O POLYNOMIALS AND FACTORING Polynomial long division: Problem type 1 Divide. (3x^(2)+20x+30)-:(x+5) Your answer should give the quotient and the remainder.

The equation that represent the function is h(x) = 30x + 50 and the equation is linear.

Ann is coordinating a fashion show and needs to hire a makeup artist. The makeup artist charges 50 dollars booking fee plus an additional 30 dollars per hour .

Let's use function to represent the total cost to hire the artist for x hours.

Therefore,

h(x) = 50 + 30x

Hence, the function is linear.

Therefore, the equation that represent the situation is h(x) = 50 + 30x

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In  linear equation, 7/10 did he buy .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

multiply the fractions by each other.

7/8*4/5

7*4=28

8*5=40

28/40

"B" would be the correct answer but, it the fraction should be reduced to 7/10.

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Answer:

13.1y

Step-by-step explanation:

Normally in questions like this, you would be given the total area and asked to find the value of y. In this case, the area is not given, so it can be assumed the question requires you to give your answer in terms of y.

The area of a rectangle is found by multiplying the length by the width. In this case, we want to add two areas together to find the total area of the two gardens:

(3.3 * 2y) + (1.3y * 5)

We can simplify both sides of the expression:

3.3 * 2y = 6.6y

1.3y * 5 = 6.5y

Now we can add these together to find the total area, in terms of y:

6.6y + 6.5y = 13.1y

The Andy's statement is correct because the end of the month amount is indeed 250% of his original amount.

To determine if Andy's statement is correct, we need to verify if the end of the month amount is indeed 250% of his original amount.

Let original amount of money that Andy had at beginning of month be = x ;

According to the problem, he began with $44, so x = $44.

Let amount of money that Andy had at the end of the month be = y;

According to the problem, he ended with $110, so y = $110.

Andy's statement is that the end of the month amount of $110 is 250 percent of his original amount of $44;

⇒ y = 2.5x

Substituting the values,

We get,

⇒ $110 = 2.5 × $44;

Simplifying,

We get,

⇒ $110 = $110.

Therefore, Andy's statement is correct.

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The length of the body of the guitar is represented by the radical expression 24√3.

We can start by simplifying 8√147.

8√147 = 8√(49 × 3) (since 49 is a perfect square)

= 8 × 7√3

= 56√3

Next, we need to find the length of the body of the guitar, given that the neck measures 8√48. We know that the total length of the guitar is 56√3, so we can set up an equation:

total length = length of neck + length of body

56√3 = 8√48 + length of body

To solve for the length of the body, we can start by simplifying 8√48:

8√48 = 8√(16 × 3) (since 16 is a perfect square)

= 8 × 4√3

= 32√3

Substituting this back into the equation:

56√3 = 32√3 + length of body

Simplifying:

length of the body = 24√3

Therefore, the answer is A) 24√3.

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The question is -

Suppose the total length of the guitar is given by the expression 8√147. Which radical expression represents the length of the body if the neck measures 8√48? A) 24√3 B) 12√3 C) 8√3 D) 9√9

The coordinate matrix [x]B , given the coordinate matrix [x]B'.
[x]B = P * [x]B' = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [2, 3, 1] =
[(6.34, -1.16, -3.03), (-1.16, 0.22, 0.45), (-1.16, 0.22, 0.45)]

The transition matrix from B to B' can be found by first finding the inverse of matrix B, then multiplying it by matrix B'. The transition matrix from B' to B can be found by first finding the inverse of matrix B', then multiplying it by matrix B. To verify that the two transition matrices are inverses of each other, we can multiply them together and see if the result is the identity matrix. Finally, to find the coordinate matrix [x]B, given the coordinate matrix [x]B', we can multiply the transition matrix from B' to B by the coordinate matrix [x]B'.

(a) Find the transition matrix from B to B'.
P−1 = B^(-1) * B' =
[(-0.04, 0.04, 0.08), (0.08, -0.08, -0.17), (0.08, -0.08, -0.17)] * [(0, −1, 8), (1, 1, −8), (2, 2, −12)] =
[(0.04, -0.12, 0.68), (-0.09, 0.25, -1.43), (-0.09, 0.25, -1.43)]

(b) Find the transition matrix from B' to B.
P = B'^(-1) * B =
[(-0.33, 0.17, 0.08), (0.08, -0.08, -0.17), (0.08, -0.08, -0.17)] * [(14, −2, −6), (−6, 1, 3), (12, −2, −5)] =
[(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)]

(c) Verify that the two transition matrices are inverses of each other.
PP−1 = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [(0.04, -0.12, 0.68), (-0.09, 0.25, -1.43), (-0.09, 0.25, -1.43)] =
[(1, 0, 0), (0, 1, 0), (0, 0, 1)]

(d) Find the coordinate matrix [x]B , given the coordinate matrix [x]B'.
[x]B = P * [x]B' = [(4.67, -0.83, -2.17), (-0.83, 0.17, 0.34), (-0.83, 0.17, 0.34)] * [2, 3, 1] =
[(6.34, -1.16, -3.03), (-1.16, 0.22, 0.45), (-1.16, 0.22, 0.45)]

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Answer:

two out of how many there is.

Step-by-step explanation:

Approximately 272 loan applicants fall within a score of 622 and 678  assuming a bell-shaped curve.

To solve this problem, we need to use the standard normal distribution formula. First, we calculate the z-scores for the two credit score values of interest:

z-score for 622 = (622 - 650) / 14 = -2

z-score for 678 = (678 - 650) / 14 = 2

Next, we look up the probabilities for these z-scores in the standard normal distribution table or using a calculator. The probability of a z-score being between -2 and 2 is approximately 0.9544. Therefore, we can estimate that approximately 95.44% of the loan applicants fall within a score of 622 and 678.

Finally, we can calculate the number of loan applicants that fall within this range by multiplying the total number of applicants by the probability:

number of loan applicants = 285 x 0.9544 ≈ 272

Therefore, we can estimate that approximately 272 loan applicants fall within a score of 622 and 678.

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Answer:

n=10

Step-by-step explanation:

(photo linked = step-by-step)

There is no real value of n that satisfies the equation c(n,6) = c(n,4). In other words, there is no real number n such that it satisfy the given combinations.

To find the value of n that satisfies the equation c(n,6) = c(n,4), we can use the formula for combinations.

The formula for combinations, often denoted as C(n, r), calculates the number of ways to choose r items from a set of n items without regard to the order.

In this case, we have c(n, 6) and c(n, 4). The equation states that the number of ways to choose 6 items from a set of n items is equal to the number of ways to choose 4 items from the same set.

Using the formula for combinations, we can set up the equation as follows:

n! / (6!(n-6)!) = n! / (4!(n-4)!)

To solve this equation for n, we can simplify the equation by canceling out the factorials:

(n(n-1)(n-2)(n-3)(n-4)(n-5)) / (6(5)4(3)2(1)) = (n(n-1)(n-2)(n-3)) / (4(3)2(1))

By canceling out common factors and simplifying, we are left with:

(n-5) = (n-4)(n-3)

Expanding the equation, we have:

[tex]n - 5 = n^2 - 7n + 12[/tex]

Rearranging the equation and combining like terms, we get:

[tex]n^2 - 8n + 17 = 0[/tex]

At this point, we can solve the quadratic equation using factoring, the quadratic formula, or other methods. However, upon inspection, we can see that this quadratic equation does not have real solutions.

Therefore, there is no real value of n that satisfies the equation c(n,6) = c(n,4). In other words, there is no real number n such that it satisfy the given combinations.

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Answer:

37

Step-by-step explanation:

Answer:

y = x+5

x+2y=16

x+2(x+5)=16

x+2x+10=16

3x+10=16

16. 3x + 10 = 16

3x+10=16

    -10  -10

3x=6

Divide 3 from both sides

x=2

y=x+5

y=2+5

y=7

17. (2,7)

It is answer choice (C). 7 and 8!

Really hope this helped! brainliest would be very appreciated!

~HAPPY DAYZ~

As we see, triangle ABC is congruent to triangle BMK so, a) length of AC = 5

b) length of BM = 4.5

c) length of KM = 3

d) length of BM = 3.42 , MC = 17.58

We have a triangle ABC and KM, a segment is parallel to AC, i.e., KM || AC. First we show that triangle ABC is congruent to triangle BMK. AC and AB are transversals that intersect parallel lines. Since the two pairs of corresponding angles created by this intersection are equal, that is,

∠ BKM =∠ BAC and ∠ BMK = ∠ BCA

By Angle-Angle congruence rule, ∆ ABC is similar to triangle BMK, i.e., ∆ABC ~ ∆BMK. When two triangles are similar, the ratios of the lengths of their corresponding sides are equal, KB/AB = KM/AC --(1) or

BM/BC = KM/AC --(2)

a) AB = 10, KB = 2, KM = 1, determine AC=?

from equation (1), KB/AB = KM/AC

=> 2/10 = 1/AC

Cross multiplication

=> 2 AC = 10

=> AC = 5

b) KM= 3, AC = 6,BC = 9, determine BM= ?

from equation (2), BM/BC = KM/AC

=> BM/9 = 3/6

Cross multiplication

=> 6 BM = 27

=> BM = 9/2

=> BM = 4.5

c)BC = 25, MC = 10, AC = 5, determine KM= ?

BM = BC - MC = 25 - 10 = 15

from equation (2), BM/BC = KM/AC

=> 15/25 = KM/5

Cross multiplication

=> 25 KM = 15×5

=> KM = 75/25

=> KM = 3

d)AK = 10, KB = 4, BC = 21, determine BM=? and MC= ?

AB = AK + KB = 10 + 4 = 14

from equations (1) and (2),BK/AB = BM/BC

=> 4/14 = BM/21

Cross multiplication

=> 14 BM = 21 × 4

=> BM = 84/14 = 24/7

=> BM = 3.42

so, MC = BC - BM = 21 - 3.42 = 17.58

Hence, required value is 3.42..

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Complete question:

Given: ∆ABC, KM|| AC. See the above figure.1.

a) AB=10, KB=2, KM=1

AC-?

b) KM=3, AC=6,BC=9

BM-?

c)BC=25, MC=10, AC=5

KM-?

d)AK=10,KB=4,BC=21

BM-?,MC-?

The value οf x is 1000 kg/m³ and the cοrrespοnding value οf y in lb/ft³ is 62.0 lb/ft³. The value οf x is 2000 lbs/yard³ and the cοrrespοnding value οf y in lb/ft³ is 74 lb/ft³.

Quantities and measurements are essential cοmpοnents οf the study οf mathematics and the physical sciences. A quantity is any prοperty οr characteristic that can be measured οr expressed in numerical terms, such as length, mass, time, temperature, and vοlume.

Frοm the prοject research part 2: Densities in lb/ft3 (pοunds per cubic fοοt). Cοnvert the densities as belοw,

Cοnvert kilοgrams per cubic meter tο the pοunds per cubic fοοt by multiplying by 0.062:

(x kg/m³) (0.062) = y lb/ft³

If we have a value οf x, we can multiply it by 0.062 tο get the cοrrespοnding value οf y in lb/ft³.

Let's say we have x = 1000 kg/m³. We can find y in lb/ft³ as fοllοws:

y lb/ft3 = (1000 kg/m3) (0.062) = 62.0 lb/ft3

Therefοre, the value οf x is 1000 kg/m3 and the cοrrespοnding value οf y in lb/ft3 is 62.0 lb/ft³.

Anοther questiοn is, Cοnvert pοunds per cubic yard tο pοunds per cubic fοοt by multiplying by 0.037:

(x lbs/yard³) (0.037) = y lb/ft³

Let's say we have x = 2000 lbs/yard³. We can find y in lb/ft³ as fοllοws:

y lb/ft³ = (2000 lbs/yard³) (0.037) = 74 lb/ft³

Therefοre, the value οf x is 2000 lbs/yard³ and the cοrrespοnding value οf y in lb/ft³ is 74 lb/ft³.

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Answer:

x=6

Step-by-step explanation:

please mark as brainliest

The answer is (-14x)/(9).

To simplify the given expression, we need to find a common denominator for all the fractions, which is 18. We can then multiply the numerators and denominators of each fraction by the same number to get the same denominator for all the fractions. Once we have the same denominator, we can combine the numerators using addition and subtraction. Finally, we can simplify the resulting fraction if possible.

The expression is: (x)/(3)+(2x)/(18)-(6x)/(3)

First, find a common denominator for all the fractions. The smallest common denominator is 18.

Next, multiply the numerators and denominators of each fraction by the same number to get the same denominator for all the fractions:

(x)/(3) * (6)/(6) = (6x)/(18)

(2x)/(18) * (1)/(1) = (2x)/(18)

(6x)/(3) * (6)/(6) = (36x)/(18)

Now, we can combine the numerators using addition and subtraction:

(6x)/(18) + (2x)/(18) - (36x)/(18) = (6x + 2x - 36x)/(18) = (-28x)/(18)

Finally, we can simplify the resulting fraction by dividing both the numerator and denominator by 2:

(-28x)/(18) = (-14x)/(9)

So the simplified expression is: (-14x)/(9)

Therefore, the answer is (-14x)/(9).

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The system of equations that does not have a solution is {(x-2y=-3),(-2x+4y=6):}.

To see why, let's first look at the other two systems of equations:

{(4x+6y=12),(6x+9y=12):}

If we divide the first equation by 2, we get:

{(2x+3y=6),(6x+9y=12):}

If we then multiply the first equation by -3, we get:

{(-6x-9y=-18),(6x+9y=12):}

If we add these two equations together, we get:

{0= -6}

This is a false statement, so there is no solution for this system of equations.

Similarly, for the system of equations {(x+y=-1),(4x-3y=24):}, we can multiply the first equation by -4 and add the two equations together to get:

{-4x-4y=4, (4x-3y=24):}

{-7y=28}

This equation has a solution, so this system of equations does have a solution.

However, for the system of equations {(x-2y=-3),(-2x+4y=6):}, if we multiply the first equation by -2 and add the two equations together, we get:

{-2x+4y=6, (-2x+4y=6):}

{0=0}

This equation is always true, so there are an infinite number of solutions for this system of equations. Therefore, this system of equations does not have a unique solution.

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Answer:

Step-by-step explanation:

You can use simple algebraic principles for this. First we distribute:

5(y + 2/5) = -13

5y + 10/5 = -13

5y + 2 = -13

Now we isolate the variable term:

5y + 2 = -13

5y = -15

Now we divide to isolate the variable itself:

5y = -15

y = -3

Hope this helps!

Hence, there is a 38.2% likelihood that the group chosen will consist of two men and two women.

A committee's primary responsibility is to aid in the smooth operation of the company. The majority of the time, the main concerns of a committee are information sharing and assisting the leadership in making decisions by providing them with the necessary knowledge.

We may employ the formula of combinations to determine the likelihood of choosing a group comprising two men plus two women from of the committee. C(7,2) = 21 ways to choose two males from a group of seven, and C(4,2) = 6 ways to choose two women from a group of four. Hence, there are 21 x 6 = 126 different ways to choose a team of two men and two women.

C(11,4) = 330 different techniques can be used to choose any four members of the committee. Thus, the following is the likelihood of choosing a team of two men and two women:

126 / 330 = 0.382 or 38.2%

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Given that there was no test this week (X0 = 0), the probability that there is a test in two weeks time (X2 = 1 or X2 = 2) is given by the sum of the probabilities of the two possible states in the two-step transition probability matrix:
P(X2 = 1 or X2 = 2|X0 = 0) = P^2[0][1] + P^2[0][2] = 0.36 + 0.12 = 0.48

To compute P(X5 = 2|X3 = 1, X1 = 0), we can use the formula for conditional probability:
P(X5 = 2|X3 = 1, X1 = 0) = P(X5 = 2, X3 = 1, X1 = 0)/P(X3 = 1, X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)*P(X1 = 0)/P(X3 = 1|X1 = 0)*P(X1 = 0)
= P(X5 = 2|X3 = 1)*P(X3 = 1|X1 = 0)/P(X3 = 1|X1 = 0)
= P(X5 = 2|X3 = 1)
= P²[1][2]
= 0.12

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[tex]\overline {BC}[/tex] corresponds to [tex]\overline {FG}[/tex] statement is true for the given question.

What is a rectangle?

A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equal sides.

Here, we have

Given: Rectangle ABCD is translated to produce image EFGH.

We have to determine the true statement that satisfies the given rectangle.

We concluded from the rectangle that BC will correspond to FG

Polygons' matching sides and corresponding angles are compared in tests for congruence and resemblance. In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

Hence, BC corresponds to FG.

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It will take Mrs. Reed 3 hours to catch up to Mr. Reed.

First we can start by figuring out how far Mr. Reed will have traveled when Mrs. Reed starts her journey.

Distance traveled by Mr. Reed in 3 hours at a speed of 40 mph:

When Mrs. Reed starts her journey, Mr. Reed is 120 miles ahead of her.

Now, let's determine how long it will take Mrs. Reed to catch up to Mr. Reed.

We can use the formula:

time = distance / relative speed

Where "distance" is the distance Mrs. Reed needs to travel to catch up to Mr. Reed, and "relative speed" is the speed at which Mrs. Reed is gaining on Mr. Reed, which is the difference between their speeds:

relative speed = 80 mph - 40 mph

relative speed = 40 mph

So, the time it will take for Mrs. Reed to catch up to Mr. Reed can be calculated as:

Therefore, it will take Mrs. Reed 3 hours to catch up to Mr. Reed.

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The unknown measures are given as follows:

BC = 2.52, AB = 1.28, m < C = 27º.

The three trigonometric ratios are defined as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle C is given as follows:

63 + 90 + m < C = 180

m < C = 27.

Side BC is opposite to the angle of 63º, while the hypotenuse is the square root of 8, hence it is obtained as follows:

sin(63º) = BC/sqrt(8)

BC = square root of 8 x sine of 63 degrees

BC = 2.52.

Side AB is opposite to the angle of 27º, hence it's length is given as follows:

sin(27º) = AB/sqrt(8)

AB = square root of 8 x sine of 27 degrees

AB = 1.28.

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The equation of the line that passes through the point (−9,−10) and is perpendicular to the given line x+6y=2y−3 is y = 4x + 26.

We first need to find the slope of the given line.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

First, let's rearrange the given equation to get it in slope-intercept form:

x + 6y = 2y - 3

4y = -x - 3

y = (-1/4)x - (3/4)

The slope of the given line is -1/4.

Since the slope of a line perpendicular to another line is the negative reciprocal of the original slope, the slope of the line we are looking for is 4.

Now we can use the point-slope form of a line to find the equation of the line:

y - y1 = m(x - x1)

y - (-10) = 4(x - (-9))

y + 10 = 4x + 36

y = 4x + 26

So the equation of the line in slope-intercept form is y = 4x + 26.

Therefore, the answer is y = 4x + 26.

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pool = length x width x height

pool = 15 x 9 x ?

270 = 135x

x = 2

the height is 2 meters.

The width of the rectangular field is 51 m. To find the width of the rectangular field, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

Given:
P = 294 m
L = 96 m

Substituting the given values into the formula, we get:

294 = 2(96) + 2W

Simplifying the equation, we get:

294 = 192 + 2W

Subtracting 192 from both sides of the equation, we get:

102 = 2W

Dividing both sides of the equation by 2, we get:

W = 51

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The correct order of the fractions is: (1)/(5), (1)/(2), (4)/(5), 1(3)/(10), 1(9)/(10).

To order the fractions using the number line, we need to compare each fraction and determine which one is smaller or larger. Here are the steps to do this:

1. Find the least common denominator (LCD) of all the fractions. In this case, the LCD is 10.

2. Convert each fraction to an equivalent fraction with the LCD as the denominator. This means multiplying the numerator and denominator of each fraction by the same number to get the LCD as the new denominator.

- (1)/(2) = (1*5)/(2*5) = (5)/(10)
- (4)/(5) = (4*2)/(5*2) = (8)/(10)
- (1)/(5) = (1*2)/(5*2) = (2)/(10)
- 1(3)/(10) = (13)/(10)
- 1(9)/(10) = (19)/(10)

3. Now that all the fractions have the same denominator, we can compare the numerators to determine the order of the fractions.
4. Arrange the fractions from smallest to largest according to their numerators:
- (1)/(5) = (2)/(10)
- (1)/(2) = (5)/(10)
- (4)/(5) = (8)/(10)
- 1(3)/(10) = (13)/(10)
- 1(9)/(10) = (19)/(10)

In conclusion, to order the set of fractions (1)/(2),(4)/(5),(1)/(5),1(3)/(10),1(9)/(10) using the number line, we need to find the least common denominator, convert each fraction to an equivalent fraction with the LCD as the denominator, and then compare the numerators to determine the order of the fractions.

The correct order is (1)/(5), (1)/(2), (4)/(5), 1(3)/(10), 1(9)/(10).

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The given statement, "by the Invertible Matrix Theorem if the equation [tex]Ax^{(0)}[/tex]has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the identity matrix," is true (T).

This is because the theorem states that a square matrix is invertible if and only if it can be transformed into the identity matrix by a sequence of elementary row operations. And if the equation [tex]Ax^{(0)}[/tex] only has the trivial solution, then the matrix must be row equivalent to the identity matrix, implying that it is invertible.

The Invertible Matrix Theorem is a powerful result in linear algebra that allows us to determine whether a square matrix is invertible or not. It states that a square matrix is invertible if and only if its determinant is nonzero, which is equivalent to saying that the matrix can be transformed into the identity matrix by a sequence of elementary row operations.

If the matrix is not invertible, then its determinant is zero, and it is said to be singular. In this case, the equation [tex]Ax^{(0)}[/tex] will have infinitely many solutions or no solutions at all, depending on the specific values of the right-hand side vector.

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He makes $8/49 for every 7 cups of juice, so his overall profits will be some multiple of $8/49.

Finding the worth of one unit of a quantity, then using this value to determine the value of a specified number of units of the quantity, is known as the unitary technique. When solving issues involving rates, ratios, and proportions, this approach is helpful. The fundamental tenet of the unitary technique is that we can use the value of one unit of a quantity to determine the value of any number of additional units of the same quantity.

given

Let's symbolise the cost of a cup of apple juice by the variable x.

So, a cup of lemon juice is sold for 3/2 times x, or (3/2)x.

Mr. Tan offers 5 cups of apple juice for every 2 cups of lemon juice. This indicates that there are 2.5 sales of lemon juice for every 1 sales of apple juice.

Assume Mr. Tan sells 5y cups of apple juice and 2y cups of lemon juice.

Based on the information provided, we can conclude that apple juice generates $12 more revenue than lemon juice.

in order to create an equation:

5yx = 2(3/2)x + 12

Simplifying:

5yx = 3x + 12

adding two to both sides:

10yx = 6x + 24

x(10y - 3) = 12

x = 12 / (10y - 3) (10y - 3)

We can now re-use this number of x to represent the revenue from apple juice in the equation:

5yx = 3x + 12

5y(12 / (10y - 3)) = 3(12 / (10y - 3)) + 12

Therefore, Mr. Tan charges $1/7 for each cup of apple juice and (3/2)($1/7) Equals $3/14 for each cup of lemon juice.

He charges (5/7)($1/7) = $5/49 for 5y = 5(1/7) = 5/7 glasses of apple juice.

For a sum of (2/7)($3/14) = $3/49, he sells 2y = 2(1/7) = 2/7 cups of lemon juice.

For each 7 cups of juice sold, Mr. Tan makes a sum of $5/49 + $3/49 = $8/49.

Consider that he offers 2n cups of lemon juice and 5n glasses of apple juice. (2n)($3/14) + (5n)($1/7) = $6n/49 + $5n/49 = $11n/49

He makes $8/49 for every 7 cups of juice sold, so his overall profits will be some multiple of $8/49.

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