Using a formula estimate the body surface area of a person whose height is 166cm and weighs 100kg. A. 2.29m^(2) B. 2.15m^(2) C. 55.9m^(2) D. 5.44m^(2)

The simplified expression is (3y-7)/(y^2-35)/3.

To simplify the given expression, we need to find the least common denominator (LCD) of the two fractions. The LCD of (y-5) and (y+7) is (y-5)(y+7).
Next, we need to multiply each fraction by the LCD in order to get the same denominator for both fractions.
(2)/(y-5) * (y+7)/(y+7) + (7)/(y+7) * (y-5)/(y-5)
= (2y+14)/(y^2-35) + (7y-35)/(y^2-35)

Now, we can combine the two fractions since they have the same denominator.
(2y+14+7y-35)/(y^2-35)
= (9y-21)/(y^2-35)
Finally, we can simplify the fraction by factoring out a 3 from the numerator.
= (3)(3y-7)/(y^2-35)
= (3y-7)/(y^2-35)/3
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The interest rate will be 7%

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount.

Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

the simple interest on ​$7000 for 7 years is ​$3430

r = S*100/(p*t)

r = (3430*100)/(7000*7)

r = 7%

Hence the interest rate will be 7%

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The answer is C

The probability that the number of heads would take a value within one standard deviation from the mean is 0.6826. This can be found by using the normal approximation to binomial probabilities.

First, we need to find the mean and standard deviation of the binomial distribution. The mean of a binomial distribution is given by np, where n is the number of trials and p is the probability of success. In this case, n = 100 and p = 0.5 (since it is a fair coin), so the mean is 100 * 0.5 = 50.

The standard deviation of a binomial distribution is given by √(np(1-p)). In this case, the standard deviation is √(100 * 0.5 * (1-0.5)) = √(25) = 5.

Now, we can use the normal approximation to find the probability that the number of heads is within one standard deviation from the mean. This is equivalent to finding the probability that the number of heads is between 45 and 55 (since the mean is 50 and the standard deviation is 5).

Using the normal approximation, we can find the z-scores for 45 and 55:

z = (x - μ) / σ

z1 = (45 - 50) / 5 = -1

z2 = (55 - 50) / 5 = 1

Now, we can use a z-table to find the probability that the number of heads is between 45 and 55. The probability that the number of heads is less than 55 is 0.8413, and the probability that the number of heads is less than 45 is 0.1587. So, the probability that the number of heads is between 45 and 55 is 0.8413 - 0.1587 = 0.6826.

Therefore, the answer is C. 0.6826.

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The equation of a parabola with zeros at 3 and 9 and goes through the point \( (6,-18) \) is
y = 2x^2 - 24x + 54.

To write the equation in general form of a parabola with zeros of 3 and 9 and goes through the point (6,-18), we can use the fact that the equation of a parabola can be written in the form y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola and a determines the width of the parabola.

First, we can use the zeros to find the vertex of the parabola. The vertex is located halfway between the zeros, so the x-coordinate of the vertex is (3 + 9)/2 = 6. We can plug this value into the equation to find the y-coordinate of the vertex:

y = a(6 - 6)^2 + k = k

Since the parabola goes through the point (6,-18), we know that k = -18.

Now we can plug in the zeros and the vertex into the equation to find the value of a:

0 = a(3 - 6)^2 - 18

0 = a(9) - 18

18 = 9a

a = 2

So the equation of the parabola is y = 2(x - 6)^2 - 18.

To write this equation in general form, we can expand the squared term and simplify:

y = 2(x^2 - 12x + 36) - 18

y = 2x^2 - 24x + 72 - 18

y = 2x^2 - 24x + 54

So the equation in general form is y = 2x^2 - 24x + 54.

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The mean, median and mode of the prices that the bags of flour are sold at are:

To find the mean, we add up all the prices and divide by the total number of prices:

Mean:

= (1.45 + 1.55 + 1.90 + 1.95 + 1.45) / 5

= 1.66

To find the median, we need to arrange the prices in order from lowest to highest:

1.45, 1.45, 1.55, 1.90, 1.95

There are five prices, so the median is the middle value, which is 1.55.

To find the mode, we need to look for the price that appears most frequently in the data set. In this case, there are two prices that appear twice, 1.45 and 1.55. So there is no unique mode for this data set.

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The f(g(x))=−4x3​and g(f(x))=x3​−15x2​+25x−125x3​.

To find f(g(x)), we need to substitute the function g(x) into the function f(x). This means that wherever we see an "x" in f(x), we replace it with the function g(x). So, f(g(x))=g(x)−5g(x)=x3​−5x3​=−4x3​. Similarly, to find g(f(x)), we substitute the function f(x) into the function g(x). So, g(f(x))=f(x)3​=(x−5x)3​=x3​−15x2​+25x−125x3​.

Therefore, f(g(x))=−4x3​and g(f(x))=x3​−15x2​+25x−125x3​.

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if f(x) = 3*2ˣ + 2 is vertically stretched by a factor of 2, then the new function g(x) is 6*2ˣ + 4.

To vertically stretch the function f(x) by a factor of 2, we need to multiply the entire function by 2.

This will stretch the function vertically, making it twice as tall as before.

Therefore, if f(x) = 3*2ˣ + 2 is vertically stretched by a factor of 2, then the new function g(x) is:

g(x) = 2*f(x)

g(x) = 2*(3*2ˣ + 2)

g(x) = 6*2ˣ + 4

So the new function g(x) is 6*2ˣ + 4.

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The situations that best represent the scenario shown in the graph of the quadratic functions, y = x² and y = x² + 3 include the following:

B. "From x = -2 to x = 0, the average rate of change for both functions is negative."

C. "For the quadratic function, y = x² + 3, the coordinate (2, 7) is a solution to the equation of the function."

D. "The quadratic function, y = x², has an x-intercept at the origin."

In Mathematics, the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y" is equal to zero (0).

In this context, we can logically deduce that the x-intercepts of the graph of the given equation y = x² is at the origin:

x = (0, 0)

For the the coordinate (2, 7), we would evaluate the quadratic function, y = x² + 3 as follows;

7 = 2² + 3

7 = 4 + 3

7 = 7 (True).

By critically observing the graph of both functions, we can logically deduce that their average rate of change is negative from x = -2 to x = 0.

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Martin buys a total of 2(5)/(6) + 4(3)/(4) = 10/6 + 19/4 = 40/24 + 57/24 = 97/24 pounds of nuts.

To find the total amount of nuts Martin buys, we need to add the amount of peanuts and the amount of almonds he buys.

First, we need to convert the mixed numbers to improper fractions. To do this, we multiply the whole number by the denominator and add the numerator. For 2(5)/(6), we multiply 2 by 6 and add 5 to get 10/6. For 4(3)/(4), we multiply 4 by 4 and add 3 to get 19/4.

Next, we need to find a common denominator in order to add the two fractions. The least common denominator for 6 and 4 is 24, so we multiply the numerator and denominator of 10/6 by 4 to get 40/24 and the numerator and denominator of 19/4 by 6 to get 57/24.

Finally, we add the two fractions by adding the numerators and keeping the same denominator: 40/24 + 57/24 = 97/24.

Therefore, Martin buys a total of 97/24 pounds of nuts.

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pls edit yours and i will give an answer

Step-by-step explanation:

Answer:

I can't order the numbers without knowing the numbers sorry

It wοuId take 3 hοurs fοr 96 cars tο pass thrοugh the intersectiοn at the same rate as 32 cars in 1 hοur.

We can use the cοncept οf prοpοrtiοnaIity tο sοIve this prοbIem. The number οf cars passing thrοugh the intersectiοn is directIy prοpοrtiοnaI tο the amοunt οf time taken. This means that if we dοubIe the number οf cars passing thrοugh, we wiII aIsο dοubIe the amοunt οf time taken.

Let x be the amοunt οf time it takes fοr 96 cars tο pass thrοugh the intersectiοn. Then, we can set up the fοIIοwing prοpοrtiοn:

32 cars / 1 hοur = 96 cars / x hοurs

Tο sοIve fοr x, we can crοss-muItipIy and simpIify:

32x = 96

x = 3

Therefοre, it wοuId take 3 hοurs fοr 96 cars tο pass thrοugh the intersectiοn at the same rate as 32 cars in 1 hοur.

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5/2 is the slope of line .

What is slope, exactly?

Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2).

                           The letter "m" is frequently used to signify slope. A line's steepness can be determined by its slope. In mathematics, slope is calculated as "rise over run" (change in y divided by change in x).

points (2,6) and (0,1)

  Slope = 1 - 6/0 - 2

             = -5/-2

             = 5/2

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Answer:

Step-by-step explanation:

A=[tex]\frac{1}{2}[/tex]bh

  =[tex]\frac{1}{2}[/tex]×34×14

  =238 in²

The solutions of the given functions are:

f(g(x)) = x+10√x+26 and g(f(x)) = √(x²+6)

f(x) = x²+1, g(x) = √x+5 are given.

To find f(g(x)), we need to substitute g(x) into the function f(x):

f(g(x)) = f(√x+5) = (√x+5)²+1 = x+10√x+26

To find g(f(x)), we need to substitute f(x) into the function g(x):

g(f(x)) = g(x²+1) = √(x²+1+5) = √(x²+6)

Therefore, the simplified answers are:

f(g(x)) = x+10√x+26

g(f(x)) = √(x²+6)

Note: It is important to include the parentheses when substituting one function into another to ensure the correct order of operations.

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The coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

here, we have,

From the given graph, triangle ABC have A(1, 3), B(7, 1) and (1, 1).

Triangle ABC is enlarged with a scale factor of -2 and the origin of the Centre to give triangle A'B'C'.

Now, A(1, 3) → -2(1, 3)→A'(-2, -6)

B(7, 1) → -2(7, 1) → B'(-14, -2)

C(1, 1) → -2(1, 1) → C'(-2, -2)

Therefore, the coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

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The Cartesian coordinates (1, -5) are equivalent to the polar coordinates (√26, 4.910188838655984) with r > 0 and 0 ≤ θ < 2π.

To convert the Cartesian coordinates (1, -5) to polar coordinates with r>0 and 0≤θ<2π, we need to use the following formulas:
r = √(x^2 + y^2)
θ = tan^-1(y/x)

First, let's find the value of r:
r = √(1^2 + (-5)^2)

r = √(1 + 25)

r = √26

Now, let's find the value of θ:
θ = tan^-1((-5)/1)

θ = tan^-1(-5)

θ = -1.373400766945016

Since we need the angle to be between 0 and 2π, we can add 2π to the negative angle to get the positive equivalent:

θ = -1.373400766945016 + 2π

θ = 4.910188838655984

Therefore, the polar coordinates of the Cartesian coordinates (1, -5) are (r, θ) = (√26, 4.910188838655984).

So the answer is:
r = √26
θ = 4.910188838655984

The Cartesian coordinates (1, -5) are equivalent to the polar coordinates (√26, 4.910188838655984) with r > 0 and 0 ≤ θ < 2π.

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Answer:

Step-by-step explanation:

You take 528- divided by 2000- and then you get your answer.

Five copies of a textbook are placed in a travel bag by Jada's instructor. 17 pounds are made up of the bag and the books. Each copy of the textbook weighs 2.8 pounds.

To find the weight of each book, we can start by using algebra. Let's call the weight of each book "b".

The weight of the bag and books together is 17 pounds, and we know the empty bag weighs 3 pounds. So the weight of the books alone is:

17 - 3 = 14 pounds

Since there are 5 copies of the textbook in the bag, we can write an equation:

5b = 14

To solve for "b", we can divide both sides by 5:

b = 2.8 pounds

It's worth noting that this is an example of a simple algebraic equation that can be solved using basic arithmetic. However, algebra is a powerful tool for solving more complex problems in math, science, and other fields. By understanding how to use variables and equations to represent real-world situations, we can gain deeper insights and make more accurate predictions about the world around us.

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To solve the equation x^(2)-5x-5=0 using the quadratic formula, we can use the formula x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a=1, b=-5, and c=-5.

Plugging in the values into the formula, we get:

x = (-(-5) ± √((-5)^(2)-4(1)(-5)))/(2(1))

Simplifying the equation, we get:

x = (5 ± √(25+20))/2

x = (5 ± √45)/2

x = (5 ± 3√5)/2

Therefore, the solution set in exact simplest form is x = (5 ± 3√5)/2.

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The total number of students in Class 705 is 32.

Let's start by using algebra to solve the problem. Let's assume that the total number of students in Class 705 is "x". We know that 12 students returned their permission slips on the first day, so the number of students who have not returned their slips is (x-12).

On the second day, 15% of the remaining students returned their slips, which means that 0.15(x-12) students returned their slips. We also know that a total of three permission slips were returned on the second day, so we can write an equation:

0.15(x-12) = 3

Simplifying this equation:

0.15x - 1.8 = 3

0.15x = 4.8

x = 32

Therefore, the total number of students in Class 705 is 32.

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The algebraic expression for "r squared minus the product of 6 and d plus 5" is r2 - 6d + 5.

An algebraic expression is an expression that contains at least one variable and uses mathematical operations such as addition, subtraction, multiplication, and division. It can also include exponents and/or roots. Algebraic expressions are used to represent mathematical relationships between different variables or constants. They can be used to represent real-world problems, such as finding the area of a rectangle.

In this expression, r2 represents "r squared", - 6d represents "minus the product of 6 and d", and + 5 represents "plus 5".

So, the final algebraic expression is r2 - 6d + 5.

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The statement which describes the decimal equivalent of 5/16 is option(a), It is a decimal that terminates after 4 decimal places.

To convert a fraction to a decimal, we need to divide the numerator by the denominator.

In this case, we want to find the decimal equivalent of the fraction 5/16,

⇒ 5 ÷ 16 = 0.3125

So, the decimal equivalent of 5/16 is 0.3125.

The option(a) states that, It is a decimal that terminates after 4 decimal places.

This statement is correct, because the decimal equivalent of 5/16 terminates after 4 decimal places.

Therefore, the correct statement is option is (a).

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The given question is incomplete, the complete question is

What statement describes the decimal equivalent of 5/16?

(a) It is a decimal that terminates after 4 decimal places.

(b) It is a decimal with a repeating digit of 5.

(c) It is a decimal that terminates after 3 decimal places.

(d) It is a decimal with repeating digits of 6.

The statements that are true are

The relative minimum function is (3, 0)

When t > 3 the function will increase

To find the maximum and minimum of a function, find the points where the function's derivative is equal to zero or undefined. These points are called critical points.

We then evaluate the function at these critical points and at the endpoints of the interval to determine the maximum and minimum values. To find the critical points of the function find the derivatives of the given function

Here we have a graph

The graph shows the number of coins in a person's collection

The function is defined as f(t) = t³ - 6t² + 9t  

To find the maximum and minimum of the function

Find the critical points where the derivative is equal to zero or undefined.

Differentiate f(t) with respect to t

=> f'(t) = 3t² - 12t + 9  

Now, set the derivative equal to zero and solve for t  

=> 3t² - 12t + 9 = 0

=> t² - 4t + 3 = 0  divide by 3

On Factoring the quadratic equation, we get:

=> (t - 3)(t - 1) = 0

=> t = 3 and t = 1

Therefore,

The critical points of the graph are t = 1 and t = 3.

Now differentiate f'(t) with respect to t

=> f''(t) = 6t - 12

At t = 1, f''(1) = 6 - 12 = - 6, which is less than zero.

Hence, f(t) has a local maximum at t = 1.

At t = 3, f''(3) = 18 - 12 = 6, which is greater than zero.

Hence, f(t) has a local minimum at t = 3.

At t = 4, f''(4) = 24 - 12 = 12

At t = 5, f''(5) = 30 - 12 = 18

Hence, f(t) will increase when t > 3

Therefore,

The statements that are true are

The relative minimum function is (3, 0)

When t > 3 the function will increase

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The area of the isosceles trapezoid with base lengths 2ft and 5ft and leg lengths 2.5ft will be 8.75ft

Isosceles trapezoid, also known as isosceles trapezium, is defined as a convex quadrilateral, which mainly consists of a line of symmetry that bisects one pair of the opposite side, it is also know that the base angles are of equal measure. It has parallel bases with the legs also being of the equal measure, on the other hand the opposite angles of the isosceles trapezoid are supplementary, which makes it a cyclic quadrilateral.

Area of an Isosceles Trapezoid = [(a+b)h]/2 square units,

when we put these values in the formula, we get:

Area = [(2+5)2.5]/2

Area = (7 × 2.5)/2

Area = 17.5/2

Area = 8.75ft²

therefore, we know that the area of the isosceles trapezoid with base lengths 2ft and 5ft and leg lengths 2.5ft will be 8.75ft

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The values of {y} less than 3.7 on the number line represent the solution set of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

Given is that Tania began a graph to show the inequality → y < 3.7.

Given is the inequality as -

y < 3.7

For all the values of {y} less than 3.7 on the number line represent the solution set of the given inequality.

Therefore, the values of {y} less than 3.7 on the number line represent the solution set of the given inequality.

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{Question in english -

Tania began a graph to show the inequality y < 3.7. Finish labeling the number line and draw the graph.}

The statement that could be true for g is g(-4) = -11.

What is a function?

A function is a mathematical relationship between a set of inputs (called the domain) and a set of outputs (called the range), where each input has a unique output. In other words, for every value of x in the domain, there is exactly one corresponding value of g(x) in the range.

For the given function g, the domain is -20 ≤ x ≤ 5 and the range is -5 ≤ g(x) ≤ 45. We also know that g(0) = -2 and g(-9) = 6.

To determine which statement could be true for g, we can check each option against the given domain and range, as well as the known values of g(0) and g(-9):

g(7) = -1: This statement is not necessarily true, as g(7) may fall outside the given range of -5 ≤ g(x) ≤ 45.

g(-13) = 20: This statement is not necessarily true, as g(-13) may fall outside the given domain of -20 ≤ x ≤ 5.

g(-4) = -11: This statement could be true, as -20 ≤ -4 ≤ 5 and -5 ≤ -11 ≤ 45. However, we cannot confirm this without additional information.

g(0) = 2: This statement is not true, as g(0) is known to be -2.

Therefore, the statement that could be true for g is g(-4) = -11.

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The corresponding value of D is 15 defective genes in 100 cc of kidney tissue.

The Poisson distribution is used to model the occurrence of rare events in a fixed interval of time or space. In this case, the geneticist is using the Poisson process to model the occurrence of defective genes in kidney tissue exposed to a toxin. The average rate of occurrence is given as 3 defective genes per 20 cc of kidney tissue.

To simulate the number of defective genes in 100 cc of kidney tissue, we need to scale the average rate accordingly. Since 100 cc is five times the size of 20 cc, the average rate for 100 cc would be 15 defective genes.

The geneticist uses a uniform distribution on (0,1) to generate a random observation, U = 0.71. To obtain the corresponding value of D, we can use the inverse transform method. Let X be the number of defective genes in 100 cc of kidney tissue, then we have:

P(X = k) = e^(-λ) (λ^k / k!)

where λ is the average rate of occurrence, which is 15 in this case.

By plugging in λ = 15 and solving for k, we get:

P(X = k) = e^(-15) (15^k / k!) = 0.71

Using a calculator or a statistical software, we can find that the value of k that satisfies this equation is k = 15. Therefore, the corresponding value of D is 15 defective genes in 100 cc of kidney tissue.

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a. The scale factor is 2.

b. The lengths of GH, HJ, and JF are 13 m, 4 m, and 8 m respectively.

A scale factor is a number that is used to resize, a geometric figure. When a figure is scaled, all of its dimensions are multiplied by the scale factor.

The resulting figure is similar to the original figure, but it may be larger or smaller, depending on the value of the scale factor.

Here we have

ABCD ∼ FGHJ

Since both figures are similar

The ratio of the corresponding sides will be equal

a. Scale factor = AB/FG = 8m/ 4m = 2

b. Calculating JF, HJ, and GH  

As we know the ratio of the corresponding sides is equal

=> AB/FG = BC/GH = CD/HJ = AD/JF

From the figure,

=> 8 m /4 m = 26 m/GH = 8 m/HJ = 16/JF  

=>  26 m/GH = 8 m/HJ = 16/JF = 2

=> 26 m/GH = 2

=> GH = 13 m

=> 8 m/HJ = 2  

=> HJ = 4

=>  16/JF = 2  

=> JF = 8 m

Therefore,

a. The scale factor is 2.

b. The lengths of GH, HJ, and JF are 13 m, 4 m, and 8 m respectively.

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Answer:

X=7    Y=2

I will lead you through it and show you how you can find x through eliminating y, and finding y through eliminating x! So, both ways! :)

Step-by-step explanation:

When looking to use the elimination method, either all x OR y  coefficients must be equal before finding one or another. That might sound a little confusing so let me explain!

Finding x by eliminating y: (they already set it up for us, this way!)

6x+6y=54              6y and -6y will cancel each other out!

2x - 6y= 2

6x=54                   Add both lines!

2x=2

8x=56                   Now, divide 8 on both sides to find x!

x=7                       The product is x equals 7! Plug into a line to find y!

6(7)+6y=54          

42+6y=54          Subtract both sides by 42

6y=12                  Divide both sides by 6

y=2

So, X=7 and Y=2 ! To check that this is true, plug both variables into one line!

2(7)-6(2)=2

14-12=2

2=2                2 equals 2, so this is true! Lets check the other line to make

                      sure!

6(7)+6(2)=54

42+12=54

54=54             Yes, this is also true! That means we found the true value of the variables. :)

Finding y by eliminating x: Now, how do we find X and Y using the elimination method if the terms are not equal? We will continue to use this problem since it meets the standards of unequal terms! However, we will find y by eliminating x!

We must get the x terms to be equal to they can cancel each other out! So, we will multiply a line by a certain variable until it matches the x term on the other line. We will multiply line 2 until it matches line 1's x term, but make sure the signs (positive/negative) are opposite so they cancel out! In other problems, one line's term may not be able to be multiplied until it reaches its term since it is not a factor of it! So, both lines would be multiplied b a specific number until they have a common multiple! Confusing? Just focus on the underlined portion of this paragraph as that is what you will need for this question. Lets work hard now! :)

6x+6y=54    Multiply line 2 by -3 so the x term will be cancel out line 1's x!

2x - 6y= 2

6x+6y=54

(2x - 6y= 2) -3           Yes, all of it!

6x+6y=54

-6x+18y=-6              Add both lines

24y=48                 Divide 24 by both sides!

y=2                       y is equivalent to 2! Plug value into a line!

6x+6(2)=54

6x+12=54        Subtract 12 on both sides!

6x=42       Divide 6 on both sides.

x=7           X is equal to 7!

So, X=7 and Y=2 , just like we found and even checked before! I hope this helped. Elimination method is my favorite method and overall favorite lesson in Algebra, for me, since it is pretty easy once you get a hang of it! Goodluck all! :)

1) 5/8

2) 15/24

3) 300/480

Answer: 5/8

10/16

15/24

Step-by-step explanation: