is -
a:b = 5:1
The coordinates of the end-points of line segment RQ are -
R(4, -1) and Q(-5, 3).
The coordinates of the point H are obtained when a point H divides a line segment with end points (p, q) and (s, t) in the ratio a:b -
H = [(as + bp)/(a + b)], [(at + bq)/(a + b)]
H = [(5*-5 + 1*4)/(5 + 1)], [(5*3 + 1*-1)/(5 + 1)]
H = (-21/6, 14/6)
H = (-3.5, 2.3)
Therefore, the coordinate points are obtained as H = (-3.5, 2.3).
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Which graph best represents a function with zeros of -3,0 and 2
The graph C. represents the polynomial with zeros of -3, 0 and 2.
What are zeros of a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information about the graph's x-intercepts for the polynomial.
Alternately, we might state that the zeros of the polynomial are the x-intercept of its graph. Thus, the needed function is represented by the graph with the coordinates -3, 0, and 2.
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The complete question is as follows:
Select the correct answer.
Which graph best represents a function with zeros of -3, 0, and 2?
On a hot summer day, jay set up a lemonade stand. He kept track of how many glasses he sold on his phone
A. Write two equations that relate the number of large glasses sold i and the number of small glasses sold s. ?
B. Solve the system of equations
C. How many small glasses were sold?
D. How many large glasses were sold?
On solving the provided question, we can say that - the value of the linear equation is 2y+8x = 140
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here, we have 2y + 8x
and x = 10 ; y = 15
2y + 8x
20 + 120 = 140
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please help me with this question!
Answer:
|5-2x|<_11
=5+2x<11
=2x=11-5
2x=6
=X<-3
6. Find the quotients.
a. 0.024 ÷ 0.015
b. 0.24 0.015
c. 0.024 ÷ 0.15
d. 24 ÷ 15
Answer:
a. 1.6
b. 16
c. 0.16
d. 1.6
Which word or phrase describes the value of the function over the interval [ -6, 0]
Answer:
C is the correct answer
From the graph we can see that at the given interval [-6,0] the graph decreases from left to right.
Initially the y-values is a little over 3 and then it decreases to about 0.5 at the end of the interval.
Thus, the graph of the function over the interval [-6,0] is decreasing.
what is the half of 8
Answer:
4
Step-by-step explanation:
Half means 1/2
Half of 8
= 1/2 x 8
= 8/2
= 4
Hence, half of 8 is 4.
Answer: 4
Step-by-step explanation:4 + 4 is 8 half of 4 is eight.
Write an algebraic expression that represents five less than the product of a number and six
Answer:
6n-5
Step-by-step explanation:
let 'n' equal 'a number'
the equation above means you are multiplying 6 and that number, then reducing it by 5
Haan' hitory cla i taking a field trip to the tate capitol building. The capitol building i 50 mile from Haan' chool. The cla plan to top after 45 minute, or 0. 75 hour, to view a local monument. The bu driver plan to drive at an average peed of 40 mile per hour
The class has a 45-minute, or 0.75-hour, climb to the summit planned to observe a nearby monument. The bus driver intended to travel at a steady 40 mph. Accordingly, the average speed is 0.888.
How long does it take to drive 60 miles at 40 miles per hour?The time required to travel 20 miles at 40 mph is 30 minutes, and the time required to go 40 miles is 60 minutes. The journey of 60 miles will therefore take 90 minutes. In most cases, an hour's worth of time, this will tell you the average speed.
As a result, Ben's average speed was 50 miles per hour when he covered 150 miles in 3 hours. 40m in an hour. 12 hour to cover 20 miles. In fifteen minutes, ten miles. It is determined by dividing something's total travel distance by its total journey time. Take the earlier automobile, for instance. The average speed of the vehicle would be 70 / 2 = 35 miles per hour if it covered 70 miles in two hours.
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Complete question is: Hassan's history class is taking a field trip to the state capitol building. The capitol building is 50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to view a local monument. The bus driver plans to drive at an average speed of 40 miles per hour. Which equation can you use to find how many hours, x, the second part of the trip will take?
A seventh grade class and 7 adults go on a field trip. Two-thirds of the people ride on a bus.
Everyone else rides in vans. If 54 people ride on the bus, how many seventh graders go on the
field trip?
54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.
what is expression ?A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.
given
To find P P, divide P
P by the total number of participants (students and chaperones), which is 81.
Seventh graders totaling 81 - 7 =
74 participated in the field trip.
54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.
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we roll a fair 6 sided die 5 times. what is the probability that we get a one or a two in exactly 3 of the 5 rolls
The probability is 5/32.
Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
To roll exactly 4 odds out of 5 rolls is [tex](\frac{1}{2} )^{4}\frac{1}{2}[/tex] where the odds are 1, 3, and 5 for 3/6=1/2 and the other 1/2 is the probability of rolling an even since we want exactly 4 odds.
Since there are 5 dice being rolled there are 5 ways to order them.
So the probability is 5/32.
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i need help Please will mark brainiest
The standard form of the polynomial -n²(n² + 5n + 6) is -n⁴ - 5n³ - 6n².
How to represent polynomial in standard form?Polynomials are algebraic expressions that consist of variables and coefficients.
The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.
Hence, let's represent the polynomial in standard form as follows:
-n²(n² + 5n + 6)
Open the brackets
-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²
Hence,
-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²
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A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 7% will need repairs twice, and 4% will require three or more repairs. What is the probability that a car chosen at random will need
The probability that a car chosen at random will need no repairs = 72%; no more than one repair = 91%; some repairs = 9%
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.
28% of all vehicles will require some sort of repair; of these, 19% will require one repair, 7% will require two repairs, and 2% will require more than two repairs.
The number of vehicles that would not require any form of repairs is equal to the entire number of vehicles less the proportion that requires repairs; for example, 100% - 28% = 72%. The total number of automobiles minus the percentage that require more than one repair equals the percentage of vehicles that will require no repairs or just one
; hence, 100% - (7% + 2%) = 91%. The total number of vehicles in need of repairs is equal to the product of those with two repairs and those with three or more.
the probability that a car chosen at random will need no repairs = 72%; no more than one repair = 91%; some repairs = 9%
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Complete each nuclear fission reaction. 235 92 u 1 0 n → 90 36 kr a 56 ba 3 1 0 n a: 239 94 pu 1 0 n → b c ba 91 38 sr 3 1 0 n b: c:
a: 235 92 U + 1 0 n → 90 36 Kr + 141 56 Ba + 3 1 0 n
b: 239 94 Pu + 1 0 n → 96 38 Sr + 143 55 Ba + 3 1 0 n
c: It is not possible to complete this nuclear fission reaction as it is not a valid input. There is no nuclide with the atomic number 94 and mass number 239.
What is nuclear fission?Nuclear reactions are those that involve the nucleus of an atom. Nuclear fission involves the splitting of an atomic nucleus and the formation of two distinct atomic species.
Nuclear fission is a nuclear reaction in which the nucleus of an atom is split into two or more smaller nuclei, along with the release of a large amount of energy. In the first reaction, an atom of Uranium-235 (U-235) is hit by a neutron, which causes the nucleus to split into Krypton-90 (Kr-90) and Barium-141 (Ba-141) along with 3 neutrons. In the second reaction, an atom of Plutonium-239 (Pu-239) is hit by a neutron, which causes the nucleus to split into Strontium-96 (Sr-96) and Barium-143 (Ba-143) along with 3 neutrons.
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I don't understand help
Volume of the triangle is 1420m³ given in the question.
What is Volume?There are various volumes for various geometric shapes. Cubes, cuboids, spheres, cylinders, cones, etc. are examples of common 3D shapes that we encounter on a daily basis.
Finding the volume is simple when dealing with shapes with a flat surface, like a cube or a cuboid. Cones, cylinders, and spheres are examples of curved shapes, and it is necessary to take into account both their curved surfaces' dimensions and their overall curvature. Possibly their diameters or radii
The term "irregular solids" refers to solids that lack precise measurements or shapes. A fixed formula that can be used to calculate the volumes of such solids is typically absent. It is possible to obtain these volumes in a variety of ways, one of which is the liquid displacement method, which is based on the Archimedes Principle.
Now volume triangle = area × height
⇒ 1/2 × 20 × 14.2 × 10
= 1420m³
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How many pieces of 2/3 yard can I cut if I have 6 1/3 yards of material
Answer:
9
Step-by-step explanation:
6 1/3 yards of material is 19/3 yards total. 6 yards broken into thirds is 18/3. 18 divided by 2 is 9. There are 9 total pieces to cut, and an extra 1/3 left over
A boat heading out to sea starts out at Point AA, at a horizontal distance of 862 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 15^{\circ}
∘
. At some later time, the crew measures the angle of elevation from point BB to be 8^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary
The distance from point A to point B is 781.5 ft.
Since the angle of elevation from point A to the lighthouse is 15 degrees, use the tangent function to find the height of the lighthouse. Let x be the height of the lighthouse,
tan(15°) = x / 862
Solve for x.
x = 862 (tan(15°))
Similarly, let y be the distance from point B to the lighthouse,
tan(8°) = x / y
Solve for y.
tan(8°) = 862 (tan(15°)) / y
y = 862 (tan(15°)) / tan(8°)
y = 1643.45 feet
Subtract 862 from 1643.45 to get the distance from point A to point B.
distance from point A to point B = 1643.45 - 862 = 781.45 ft = 781.5 ft
Therefore, the distance from point A to point B is 781.5 ft.
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What is the 2 step rule in math?
The Two steps equation in mathematics are the equations that can be solved within exactly two steps.
What is a Two Step Equation ?
The Two Step Equation are the algebraic problems that just take two steps to solve. It is a linear equation in one variable.
When solving the two step equation, we have to perform operation on both sides of the equation .
For Example : Solve [tex]2x+6=12[/tex] ;
Step1 : we Subtract -6 from both sides to isolate variable x.
⇒ [tex]2x + 6 - 6 = 12 - 6[/tex]
⇒ [tex]2x = 6[/tex]
Step2 : We Divide both the sides of equation by 2 and solve for x.
⇒ [tex]\frac{2x}{2} =\frac{6}{2}[/tex]
⇒ [tex]x = 3[/tex] ;
Therefore , the equation is solved in two steps .
The given question is incomplete , the complete question is
What is the two step equation in math ?
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What is the length of ab
A triangle is a three-sided polygon with three vertices. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The correct answer Is option c) 6.
What is triangle?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
The diagram shows us a triangle [tex]$\mathrm{ABC}$[/tex], which
[tex]$$m \angle A=m \angle C=63^{\circ}, \quad A B=3 x$$[/tex]
units and [tex]$B C=(4 x-2)$[/tex] units.
The task Is to determine the length of the slde [tex]$\mathrm{AB}$[/tex].
[tex]$\mathrm{ABC}$[/tex] has the following
[tex]$$m \angle A=m \angle C$$[/tex]
In a triangle, we understand that
If the measurements of two angles are equal, then the lengths of the sides or each side are also equal.
so we must have
[tex]B C=A B \\\Rightarrow 4 x-2=3 x \Rightarrow 4 x-3 x=2 \Rightarrow x=2 .\end{aligned}$$[/tex]
As a result, [tex]$\mathrm{AB}$[/tex] will be of length
[tex]$$A B=3 x=3 \times 2=6$$[/tex]
As a result, the side [tex]$A B$[/tex] is 6 units long.
Therefore, the correct answer Is option c) 6.
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What is the x-intercept of the graph of y x2 − 4x 4?
The x-intercept for the graph of y is found to be at x = 2.
Define the term x-intercept?The points where such a line crosses an axis are known as the x-intercept and the y-intercept, respectively.The graph's intersection with the x-axis is known as the x-intercept.Therefore, the y coordinate would be zero at that time.The quadratic equation given is
y = x² - 4x + 4
Put y = 0
0 = x² - 4x + 4
It becomes perfect square for (x - 2).
It can be written as;
(x - 2)² = 0
Take square root on the both sides
x - 2 = 0
x = 2
Thus, the x-intercept for the graph of y is found to be at x = 2.
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The correct question is-
What is the x-intercept of the graph of y = x² - 4x + 4?
Select all the as that inequalities that have the same solution as -4x<20
A. -x<5
B. 4x>-20
C. 4x<20
D. X<-5
E. X>5
F. X>-5
Answer:
A, B, F
Step-by-step explanation:
Divide both sides of -4x<20 by 4, and we have A
Multiply both sides of -4x<20 by -1, since -1 is a negative number, we reverse the inequality, and we have B
Multiply both sides of -x<5 (A) by -1, since -1 is a negative number, we reverse the inequality, and we have F
The width of a rectangle is 5x-1.5 feet and the length is 1.5x+5 feet. Find the perimeter of the rectangle.
7th grade
The perimeter of the rectangle is 13x+7 feet
What is the area of the rectangle?The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.
Given here: The width of a rectangle is 5x-1.5 feet and the length is 1.5x+5 feet. Therefore the perimeter of the rectangle is given by
= 2(5x-1.5+1.5x+5)
=2(6.5x+3.5)
= 13x+7
Hence, The perimeter of the rectangle is 13x+7 feet
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YG and h are parallel. what is the value of n
Answer:
139⁰
Step-by-step explanation:
since g and h are parallel
then n= 139⁰ (corresponding angles)
Solve the Linear system by using substitution.
y= -3x -1
4x+3y=2
The solution for the given system of equations is (-1, 2).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of linear equations are y=-3x-1 ------(I) and 4x+3y=2 ------(II).
Substitute y=-3x-1 in equation (II), we get
4x+3(-3x-1)=2
4x-9x-3=2
-5x=5
x=-1
Substitute x=-1 in equation (I), we get
y=-3(-1)-1
y=2
Therefore, the solution for the given system of equations is (-1, 2).
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I GIVE THANKS AND MARK BRAINLIEST
WHAT ARE THE CORRECT ANSWER(S)?
On solving the provided question, we can say that - the slope of the following will be slope, m = [tex]4-6/4-2 = -2/2 = -1[/tex]
what is slope?A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
here,
(x1,x2) = (6,4)
(y1,y2) = (2,4)
slope, m = 4-6/4-2 = -2/2 = -1
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On solving the provided question, we can say that - the slope of the following will be slope, m = -1
what is slope?
A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
here,
(x1,x2) = (6,4)
(y1,y2) = (2,4)
slope, m = 4-6/4-2 = -2/2 = -1
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Benjamin invested $66,000 in an account paying an interest rate of 63%
compounded annually. Christian invested $66,000 in an account paying an interest
rate of 5% compounded continuously. After 19 years, how much more money would
Benjamin have in his account than Christian, to the nearest dollar?
Answer:
$16,755
Step-by-step explanation:
You want the difference in interest earned on $66,000 after 19 years between an account earning 6 3/8% compounded annually, and one earning 5 3/4% compounded continuously.
Interest formulasThe formula for the account value multiplier when interest is compounded annually is ...
k = (1 +r)^t . . . . . . compounded annually at rate r for t years
When interest is compounded continuously, the multiplier is ...
k = e^(rt)
ApplicationThe difference in account values between the two rates is ...
∆value = $66,000·(1 +0.06375)^19 -e^(0.0575·19))
∆value ≈ $16,754.70
Benjamin will have about $16,755 more than Christian after 19 years.
A cylindrical aluminum soda can is to hold 12 ounces of tasty beverage. What are the dimensions of the can that will minimize the amount of aluminum used
A cylindrical can with volume 355 ml will use the least aluminum if its radius is about 3.84 cm and its height is about 7.67 cm.
What is a reasonable approximation for the volume of a soda can?The soda cans are advertised as having a volume of 12 ounces, or 355 milliliters. The remaining head space is just under 25 ml. The can weighs about 13 g by itself. 39 g, or about 11%, of sugar, make up 355 ml of Coke.
How much pressure does a 12 oz. soda can typically hold?When canned at 4 °C and stored at 20 °C, 12 oz. soda cans typically have pressures of about 120 kPa and 250 kPa, respectively. A 7UP® can that has been refrigerated contains 210 kPa of pressure. Pepsi-Cola®, on the other hand, has 276 kPa at about 16 °C.
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What is the coefficient of x² in 2 X² x³?
The coefficient of x² in 2 x² x³ is 2 n with number.
2 x² x³
= 2 x² (x³)
= 2 x² (x x x)
= 2 x² x x x
The coefficient of x² is 2.The expression 2 x² x³ can be written as 2 x² (x³). This can be further simplified to 2 x² (x x x). The coefficient of x² is 2, which means that the coefficient of x² in 2 x² x³ is 2. The coefficient of a term is the numerical factor of the term, or the number that is multiplied with the term. In this case, the coefficient of x² is 2, as it is the number multiplied with x².
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What line is parallel to 2x 3y 6 at 2 3 )?
The line parallel to the given line 2x+3y=6 is 2x+3y=13.
The general equation of a line is y=mx+c where m is the slope of the line and c is the y-intercept.
The slope of the given line 2x+3y=6 is
3y=(-2x)+6
y=(-2/3)x+2
y=mx+c where m is the slope of the line
so the slope of the given line is (-2/3)
as the slope of two parallel lines is equal so the slope of the line parallel to the given line is also (-2/3)
(y-y1)=m(x-x1) where x1 is the x-coordinate and y1 is the y-coordinate.
Here x1=2 and y1=3
(y-3)=m(x-2)
y-3=(-2/3)x+4/3
3y-9=(-2x)+4
3y+2x=13
2x+3y=13
The line 2x+3y=13 is parallel to the given line 2x+3y=6.
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