Answer:
see below
Step-by-step explanation:
\(p(x)=x^3-3x-1\) and \(q(x)=x-1\)
\(p(x)+q(x)=(x^3-3x-1)+(x-1)=x^3 -2x-2\)
\(p(x)-q(x)=(x^3-3x-1)-(x-1)=x^3 -3x-1-x+1=x^3-4x\)
\(p(x) \times q(x)=(x^3-3x-1)(x-1)=x^4-x^3-3x^2+2x+1\)
\(\frac{p(x)}{q(x)} =\frac{x^2-3x-1}{x-1} =x^2+x-2-\frac{3}{x-1}\)
Step-by-step explanation:
p(x) + q(x) = x^3 - 3x - 1 + x - 1= x^3 - 2x - 2
p(x) - q(x) = x^3 - 3x - 1 - x + 1 = x^3 - 4x
p(x) x q(x) = (x^3 - 3x - 1) (x-1) = x^4- x^3 - 3x^2 +3x -x +1 = x^4 - x^3 -3x^2 + 2x +1
p(x) : q(x) = x^3 - 3x - 1/ x - 1= x( x^2 - 3 - 1) / x - 1
For the number line shown, which statement is not true? A number line shows a to the left of 0 and b to the right of 0. Point a is closer to 0 than point b.
The statement which is not true is |a| > b option (A) |a| > b is correct after applying the concept of the number line.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
The number line is shown in the picture,
From the number line, we can draw a conclusion that:
The true statements are:
- |b| < b
|a| > a
|a| < |b|
The false statement:
|a| > b
It should be:
|a| < b
Thus, the statement which is not true is |a| > b option (A) |a| > b is correct after applying the concept of the number line.
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Help with geometry on equations of circles. What would be the center of the circle and what is the length of the radius of this circle?
The coordinates of the center is (32, 40.5).
length of the radius of the circle is 73 units.
How to find the center coordinatesThe coordinates of the center is solved using the formula for midpoints expressed as
Midpoint x-coordinate = (x₁ + x₂) / 2
Midpoint y-coordinate = (y₁ + y₂) / 2
Plugging in the values:
x₁ = 8 and y₁ = 13
x₂ = 56 and y₂ =68
Midpoint x-coordinate
= (8 + 56) /2
= 64/2
= 32
Midpoint y-coordinate
= (13 + 68) /2
= 81/ 2
= 40.5
distance formula will be used to find the length of the radius of the circle
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Plugging in the values:
= √[(56 - 8)² + (68 - 13)²]
= √(48² + 55²)
= √(2304 + 3025)
= √5329
= 73
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Which of the following could be the equation of a trend line for the data shown in the scatter plot?
o A. y=-1.4x + 13
O B. y = -14x + 13
OC. y = 1.4x + 1
OD. y = -7x
Answer:
plugg in x values into the given functions.
it's option A
The length (L) of the figure is 14 mm and the width (w) is 6 mm. What is the perimeter of the shaded region? Round to the nearest tenth
The perimeter of the shaded region is 40 mm. It is calculated by adding twice the length (2L) to twice the width (2w) of the figure.
To find the perimeter of the shaded region, we need to determine the lengths of the sides of the shaded region. From the given information, we know that the length (L) of the figure is 14 mm and the width (w) is 6 mm.
The shaded region consists of two lengths and two widths of the figure. Therefore, the perimeter of the shaded region is given by:
Perimeter = 2L + 2w
Substituting the values, we have:
Perimeter = 2(14 mm) + 2(6 mm)
Perimeter = 28 mm + 12 mm
Perimeter = 40 mm
Therefore, the perimeter of the shaded region is 40 mm.
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What is the Y-INTERCEPT of the equation y = 2x + 3?
What is the slope of the equation y = 2x+3
Write and equation for a slope of -7 and a y - intercept of -15
Write 6x+y=24 in slope-intercept form
Answer:
y intercept is (0,3)
the slope is 2
slope intercept form: y= -6x+24
Step-by-step explanation:
6. 112 how big is the tip percentage at a restaurant? use technology and the restauranttips dataset to find a 95% confidence interval for the mean tip percentage (pcttip) at the restaurant. Interpret the answer in context
The 95% confidence interval for the mean tip percentage is (3.49, 4.22)
How to find confidence interval?Confidence interval is the two-sided limit consisting of the lower limit and the upper limit and the value between the two limits is the parameter value.
For this question, we have given a graph of the data, so we only need to see the data and interpret that to answer the question.
First, since confidence interval is 95% so we must see 2.5% limit for two side or equal to 0.025.
For the lower limit, see upper value of dot plot then see separate lowest 0.025 of data is 3.491 or 3.49.
For the upper limit, see lower value of dot plot then see separate highest 0.025 of data is 4.224 or 4.22.
Thus, the 95% confidence interval is (3.49, 4.22) for the mean tip percentage.
Your question is incomplete, but most probably your full question was (image attached)
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MATLAB DATA CREATION Create a 120-by-5 matrix of elements for 120 student exam grades for 5 units to be stores as matrix grades. This part is random data generation. So, you are expected to be innovat
A 120-by-5 matrix named "grades" has been created to represent the exam grades of 120 students across 5 units. The matrix contains randomly generated marks in column 1 and corresponding grades in column 2, with scores ranging from 0 to 100.
To create the matrix "grades" with dimensions 120-by-5, random data generation techniques can be employed. The first column represents the marks obtained by each student, while the second column stores the corresponding grades. The scores range from 0 to 100, indicating the full range of possible marks in the exams.
To generate random data, MATLAB offers several functions such as "rand" or "randi". In this case, the "randi" function can be utilized to generate random integers within the desired range. By using a loop to iterate through each row of the matrix, random marks can be assigned to each student.
Additionally, the grades can be assigned based on the marks obtained using appropriate thresholds. These thresholds can be predefined, or a grading scheme can be designed to determine the grades based on the marks.
By following these steps, the matrix "grades" can be populated with random exam scores and corresponding grades for 120 students across 5 units.
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MATLAB DATA CREATION Create a 120-by-5 matrix of elements for 120 student exam grades for 5 units to be stores as matrix grades. This part is random data generation. So, you are expected to be innovative in your data creation. The exams are scored on a single scale of 0 to 100. Use column 1 for marks and column 2 for grades.
Given: EFGH is a rectangle
Prove: Segment FH is congruent to Segment GE
Answer:
Step-by-step explanation:
Statements Reasons
1). FGH is a rectangle 1). Given
2). EFGH is a parallelogram 2). a. All rectangles are parallelogram
3). EF ≅ b. GH 3). Opposite sides of a parallelogram are
equal in measure
4). EH ≅ EH 4). c. Reflexive property
5). ∠FEH and ∠GHE are the 5). d. Property of a rectangle
right angles
6). ∠FEH ≅ e. ∠GHE 6). Right angle theorem
7). ΔFEH ≅ ΔGHE 7). f. SAS postulate of congruence
8). FH ≅ GE 8). g. CPCTC (corresponding parts of
congruent triangles are congruent)
show that the general solution of x = p(t)x g(t) is the sum of any particular solution x( p) of this equation and the general solution x(c) of the corresponding homogeneous equation.
The general solution of the equation \(\(x = p(t) x g(t)\)\) can be represented as the sum of a particular solution \(\(x_p\)\) and the general solution \(\(x_c\)\) of the corresponding homogeneous equation. This implies that any solution of the original equation can be expressed as the sum of these two components, and the sum satisfies the equation.
In order to demonstrate this, we establish two key points. Firstly, we show that any solution of the original equation can be written as the sum of a particular solution \(\(x_p\)\) and a solution of the homogeneous equation. By subtracting \(\(x_p\)\) from the original equation, we define a new variable\(\(y\)\) that satisfies the homogeneous equation. Therefore, any solution \(\(x\)\) can be expressed as \(\(x = x_p + y\)\), with \(\(x_p\)\) as a particular solution and \(\(y\)\) as a solution of the homogeneous equation.
Secondly, we establish that the sum of a particular solution \(\(x_p\)\) and a solution of the homogeneous equation \(\(x_c\)\) satisfies the original equation. By substituting \(\(x = x_p + x_c\)\) into the equation \(\(x = p(t) x g(t)\),\) we distribute \(\(p(t) g(t)\)\) and observe that \(\(x_p\)\) satisfies the equation. Furthermore, we can rewrite the equation as \(\(x_c = p(t) x_c g(t)\)\). Ultimately, after substituting these expressions back into the equation, we find that \(\(x_p + x_c\)\) is equivalent to \(\(x_p + x_c\)\).
Consequently, we have successfully shown that the general solution of \(\(x = p(t) x g(t)\)\) is the sum of a particular solution \(\(x_p\)\)and the general solution \(\(x_c\)\)of the corresponding homogeneous equation.
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Your the best if you could help
Answer:
see below
Step-by-step explanation:
1. a = 18, 2. n = -19, 3. x = -17, 4. v = -6, 5. a = 9, 6. x = -2, 7. k = -4, 8. m = -19
9. n = 3, 10. a = -7, 11. n = -5, 12. n = -6, 13. x = -1/3, 14. m = 2/3 15. m = -9.8
16. n = 7.9, 17. x = 0, 18. b = 2, 19. v = -8, 20. b = -4, 21. n = 3, 22. p = 3.3
There are some oranges and apples in a box.
The total number of oranges and apples is 54
The ratio of the number of oranges to the number of apples is 1:5
Work out the number of apples in the box.
Answer:
45
Step-by-step explanation:
The total amount of oranges and apples in the box are 54.
54/(1+5)
54/6
= 9
Oranges to apples is in the ratio 1:5
1×9 : 5×9
9 : 45
The number of oranges in the box are 9.
The number of apples in the box are 45.
Answer:
45 apples and 9 oranges
Step-by-step explanation:
Total = 54
Ratio = 1:5
Total Parts = 1+5 = 6
Oranges:
=> \(\frac{1}{6} * 54\)
=> 1*9
=> 9 oranges
Apples:
=> \(\frac{5}{6} * 54\)
=> 5*9
=> 45 apples
Why can a stone arch be twice as wide as a stone lintel (two columns supporting a horizontal stone) if both are built of the same material
A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.
A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.
It requires only a small fraction of the arch's width to support itself while a lintel requires the full width of the structure that it spans. Thus, a stone arch can span a larger gap than a stone lintel and be twice as wide while using the same material.
For example, the Roman Colosseum uses an arch to span the entrances and exits while the walls supporting the upper levels use a series of stone lintels to support the structure.
Moreover, the arc prevents the need for a central support structure, which would be in the way of any events taking place in the structure. The technology of arches made them fundamental to ancient Roman architecture. For example, the arches were used to construct aqueducts, which provided a steady supply of water to the city of Rome.
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Are the ratios 12/4 and 3/1 equivalent
yes
Or
no
Answer: yes
Step-by-step explanation:
12 3
4 1
to get to 3 from 12 you divide by 4 and to get from 4 to 1 you also divided by 4
A circle has a diameter with endpoints A (-4,4) and B (2,-3) . Which coordinates represent the center of the circle?
Answer:
The coordinates of the center of the circle is (-1,-0.5)
Step-by-step explanation:
The coordinates of the center are only the midpoint coordinates of the endpoint
Mathematically, that will be;
(x,y) = (x1 + x2)/2, (y1 + y2)/2
= (-4+2)/2, (4-3)/2
= (-2/2),(-1/2)
= (-1, -0.5)
The graph of y = 5x4 - x5 has an inflection point (or points) at
A. x = 3 only
B. x = 0, 3
C. x = -3 only
D. x = 0, -3
The inflection points of the given function are at x = 0 only. The answer is D.
How to find the inflection points of the given function?To find the inflection points of the given function, we need to find the second derivative of the function and set it equal to zero.
y = 5x^4 - x^5
y' = 20x^3 - 5x^4
y'' = 60x^2 - 20x^3
Setting y'' = 0, we get:
60x^2 - 20x^3 = 0
20x^2(3 - x) = 0
x = 0 or x = 3
Now, we need to determine whether these values of x correspond to inflection points. To do this, we can examine the sign of the second derivative in the intervals around each value of x.
For x < 0, y'' is positive (since both terms are positive), so there is a local minimum at x = -3.
For 0 < x < 3, y'' is negative (since 60x^2 < 20x^3), so there is a point of inflection at x = 0.
For x > 3, y'' is positive (since both terms are positive), so there is a local minimum at x = 3.
Therefore, the inflection points of the given function are at x = 0 only. The answer is D.
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3. Find the actual area of the hallway.
4. Find the actual area of the kitchen.
(REMEMBER: Final label is ft.)
Hallway = (1/2 in. (width) x (2 in. (length) + 3 in. (length)) x 6 ft. (actual size)
Hallway = (1/2 in. (width) x 5 in. (length)) x 6 ft. (actual size)
Hallway = 5/2 in. (area) x 6 ft. (actual size)
Hallway = 15 ft^2 (final answer)
Kitchen = (3 in. (width) x 3 in. (length)) x 6 ft. (actual size)
Kitchen = 9 in. (area) x 6 ft. (actual size)
Kitchen = 54 ft^2 (final answer)
Hallo this is on demos so please try and halp :D( i just organized it thats not what I think)
Answer:
Sorry
Step-by-step explanation:
Help greatly appreciated.
Find the values of x and y. I need help knowing which formula to use and what to plug into the formula. Thank you.
The value of x is 4√6. The value of y is 4√2.
What are similar triangles?
If two triangles have the same ratio of corresponding sides and an equal pair of corresponding angles, they are similar. When two or more figures have the same shape but differ in size, they are referred to as similar figures.
Consider △ABC:
Height = AC = x, Hypoteneous = BC = 4+8 = 12.
Consider △ADC:
Height = DC = 8, Base = AD = y, Hypoteneous = AC = x
Consider △ABD:
Height = AD = y, Base = 4.
The triangle ABC is similar to ADC, and ABC is similar to ABD. Since all have one right angle and one angle is common.
The ratio of the corresponding sides of similar triangles is constant.
Consider △ABC and △ADC:
AC/DC = BC/AC
x/8 = 12/x
x² = 12×8
x = 4√6.
Since ABC is similar to ADC and ABC is similar to ABD. Then ADC is similar to ABD.
Consider △ADC and △ABD:
DC/AD = AD/BD
8/y = y/4
y² = 4×8
y = 4√2
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what value of z makes this equation true?
(the equation is 10−3(z−2)=5z+7)
A z=−92
B z=−38
C z=98
D z=32
Answer:
z = 9/8
Step-by-step explanation:
10 −3(z−2) = 5z + 7
10 - 3z + 6 = 5z + 7
-3z + 16 = 5z + 7
-3z - 5z = 7-16
-8z = -9
z = 9/8
Using control charts, define five situations in which a process
is out of control and how it is recognizable on a control
chart.
Control charts are used to monitor and identify when a process is out of control. There are several situations that indicate an out-of-control process, and these can be recognized on a control chart. Here are five such situations:
A point falls outside the control limits: If a data point falls above the upper control limit or below the lower control limit, it indicates that the process is out of control. This suggests that there may be a significant change or variation in the process.
Nonrandom patterns: Nonrandom patterns in the data points on a control chart, such as a consistent upward or downward trend, cycles, or oscillations, suggest that the process is not stable. These patterns indicate the presence of special causes of variation.
Runs and streaks: A run or streak refers to a series of consecutive data points that are either above or below the central line on the control chart. Runs or streaks suggest a lack of randomness and indicate that the process is not in control.
Lack of points within control limits: If there are long stretches of data points that are consistently clustered near one control limit or the central line without points within the control limits, it suggests that the process is not stable and may be exhibiting a systematic bias or shift.
Excessive variation: If there is excessive variation in the data points on the control chart, indicated by a wide spread of points around the central line, it suggests that the process is not under control. This can be recognized when the data points exceed the expected range of variation. These situations provide clear indications that a process is out of control and requires investigation and corrective actions to address the underlying causes of the variations. Control charts help in quickly identifying these situations and facilitating timely interventions to maintain process stability and quality.
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e=-2.4t+75 how far does the anchor drop every 5 seconds?
what values of b and c make WXY congruent to FEG in
The Hypotenuse-Leg Theorem states that two right triangles are congruent if and only if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of the other right triangle.
From this theorem, we know that corresponding sides must be equal for those triangles to be congruent. Then, we get two equations
\(\begin{gathered} c-2=2c-22 \\ 4b+18=b+48 \end{gathered}\)Let's start solving the equation for b.
\(4b+18=b+48\)We can start by subtracting 18 from both sides of the equation
\(\begin{gathered} 4b+18-18=b+48-18 \\ 4b=b+30 \end{gathered}\)Now, we can subtract b from both sides.
\(\begin{gathered} 4b-b=b+30-b \\ (4-1)b=30 \\ 3b=30 \end{gathered}\)And finally, dividing both sides by 3 we have
\(\begin{gathered} \frac{3b}{3}=\frac{30}{3} \\ b=10 \end{gathered}\)Now we have our b value. b = 10. Now, let's calculate the value for c.
\(c-2=2c-22\)We can start by adding 22 to both sides of the equation
\(\begin{gathered} c-2+22=2c-22+22 \\ c+20=2c \end{gathered}\)Now, we can just subtract c from both sides to get our value
\(\begin{gathered} c+20-c=2c-c \\ 20=(2-1)c \\ c=20 \end{gathered}\)Then, we have our c value, c = 20.
Danny and his younger brother, Jeff, are comparing their trophy collections. Danny has 3 soccer trophies and 6 basketball trophies. Jeff has 2 soccer trophies and 4 basketball trophies. Do Danny and Jeff have the same ratio of soccer trophies to basketball trophies?
Answer:
Yes
Step-by-step explanation:
The ratio for Danny would be 3 / 6 which simplifies to 1 / 2
For Jeff the ratio would be 2 / 4 which simplifies to 1 / 2 as well
Assume Noah Co has the following purchases of inventory during their first month of operations
First Purchase
Second Purchase
Number of Units
130
451
Cost per unit
3.1 3.5
Assuming Noah Co sells 303 units at $14 each, what is the ending dollar balance in inventory if they use FIFO?
The ending dollar balance in inventory, using the FIFO method, is $973.
The cost of each sold unit must be tracked according to the sequence of the unit's purchase if we are to use the FIFO (First-In, First-Out) approach to calculate the ending dollar balance in inventory.
Let's begin by utilizing the FIFO approach to get COGS or the cost of goods sold. In order to attain the total number of units sold, we first sell the units from the earliest purchase (First Purchase) before moving on to the units from the second purchase (Second Purchase).
First Purchase:
Number of Units: 130
Cost per unit: $3.1
Second Purchase:
Number of Units: 451
Cost per unit: $3.5
We compute the cost based on the cost per unit from the First Purchase until we reach the total amount sold to estimate the cost of goods sold (COGS) for the 303 units sold:
Units sold from First Purchase: 130 units
COGS from First Purchase: 130 units × $3.1 = $403
Units remaining to be sold: 303 - 130 = 173 units
Units sold from Second Purchase: 173 units
COGS from Second Purchase: 173 units × $3.5 = $605.5
Total COGS = COGS from First Purchase + COGS from Second Purchase
Total COGS = $403 + $605.5 = $1,008.5
To calculate the ending dollar balance in inventory, we need to subtract the COGS from the total cost of inventory.
Total cost of inventory = (Quantity of First Purchase × Cost per unit) + (Quantity of Second Purchase × Cost per unit)
Total cost of inventory = (130 units × $3.1) + (451 units × $3.5)
Total cost of inventory = $403 + $1,578.5 = $1,981.5
Ending dollar balance in inventory = Total cost of inventory - COGS
Ending dollar balance in inventory = $1,981.5 - $1,008.5 = $973
Therefore, the ending dollar balance in inventory, using the FIFO method, is $973.
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The fish population in a certain lake rises and falls according to the formula F= 1000(30 + 17+ - 12) Here F is the number of fish at time t, where t is measured in years since January 1, 2002, when the fish population was first estimated. (a) On what date will the fish population again be the same as on January 1, 2002? (b) By what date will all the fish in the lake have died?
The fish population will be the same as on January 1, 2002 on January 1, 2017 and all the fish in the lake will have died by 2019
(a) On what date will the fish population again be the same as on January 1, 2002?The function is given as:
F(t) = 1000(30 + 15t - t^2)
Start by calculating F(0) --- population in 2002
So, we have:
F(0) = 1000(30 + 15(0) - 0^2)
F(0) = 30000
Substitute 30000 for F(t) in F(t) = 1000(30 + 15t - t^2)
1000(30 + 15t - t^2) = 30000
Divide by 1000
30 + 15t - t^2 = 30
Simplify
t^2 - 15t = 0
Divide through by t
t - 15 = 0
Solve
t = 15
This means that
Year = 2002 + 15
Year = 2017
Hence, the fish population will be the same as on January 1, 2002 on January 1, 2017
(b) By what date will all the fish in the lake have died?This means that F(t)= 0
So, we have:
1000(30 + 15t - t^2) = 0
Divide by 1000
30 + 15t - t^2 = 0
Rewrite as
t^2 - 15t - 30 = 0
Using a graphing calculator, we have
t = 17 (approximated)
This means that
Year = 2002 + 17
Year = 2019
Hence, all the fish in the lake will have died by 2019
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A hotel manager is adding a tile border around the hotel's rectangular pool. let n represent the width of the pool, in feet. the length is 3 more than 2 times the width, as shown. Write two expressions that represent the perimeter of the pool.
HURRY PLS
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Step-by-step explanation:
a bakery can make 30 donuts every 15 minutes. the rate at which the bakery make is how many donuts per minute
Answer:
30 donuts/15 minutes = 2 donuts per minute
Step-by-step explaUnit rate is done by dividing, like 50 miles/2 hours = 25 mphnation:
2 donuts
First you have ur numbers 30 and 15 divide them 30/15=2 every minute 2 donuts can be made! :)
A company makes steel rods shaped like cylinders. Each rod has a diameter of 6 centimeters and a height of 40 centimeters. The company uses, on average, 48,607cm^3 of steel each hour to make these rods. How many rods does the company make, on average, each hour?
Answer:
The number of rods used by the company is 43 rods/hour
Step-by-step explanation:
Given;
diameter of the cylinder, d = 6 cm
radius of cylinder, r = d/2 = 3 cm
height of the cylinder, h = 40 cm
Volume of the steel rod is given by;
V = πr²h
V = π(3)²(40)
V = 1131.12 cm³
The number of rods used by the company on average each hour is given by;
\(n = \frac{48,607 \ cm^3}{hour} *\frac{1}{1131.12 \ cm^3}\\\\ n = 43 \ rods/hour\)
Therefore, the number of rods used by the company is 43 rods/hour
No fake answers, thank you. I will happily give brainiest to anyone that answers them all correctly.
Is 3x-5y=20 and y=3/5x-1 perpendicular parallel or neither
They have the same slope, the lines are parallel to one another.
If two non-vertical lines that are in the same plane has the same slope, then they are said to be parallel. Two parallel lines won't ever intersect.
The slopes of two perpendicular lines are negative reciprocals. The product of the slopes of two perpendicular lines is -1
We need to put these equations into y=mx+b format.
3x-5y=20
-5y=-3x+20. (take 5x from both sides)
y=3/5 x -4 ( divide both sides by -3)
The slope is 3/5
y=3/5x-1
The slope is 3/5
Therefore, we can conclude that the lines are parallel to each other as they have same slope.
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