The ratio of two numbers is 7 to 3 and the sum of their squares is 232. Find the numbers.

Answers

Answer 1
Let the two numbers be 7x and 3x.

We know that (7x)^2 + (3x)^2 = 232.

Expanding this equation, we get 58x^2 = 232.

Dividing both sides by 58, we get x^2 = 4.

Therefore, x = +/- 2.

Plugging this value of x into the expression for the two numbers, we get that the numbers are 14 and 6, or -14 and -6.
Answer 2
Let's call the two numbers in this problem "x" and "y". We know that the ratio of x to y is 7 to 3, so we can write:

x/y = 7/3

We can use this information to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:

y = (3/7) x

Now we know that one of the numbers is equal to (3/7) times the other. We also know that the sum of their squares is 232, so we can write:

x^2 + y^2 = 232

Substituting y = (3/7) x, we get:

x^2 + (3/7)^2 x^2 = 232

Simplifying, we get:

(1 + (3/7)^2) x^2 = 232

(1 + 9/49) x^2 = 232

(58/49) x^2 = 232

x^2 = (232 * 49) / 58

x^2 = 196

Taking the square root of both sides, we get:

x = 14

Now we can use the equation y = (3/7) x to find y:

y = (3/7) * 14 = 6

Therefore, the two numbers are 14 and 6.

Related Questions

Please answer correctly and explain reasoning for brainliest (If correct) and thanks!
What are the coordinates of A’?

Answers

Check the picture below.

Match each drawing on the left with its word description on the right , some of the answer choices on the right may not be used. Line segment AB , Line AB , Point AB , Ray AB , Ray BA

Answers

1) Line AB

2) Ray AB

3) Line segment AB

4)Ray BA

The first drawing is a line AB because a line passing through two different points A and B

The second drawing is ray AB because it started at A

The third drawing is a line segment AB because it is part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints

The fourth drawing is ray BA

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inverse statement of M implies N

Answers

The inverse statement of M implies N is a negation of both the conclusion and the hypothesis.

What is an inverse statement?

An inverse statement is one in which both the hypothesis and the conclusion are negated. Let us assume a statement with the hypothesis and conclusion as follows: If they annul the law, we will drive carelessly.

The inverse of this statement will be: If they do not annul the law, we will not drive carelessly. So, both the hypothesis and the conclusion are rewritten in negative terms.

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Please help Thanks
there is a FRACTION symbol two variable symbols y and x

Answers

Step-by-step explanation:

The equation of the line (by inspection) is y = 1/2 x

if an avocado is 1$ per pound how many is it for 9 pounds?

Answers

If an avocado costs $1 per pound, the cost of 9 pounds, using multiplication, is $9.

What is multiplication?

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication involves the multiplicand, the multiplier, and the product.

The cost per pound of an avocado = $1

The total quantity considered = 9 pounds

Proportionately, the total cost of 9 pounds = $9 ($1 x 9)

Thus, based on multiplication operation, the total cost of 9 pounds is $9.00.

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Mannys pay varies directly with the number of lawns he mows. He earns $100 for mowing 4 lawns. Find k in the equation for Mannys pay. Use P=kl

Answers

Answer:

10000

otra solución es: 10⁴

what would the speed be if the tailwind of an airplane is 150 mph and the headwind remains at 100 mph

Answers

Answer:

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind.

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mph

To calculate the speed of the airplane, we need to subtract the speed of the headwind from the speed of the tailwind. Speed of airplane = (Speed of tailwind) - (Speed of headwind)Speed of airplane = (150 mph) - (100 mph)Speed of airplane = 50 mphTherefore, the speed of the airplane would be 50 mph.

What’s the correct answer to problem 14?

Answers

The distance between the two lines is about 6/√17 units, which is approximately 1.46 units

To find the distance between two parallel lines, we need to find the length of the perpendicular segment that connects them.

Both lines have the same slope (4), so they are parallel and never intersect.

The shortest distance between them will be the perpendicular distance between any point on one line and the other line.

Let's choose a point on the first line, say (0, -1), and find the perpendicular distance from this point to the second line.

We can use the formula for the distance between a point (x₁, y₁) and a line in slope-intercept form y = mx + b:

Distance = |m(x₁) - y₁+ b| /√m² + 1

Plugging in the values for the second line, we get:

Distance = |4(0) - (-1) + 5| / √4² + 1

Distance = 6 / sqrt(17)

Therefore, the distance between the two lines is about 6/√17 units, which is approximately 1.46 units

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ASAP
A rectangular prism is shown in the image.

A rectangular prism with dimensions of 3 yards by 5 yards by 5 and one half yard.

What is the volume of the prism?

forty one and one fourth yd3
fifty six and one fourth yd3
eighty two and one half yd3
165 yd3

Answers

As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards. Thus, option C—eighty two and a half yards—is the correct response.

what is volume ?

The quantity of room an object takes up in three dimensions is measured by its volume. It is frequently expressed in cubic units like cubic metres, cubic feet, and cubic centimetres. Mathematics formulas that are particular to the shape of the object can be used to calculate its volume, such as V = l w h for a rectangular shape or V = (4/3)r3 for a sphere.

given

V = lwh is the formula for calculating the volume of a rectangular prism, where l, w, and h stand for the prism's length, width, and height, respectively.

Here, the dimensions are 3 yards in length, 5 yards in breadth, and 5.5 yards in height.

As a result, the prism's volume is given by V = lwh = 3 x 5 x 5.5 = 82.5 cubic yards.

Thus, option C—eighty two and a half yards—is the correct response.

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Some varsity soccer players are paired with a junior varsity (JV) player for training purposes: 2/3 of the varsity are partnered with 3/5 of the JV. What fraction of the players are partnered for training?

Answers

Let's say there are $v$ varsity players and $j$ JV players.

The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:

$\sf\implies\:(2/3)v$

And the number of JV players partnered with a varsity player is:

$\sf\implies\:(3/5)j$

Since these two numbers represent the same group of paired players, they must be equal:

$\sf\implies\:(2/3)v = (3/5)j$

To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:

$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired

$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired

So the total fraction of players who are paired is:

$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)

Simplifying:

$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$

Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.

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[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

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Georgia has 322 beads. She buys 38 more beads. She will use a 120 beats to make bracelets and use the rest of the beads to make necklaces. Each necklace has 9 beads. What is the greatest number of necklacea georgia can make?

Answers

Applying mathematical operations, the greatest number of necklaces Georgia can make is 26.

How the mathematical operations are applied:

The total number of beads available for making bracelets and necklaces is an addition operation between the beginning inventory of beads and the additional units purchased.

A subtraction operation is performed to determine the remainder after making bracelets.

Finally, a division operation determines the greatest number of necklaces to make.

The beginning inventory of beads = 322

The units purchased = 38 beads

The total number of beads that Georgia has = 360 (322 + 38)

The number of beads required to make bracelets = 120

The remainder after making bracelets = 240 (360 - 120)

The number of beads required for each necklace = 9

The greatest number of necklaces Georgia can make = 26 (240 ÷ 9)

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Find the degree of the monomial. 3a^8b^7

Answers

The degree is 8 because it is the biggest exponent

40% of the fish are carp and 60% of the fish are bass. What’s the probability that the next three fish I catch are all carp?

Answers

Answer:

0.064 or 6.4%

----------------------------

The probability of catching a carp is 40% since 40% of the fish are carp.

We assume the fish is replaced each time so the probability of three carps is:

P = 0.4³ = 0.064 or 6.4%

Find the probability that
event A or B takes place.


Answers

Probability that event A or B takes place is, P(A or B) = 16/21.

Here from the Venn diagram we can obtain that,

Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21

Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21

Probability of occurring event A and event B both = 4/21

So, P(A) = 6/21

P(B) = 14/21

P(A and B) = 4/21

We know that the union of events formula,  

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 6/21 + 14/21 - 4/21

P(A or B) = (6 + 14 - 4)/21

P(A or B) = 16/21

Hence the value of P(A or B) = 16/21.

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Given that f (x) = StartFraction 2 Over x squared EndFraction, What is the value of f(x) when x = 2? a. 2.5 c. 1 b. 2 d. 0.5

Answers

For the given function the value of f(x) when x = 2 is 0.5, option (d) is correct.

The given function f(x) = 2/x² represents a hyperbolic curve with a vertical asymptote at x=0 and a horizontal asymptote at y=0. As x approaches infinity or negative infinity, the value of the function approaches 0.

The given function is:

f(x) = 2 ÷ x²

We are asked to find the value of f(x) when x = 2.

Substituting x = 2, we get:

f(2) = 2 ÷ 2²

= 2 ÷ 4

= 1/2

= 0.5

Alternatively, we can use the fact that 2² = 4 and simplify the expression as follows:

f(x) = 2 ÷ x²

= 2 ÷ 4

= 1/2

Then, substituting x = 2, we get the same result:

f(2) = 1/2

f = 0.5

Hence, option (d) is correct.

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On Low Budget Airlines, the maximum weight of the luggage a passenger can bring without charge is 50 pounds. Mary Ellen has decided to weigh each item as she packs her bag. Use rounding to the nearest one pound to estimate the weight of her luggage.
The estimated weight is pounds.

Answers

Answer: 50 pounds

Step-by-step explanation:

The maximum weight of the luggage a passenger can bring without charge is 50 pounds.

Mary Ellen has decided to weigh each item as she packs her bag.

weight of Suitcase = 3.65 lbs

weight of clothing = 4.35 lbs

weight of shoes = 8.67 lbs

weight of toiletries = 11.35 lbs

weight of extras = 21.63 lbs

Now we will add the weights of each items

Total weight = 3.65 + 4.35 + 8.67 + 11.35 + 21.63 = 49.65

Rounding to the nearest to the one pound will be = 50 lbs

(Since 0.65 is greater than 0.5 so by rounding off 0.65 will become 1.)

Therefore the estimated weight is 50 pounds.

write an equation of the line that passes through each pair of points (-8,0), (0,7)

Answers

y = mx + b
We already know b which is the y intercept (0,7)
y = mx + 7
Plug in given x and y (-8,0)
0 = m(-8) + 7
-7 = -8m
m = 7/8

Final equation:
y = 7/8x + 7

For the functions f and g find a. (f+g)(x), b. (f-g)(x), c. (f

Answers

The value of the given functions are:

(a) (f + g)(x) = (x -8 + 14) = x + 6

(b) (f-g)(x) = (x -8 - 14) = x - 22

(c) (f • g)(x) = (x - 8 (14)) = 14x - 112

(d) (f/g)(x) = (x - 8)/ 14

What is function?

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have the functions are as follows:

f(x)=x - 8,

g(x)=5 + 9

To solve :

a. (f + g)(x),

b. (f-g)(x),

c. (f • g)(x), and

d. (f/g)(x)

Now,

(a) (f + g)(x) = (x -8 + 14) = x + 6

(b) (f-g)(x) = (x -8 - 14) = x - 22

(c) (f • g)(x) = (x - 8 (14)) = 14x - 112

(d) (f/g)(x) = (x - 8)/ 14

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The given question is incomplete, complete question is:

For the functions f and g find a. (f+ g)(x), b. (f-g)(x), c. (f• g)(x), and d. (f/g)(x) f(x)=x - 8, g(x)=5 + 9

Mrs. Garza is buying boxes of crayons for her classroom. The table below shows the
number of crayons she can buy.

Which equation will help Mrs. Garza determine the number of crayons she will get with 7 boxes?

A N=16+B
B. N-=16-B
C. N=16B
D. N=16/B

Answers

it would be C, because you want to multiple the amount of crayons by the number of boxes

Which expression is equivalent to 5^3 × 10^-2?

Answers

Answer:

[tex]5 {}^{3} \times 10 {}^{ - 2} \\ = 5 {}^{3} \times \frac{1}{10 {}^{2} } \\ = 5 {}^{3} \times \frac{1}{2 {}^{2} 5 {}^{2} } \\ = 5 \times \frac{1}{4 \\ } \\ = \frac{5}{4} [/tex]

hope it helps

solve the equation 3x+4/3 - 2x/x-3 =x

Answers

Answer:

x = -6.

Step-by-step explanation:

1. Write the equation.

[tex]\sf \dfrac{3x+4}{3} -\dfrac{2x}{x-3} =x[/tex]

2. Multiply by "3" on both sides ob the equation.

Applying the distributive property of multiplication on the left hand side:

[tex]\sf (3)(\dfrac{3x+4}{3} -\dfrac{2x}{x-3}) =x(3)\\ \\ \\{3x+4} -\dfrac{(3)2x}{x-3}=3x\\ \\ \\{3x+4} -\dfrac{6x}{x-3}=3x[/tex]

3. Multiply by "x-3" on both sides ob the equation.

Applying the distributive property of multiplication:

[tex]\sf (x-3)({3x+4} -\dfrac{6x}{x-3})=3x(x-3)\\ \\ \\(x-3)({3x+4}) -6x=3x(x-3)\\ \\ \\(x)(3x)+(x)(4)+(-3)(3x)+(-3)(4) -[6x]=3x(x-3)\\ \\ \\[/tex]

Check the image below to see an illustration of this process.

[tex]\sf 3x^{2} +4x-9x-12 -[6x]=3x(x-3)\\ \\ \\3x^{2} +4x-9x-12 -6x=3x(x-3)\\ \\ \\3x^{2} -11x-12 =3x(x-3)[/tex]

Now simplifying on the right hand side (applying the same logic as last step).

[tex]\sf 3x^{2} -11x-12 =3x(x-3)\\ \\ \\3x^{2} -11x-12 =(3x)(x)+(3x)(-3)\\ \\ \\3x^{2} -11x-12 =3x^{2}-9x[/tex]

4. Add "9x" on both sides of the equation.

[tex]\sf 3x^{2} -11x-12+9x =3x^{2}-9x+9x\\ \\ \\3x^{2} -2x-12 =3x^{2}[/tex]

5. Subtract "3x²" from both sides.

[tex]\sf 3x^{2} -2x-12-3x^{2} =3x^{2}-3x^{2}\\ \\ \\-2x-12 =0[/tex]

6. Add "12" on both sides.

[tex]\sf -2x-12+12=0+12\\ \\ \\-2x=12[/tex]

7. Divide by "-2" ob both sides.

[tex]\sf \dfrac{-2x}{-2} =\dfrac{12}{-2} \\ \\ \\x =-6[/tex]

8. Verify the answer.

If "x= -6" is the correct answer, substituting "x" by "-6" on the original equation should return the same value on both sides of the equal (=) symbol. Let's test!

[tex]\sf \dfrac{3(-6)+4}{3} -\dfrac{2(-6)}{(-6)-3} =(-6)\\ \\-6=-6[/tex]

That's correct!

x = -6 is the corect answer.

8. A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. (i) What is the car's angular speed in radians per hour? (ii) What is the car’s linear speed in miles per hour?

Answers

Answer:

the car's angular speed is 72,000π radians per hour.

the car's linear speed is approximately 100.53 miles per hour.

Step-by-step explanation:

To find the car's angular speed in radians per hour, we can start by finding the angular speed in radians per second.

The formula for angular speed is:

ω = 2πf

where ω is the angular speed in radians per second, and f is the frequency or rate of rotation in revolutions per second.

In this case, the wheel is spinning at a rate of 10 revolutions per second, so:

ω = 2π(10) = 20π radians per second

To convert this to radians per hour, we can multiply by the number of seconds per hour:

20π radians per second × 3600 seconds per hour = 72,000π radians per hour

To find the car's linear speed in miles per hour, we can use the formula:

v = rω

where v is the linear speed, r is the radius of the wheel, and ω is the angular speed in radians per second.

The radius of the wheel is half the diameter, or 9 inches. To convert this to miles, we can divide by 12 and then by 5280:

9 inches ÷ 12 inches per foot ÷ 5280 feet per mile = 0.000142045 miles

Now we can substitute the values we have found:

v = (0.000142045 miles) × (18/2 inches) × (20π radians per second)

v ≈ 100.53 miles per hour

Answer:

(i) 10 revolutions = 10(2π) = 20π radians

10 revolutions/sec =

(20π radians/sec)(3,600 sec/hr) =

72,000π radians/hr

(ii) C = 18π inches

10 revolutions × 18π inches =

180π inches

(180π in./sec)(3,600 sec/hr) =

(648,000π in./hr)(1 mi./63,360 in.)

= 225π/22 miles/hour

= about 32.13 miles/hour

Abel cycled at an average speed of 10 km/h from his home to the neighbourhood park.
On reaching the park, he cycled back home along the same route at an average speed of
8 Km/h. He took 1 1/5 hours for the whole journey. How long did he take to cycle from the park
to his home?

Answers

Answer:

Time = Distance / Speed

Time is taken from home to park = d / 10

Abel cycled back from the park to his home at an average speed of 8 km/h. The time taken for this part of the journey can be calculated using the same formula:

Time = Distance / Speed

Time is taken from park to home = d / 8

According to the given information, the total time taken for the whole journey is 1 1/5 hours, which is equivalent to 6/5 hours.

Total time is taken = Time from home to park + Time from park to home

6/5 = d/10 + d/8

To simplify the equation, let's find the least common multiple (LCM) of 10 and 8, which is 40:

(6/5) * 40 = (d/10) * 40 + (d/8) * 40

48 = 4d + 5d

48 = 9d

d = 48/9

d = 16/3 km

Now, to find the time taken from the park to Abel's home, we substitute the distance value:

Time from park to home = (16/3) / 8

Time from park to home = (16/3) * (1/8)

Time from park to home = 16/24

Time from park to home = 2/3 hour

Since 2/3 of an hour is equal to 40 minutes, Abel took 40 minutes to cycle from the park to his home.

Therefore, Abel took 40 minutes (or 2/3 of an hour) to cycle from the park to his home.

Please help me who knows how to do this

Answers

X^2 - x - 12

Step 1: X^2+3x-4x-12

Step 2: (X^2+3x)+(-4x-12)

Step 3: X(x+3)-4(x+3)

Answer: (x-4)(x+3)

The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?
A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.

Answers

Answer:

B) The other number is even.

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

Answers

The two equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p include the following:

B. 2.3p – 10.1 = 6.49p – 4

C. 230p – 1010 = 650p – 400 – p

How to determine the required equations?

From the information provided, we have the following equation:

2.3p – 10.1 = 6.5p – 4 – 0.01p

Next, we would simplify the given equation by collecting like terms as follows;

2.3p - 10.1 = 6.5p - 0.01p - 4 = 6.49p - 4

2.3p - 10.1 = 6.49p - 4

What is the multiplication property of equality?

In Mathematics, the multiplication property of equality states that both sides of an equation will remain the same and equal, when both sides of the equations are multiplied by the same number.

By multiplying both sides of the given equation by 100, we have the following;

100 × (2.3p - 10.1) = 100 × (6.5p - 4 - 0.01p)

230p - 1010 = 650p - 400 - p

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You spin the spinner once. 234 What is P(not greater than 2)? Write your answer as a fraction or whole number.

Answers

Answer
The probability that it stops at a particular
Quarter(P(4)) is 0.25.
How probability is calculated?
The spinner is divided into 4 parts and each part is having equal area therefore probability of spinner needle stopping at any part of the 4 parts is equal to that of all the other parts.
Hence each having equal probability that is 1/4=0.25.

Describe two trends you can find in the graph below. Use calculations and numbers to support your thinking.

Answers

The two trends on the graph are:

Positive correlationNegative correlation

Describing the two trends on the graph

From the question, we have the following parameters that can be used in our computation:

The graph

The two trends on the graph are:

Positive correlationNegative correlation

For the positive correlation, we have

Upward trend from January till August

This is because the function values increase approximately in this domain

For the negative correlation, we have

Upward trend from August till December

This is because the function values decrease approximately in this domain

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Jill's neighborhood has a mean of 3 children per household.

What happens to the mean if a family with 7 children moves away?

Responses

The mean remains the same.

The mean increases.

The mean decreases.

Answers

The correct option is the last one, the mean will decrease.

What happens to the mean if a family with 7 children moves away?

For a set of N values {x₁, x₂, ..., xₙ} the mean is defined as the sum of the N values divided by N, this is:

mean = (x₁ + x₂ + ... + xₙ)/N

Now, here the mean is 3, and a family with 7 children (more than the mean) moves away.

That will cause a decrease in the mean, because we are removing one of the larger values.

The correct option is the last one.

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100 POINTS

Question:

Answers

Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Graphical methods are commonly used for determining whether the data support an interpretation of mixing of two potential sources or fractionation of a single source.

A graphic solution can be done by hand (on graph paper), or with the use of a graphing calculator. Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the (x,y) ordered pair where the two lines intersect (cross).

BRAINLINEST PLEASE

Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Graphical methods are commonly used for determining whether the data support an interpretation of mixing of two potential sources or fractionation of a single source.

A graphic solution can be done by hand (on graph paper), or with the use of a graphing calculator. Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the (x,y) ordered pair where the two lines intersect (cross).

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