Can someone PLEASE help me with this three part question? It’s due today!! I need help ASAP

The total cost of tiling a triangular area having a baselength of 3 meters and a height of 9 meters is $131.29.

Given base length of triangular area is 3 metersHeight of triangular area is 9 metersCost of tiling one square meter = $9.71 We need to find the total cost of tiling the triangular area. The area of a triangle is given by the formula as shown below,

Area of a triangle = 1/2 × base length × height, Therefore, Area of the given triangle = 1/2 × 3 meters × 9 meters= 13.5 square meters. Now, the total cost of tiling the triangular area can be found by multiplying the area by the cost per square meter. Total cost of tiling triangular area = 13.5 square meters × $9.71/square meter = $131.29 (approx)

Hence, the total cost of tiling a triangular area having a baselength of 3 meters and a height of 9 meters is $131.29.

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The zeros and their multiplicities of the function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 are:

x = -4, multiplicity 1

x = (-5 + √(41))/(2), multiplicity 1

x = (-5 - √(41))/(2), multiplicity 1

The zeros of a function f(x) are the values of x that make f(x) equal to 0. The multiplicity of a zero is the number of times that zero appears as a solution. To find the zeros and their multiplicities of the given function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48, we can use synthetic division or factoring.

First, let's use synthetic division to find one of the zeros:

2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 = 0

Using synthetic division, we can find that x = -4 is a zero of the function:

(-4) | 2  11  -2  -74  -60  48
    | 0  -8  20   88  104 -176
    ---------------------------
      2   3  18   14   44 -128

Now we can divide the original function by (x+4) to find the remaining zeros:

f(x) = (x+4)(2x^(4)-x^(3)+14x^(2)+10x-32)

Using the quadratic formula, we can find the remaining zeros of the function:

x = (-b ± √(b^(2)-4ac))/(2a)

x = (-(10) ± √((10)^(2)-4(2)(-32)))/(2(2))

x = (-10 ± √(164))/(4)

x = (-10 ± √(4*41))/(4)

x = (-10 ± 2√(41))/(4)

x = (-5 ± √(41))/(2)

So the zeros of the function are x = -4, x = (-5 + √(41))/(2), and x = (-5 - √(41))/(2).

The multiplicity of each zero is 1, since each zero appears only once as a solution.

Therefore, the zeros and their multiplicities of the function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 are:

x = -4, multiplicity 1

x = (-5 + √(41))/(2), multiplicity 1

x = (-5 - √(41))/(2), multiplicity 1

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By completing the square, the expression x²+10x+140 can be rewritten in the form (x+A)²+B. Where A=5 and B=-115.

To do this, we need to find the values of A and B.

Start with the original expression: x²+10x+140
Move the constant term to the right side of the equation: x²+10x = -140
Take half of the coefficient of the x term and square it: (10/2)²= 25
Add this value to both sides of the equation: x²+10x+25 = -140+25
Simplify the right side of the equation: x²+10x+25 = -115
Factor the left side of the equation: (x+5)² = -115

Therefore, the expression x²+10x+140 can be rewritten as (x+5)²-115, where A=5 and B=-115.

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The zeros of the polynomial p(x)=x²+16 are x = 4i and x = -4i. The zeros of the polynomial can be found using the Quadratic Formula: x = (-b ± √(b²-4ac))/(2a), where a, b, and c are the coefficients of the polynomial. In this case, a = 1, b = 0, and c = 16.

Plugging in these values into the Quadratic Formula, we get:

x = (-0 ± √(0²-4(1)(16)))/(2(1))

Simplifying the expression, we get:

x = (0 ± √(-64))/(2)

Since the square root of a negative number is a nonreal number, we can write this as:

x = (0 ± 8i)/(2)

Simplifying further, we get:

x = 0 ± 4i

So the zeros of the polynomial are x = 4i and x = -4i, both of which are nonreal numbers.

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a. The variables for this problem is x + y = 140

b. a system of equations that represents this situation is 20x + 10y = 2270

An attribute οr phenοmenοn that may be quantified as a variable and that changes in value οver time. As a result, a variable is a quantity that can be calculated and is subject tο change.

Bοth discrete and cοntinuοus variables are pοssible.

a. Tο sοlve this questiοn we will need twο variables x and y.

Let number οf adults be x and number οf kids be y then we get,

x + y = 140

b. Tο write a system fοr sοlving this questiοn we are given the price οf tickets.

20x + 10y = 2270

and, x + y = 140

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The percent of change from 4/3 to 3/5 is 6.1%

To find the percent of change from 4/3 to 3/5, we'll use the following formula:

Percent change = ((Old value - New value) / old value) x 100%

First, we'll identify which value is the old value and which is the new value.

The old value is 4/3 and the new value is 3/5.

Substitute the known values in the above equation, so, we have the following representation

Percent change = ((4/3 - 3/5) / 4/3) x 100%

Evaluate

Percent change = 6.1%

Hence, the percent change is 6.1%

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The correct answer is B. 2.15m^(2). The estimated body surface area of the person is 2.15m^(2).

To estimate the body surface area of a person, we can use the Mosteller formula:
BSA = square root of [(height in cm x weight in kg)/3600]

Plugging in the given values for height and weight:
BSA = square root of [(166cm x 100kg)/3600]
BSA = square root of 1660000/3600
BSA = square root of 461.11
BSA = 2.15m^(2)

Therefore, the estimated body surface area of the person is 2.15m^(2). Hence, B is the correct answer.

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Answer: x = 9

Step-by-step explanation:

We must use Pythagorean's Theorem, a² + b² = c².

Let a = x

a² + 12² = 15²

a² + 144 = 225

a² = 81

a = 9

x = 9

Hope this helps!

The height of the formation is [tex]31meter[/tex], to the nearest meter.

Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base but something above it. Height is used to describe everything that may be measured vertically, high or low.

In essence, height relates to elevation, which is the height above a certain level. Furthermore, height refers to any quantifiable distance above a particular level as well as extend upwards (as it is from foot to head). For instance, the elevation of a tower, tree, person, mountain, etc.

We can use the tangent function to calculate the formation's height.

[tex]tan(36^{0} )=\frac{h}{3}[/tex]

Here, we have to multiply both sides by [tex]43[/tex] we get,

[tex]43tan(36^{0} )=h[/tex]

[tex]h=31meter[/tex]

Therefore, the height of the formation to the nearest meter is [tex]31meter[/tex].

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a. The greatest possible distance from  Austin to san Antonio is 335.77 mi, b. the Least possible distance to Austin to san Antonio is 120.03 mi.

Distance refers to the physical length or space between two points or objects. It is an important concept in mathematics, physics, and everyday life. Distance can be measured in various units such as meters, feet, kilometers, miles, or light-years, depending on the context and scale of the measurement.

In mathematics, distance is often measured using the Euclidean distance formula, which calculates the distance between two points in a plane or in three-dimensional space. The formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where d is the distance between the two points, (x1, y1) and (x2, y2).

In physics, distance is often used to describe the separation between two objects or particles. The distance between two objects can affect the strength of gravitational or electromagnetic forces between them. Distance is also an important concept in special relativity, where it is affected by the relative motion of observers and the distortion of spacetime.

a. Greatest possible distance from  Austin to san Antonio= Distance from Austin →Houston → san Antonio.

Austin - Houston = 146.43 mi

Houston - San Antonio = 189.34 mi

Total  distance= 146.43+ 189.34= 335.77 mi

b. Least possible distance to Austin to san Antonio= the shortest distance = x

By pythagoras theorem

(189.34)²= (146.43)²+ x²

x²= (189.34)²- (146.43)²

x²= 35849.63- 21441.744

x²= 14407.89

x=√14407.89

x= 120.03

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The complete question is:

To simplify the expression (8d^((3)/(2))*7h^((5)/(6)))(7h^((3)/(2))*8d^((5)/(6))), we need to use the distributive property and the laws of exponents.

First, we can distribute the 8d^((3)/(2)) and 7h^((5)/(6)) to the 7h^((3)/(2)) and 8d^((5)/(6)):
= (8d^((3)/(2))*7h^((3)/(2)))*(7h^((5)/(6))*8d^((5)/(6)))
Next, we can use the laws of exponents to simplify the expressions with the same base:
= (8^2*d^((3)/(2)+(5)/(6))*7^2*h^((5)/(6)+(3)/(2)))
= (64*d^((11)/(6))*49*h^((9)/(6)))
Finally, we can simplify the exponents and multiply the constants:
= (3136*d^((11)/(6))*h^((3)/(2)))

Therefore, the simplified expression is 3136*d^((11)/(6))*h^((3)/(2)).

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1. a) The price is 5 dollars. b) The rate of change of demand with respect to price, p, when x = 4 is 5/6 thousands of units per dollar. c) The elasticity of demand when x = 4 is 25/24.

2. a) The price is 2*sqrt(3) dollars. b) The rate of change of demand with respect to price, p, when x = 10 is - (3 * sqrt(3))/(7) thousands of units per dollar. c) The elasticity of demand when x = 10 is -6/7.

3. Demand is increasing at -23.30 thousands of units per week.

4. If the daily production is 800 cases, then revenue is decreasing at a rate of -1200 dollars per day.

5. Supply is rising at a rate of 150.90 thousands of styluses per week.

1)
(a) Compute the price, p, when x = 4.
Price, p = −3(4)^2 − 4(4) + 69 = -48 -16 + 69 = 5 dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 4.
Rate of change of demand, x' = - (2 * -3 * x + 4)/(-3 * 2 * x) = -(-24 + 4)/(-24) = 20/24 = 5/6 thousands of units per dollar
(c) Compute the elasticity of demand when x = 4.
The elasticity of Demand = (x'/x) * (p) = (5/6)/(4) * (5) = 25/24

2)
(a) Compute the price, p, when x = 10.
Price, p = sqrt((216 - 10^2 - 8*10)/3) = sqrt((216 - 100 - 80)/3) = sqrt(12) = 2*sqrt(3) dollars
(b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 10.
Rate of change of demand, x' = - (2 * 3 * p)/(2 * x + 8) = - (6 * 2 * sqrt(3))/(20 + 8) = - (12 * sqrt(3))/(28) = - (3 * sqrt(3))/(7) thousands of units per dollar
(c) Compute the elasticity of demand when x = 10.
Elasticity of Demand = (x'/x) * (p) = (- (3 * sqrt(3))/(7))/(10) * (2*sqrt(3)) = -6/7

3)
The weekly demand equation is given by p + x + 3xp = 53,
where x is the number of thousands of units demanded weekly and p is in dollars. If the price p is decreasing at a rate of 70 cents per week when the level of demand is 5000 units, then demand is increasing at a rate of (53 - 5000 - 70)/(3*70 + 1) = -4917/211 = -23.30 thousands of units per week.

4)
A company is decreasing production of math-brain protein bars at a rate of 100 cases per day. All cases produced can be sold. The daily demand function is given by p(x) = 20 − x/200,
where x is the number of cases produced and sold, and p is in dollars.
If the daily production is 800 cases, then revenue is decreasing at a rate of (20 - 800/200) * (-100) + (800) * (-1/200) * (-100) = (20 - 4) * (-100) + (800) * (1/2) = -1600 + 400 = -1200 dollars per day.

5)
The wholesale price p of e-tablet writing styluses in dollars is related to the supply x in thousands of units by 400p^2 − x^2 = 14375,
If 5,000 styluses are available at the beginning of a week, and the price is falling at 30 cents per week, then supply is rising at a rate of (2 * 400 * p * (-0.30) - 2 * x * x')/(2 * -1 * x) = (800 * p * (-0.30) - 0)/(2 * -5000) = (800 * sqrt(14375 + 5000^2)/400 * (-0.30) - 0)/(2 * -5000) = (800 * sqrt(14375 + 25000000)/400 * (-0.30))/(2 * -5000) = (2 * sqrt(14375 + 25000000) * (-0.30))/(-5000) = 0.012 * sqrt(14375 + 25000000) = 150.90 thousands of styluses per week.

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the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.

In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. It can be as simple as a single number or variable, or as complex as a long sequence of operations involving multiple variables and operators.

The expression |a|≤5 means that the absolute value of a is less than or equal to 5. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative.

So, if |a|≤5, then a must be between -5 and 5, including both.

To see why this is true, consider two cases:

If a is greater than or equal to zero, then |a| = a, and so we have a ≤ 5.

If a is less than zero, then |a| = -a, and so we have -a ≤ 5, which is equivalent to a ≥ -5.

Therefore, the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.

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Answer:

the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.

Step-by-step explanation:

What is expression ?

In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. It can be as simple as a single number or variable, or as complex as a long sequence of operations involving multiple variables and operators.

According to the given conditions :

The expression |a|≤5 means that the absolute value of a is less than or equal to 5. The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative.

So, if |a|≤5, then a must be between -5 and 5, including both.

To see why this is true, consider two cases:

If a is greater than or equal to zero, then |a| = a, and so we have a ≤ 5.

If a is less than zero, then |a| = -a, and so we have -a ≤ 5, which is equivalent to a ≥ -5.

Therefore, the values of a that satisfy the inequality |a|≤5 are those that satisfy both a ≤ 5 and a ≥ -5. This is why the expression equivalent to |a|≤5 is a ≥ –5 and a ≤ 5.

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The ratio of the amount Joe saved the money against Keith is 1:2.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

Ratios contrast two figures by ordinarily dividing them.

A/B would be your formula if you were comparing one data point (A) to another data point (B).

This indicates that you are multiplying information A by information B.

For instance, your ratio will be 5/10 if A is 5 and B is 10.

So, the total money saved is $45.

Joey saved $15.

Then, Keith saved:
45 - 15 = 30

The ratio would be:

15/30

1/2

1:2

Therefore, the ratio of the amount Joe saved the money against Keith is 1:2.

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The lateral surface area of the cylinders {W} and {Y} are same.

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given are the dimensions of the cylinder as shown in the image.

The lateral surface area of the cylinder is -

L.S.A = 2πrh

{ 1 } -

L.S.A {W} = 2π x 3 x 9 = 54π

{ 2 } -

L.S.A {X} = 2π x 4 x 2 = 16π

{ 3 } -

L.S.A {Y} = 2π x 4.5 x 6 = 54π

Therefore, the lateral surface area of the cylinders {W} and {Y} are same.

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Answer:

3rd choice down

f(x) = -1/2x + 8

Step-by-step explanation:

find the slope of the line using the 2 given points:

slope = m = (8-14) / (0--12) = -6/12 = -1/2

read the y intercept right off the graph at point (0,8):

b = 8

f(x) = mx + b = -1/2x + 8

Answer:

on what?

Step-by-step explanation:

How do you get rid of an inner bully?

5 Ways to Stop that Inner Bully

Become aware of what you are saying to yourself. ...

Replace this with mindful attention to your feelings. ...

Realize you are not alone in your suffering. ...

Use soothing self-talk. ...

Access Your Wise Mind.

Answer:

Для применения метода деления отрезка пополам нужно использовать тот факт, что функция x^3 + 2x + 4 непрерывна на всей числовой оси. Кроме того, нужно заметить, что функция монотонно возрастает на всей числовой оси, так как ее производная 3x^2 + 2 всегда положительна.

Начнем с интервала [a, b], где a = -2 и b = 0. Тогда значение функции в точке a равно -4, а значение функции в точке b равно 4. Значит, на этом интервале есть хотя бы один корень уравнения x^3 + 2x + 4 = 0.

Посередине интервала [a, b] находим точку c = (a + b) / 2 = -1. Значение функции в точке c равно 1, то есть на интервале [c, b] нет корней уравнения.

Затем выбираем интервал [a, c] и повторяем процесс. Находим точку d = (a + c) / 2 = -1.5. Значение функции в точке d равно -1.375, то есть на интервале [d, c] есть корень уравнения.

Продолжаем делить отрезки пополам и находить корни, пока не достигнем требуемой точности. Например, следующая точка будет e = (d + c) / 2 = -1.25. Значение функции в точке e равно 0.234375, то есть на интервале [e, c] есть корень уравнения.

Таким образом, метод деления отрезка пополам дает корень уравнения x^3 + 2x + 4 = 0 на интервале [-1.25, -1.125], который можно записать в виде x ≈ -1.1875 (с точностью до Ɛ=0,01).

Answer:

1.8 i think

Step-by-step explanation:

i used a calculator

Answer: B

Step-by-step explanation:

A perfect square is in the name: square!

Any number squared means that it can represent a square, since the side lengths are equal. In this example, 6^2 is a perfect square since a square with equal side lengths of 6*6 would be perfect; any other length measures would not make it a square. Hope this helps explain it!

Answer:

6^2

Step-by-step explanation:

62 = (6 ×  6) = 36. Here, 36 is a perfect square because it is the product of two equal integers, 6 × 6 = 36.

M' A'T" H' is (1,1) and (2.5) equals 3.6 to form a quadrilateral. A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.

Let the scale factor of quadrilateral is center at 2.5 at (1, 1) then

(1,1) and (2.5) equals 3.6

(1,1) + (2.5) =  3.6

Therefore, the statement exists true about the dilation is

D. [tex]\frac{}{A'T'}[/tex] will overlap [tex]\frac{}{AT}[/tex]

A. [tex]\frac{}{M'A'}[/tex] will overlap [tex]\frac{}{MA}[/tex]

E. The slope of [tex]\frac{}{HT}[/tex] is equal to the slope of [tex]\frac{}{H'T'}[/tex]

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The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.

To find the required percentage, find the number of customers that chose chocolate creamer and total the number of customers who came to choose the creamer in the hour.

Divide the number of customers that chose chocolate creamer by the total number of customers and multiply by 100.

Here we have

The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour

The bale given is

                          Vanilla      Chocolate    

Age 18 - 30            2               6

Age 30 +                4               8      

Here, number of customers = 2 + 4 + 6 + 8 = 20

No of customers that choose chocolate creamer = 6 + 8 = 14

The percentage of customers that put chocolate creamer

=  [ 14/20 ] × 100 =  70%

Therefore,

The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.

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Answer: 70%

Step-by-step explanation:

The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is approximately 0.1736 or 17.36%. The probability that the ballot measure might pass in Region B can be calculated using a confidence interval approach.

The confidence interval for the population proportion of voters who support the ballot measure in Region B:

CI = p ± z × SE

where p is the sample proportion, z is the critical value for the desired confidence level (e.g., z=1.96 for 95% confidence), and SE is the standard error of the sample proportion.

the standard error of the sample proportion:

SE = [tex]sqrt [p ×\frac{(1-p)}{n} ][/tex]  = [tex]sqrt[0.51 ×\frac{(1-0.51)}{400} ][/tex] = 0.025

where p is the sample proportion and n is the sample size.

the confidence interval using a 95% confidence level:

CI = 0.51 ± 1.96  0.025 = (0.46, 0.56)

Therefore, we can be 95% confident that the true population proportion of voters who support the ballot measure in Region B falls within the range of 0.46 to 0.56. Since the lower bound of the confidence interval is above 0.50, there is a possibility that the ballot measure might pass in Region B. However, the exact probability would depend on the actual population proportion and the sample size.

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Answer:

5,6 and 7.

Step-by-step explanation:

I am not sure what the three step method is, but here is how I solved it.

Consecutive integers means integers in a row.  For example, 5,6 7 are consecutive integers or -4,-3,-2 are consecutive integers.

Integers are all the whole numbers (0,1,2,3...) and their opposites (..., -3, -2, -1)  1/2 or -.23 are not integers.

Let x = the first number

Let x + 1 = the second number

Let x + 2 = the third number

x + (x + 1) + (x + 2) = 18  I do not need the parentheses, but I want you to see that  the first number, plus the second number, plus the third number equals 18.

x + x + 1 + x + 2  = 18  Combine like terms

3x + 3 = 18  Subtract 3 from both sides of the equation

3x + 3 - 3 = 18 - 3

3x = 15  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] = [tex]\frac{15}{3}[/tex]

x = 5

The first number is 5.  The second number is 6 and the last number is 7.

Check:

5 + 6 + 7 = 18

18 =18 Checks.

Helping in the name of Jesus.

The function is relative minima

If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative maximum of f. If f(b) < f(x) in an open interval containing b, x ≠ b, then the function value f(b) is a relative minimum of f.

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The runner should choose the second cooler, because the probability of selecting a sports drink and a water from the first cooler is about 24.98% and the second cooler is about 25.86%.

To calculate the probability of selecting a sports drink and a water bottle from each cooler, we need to use the following formula:

Probability of selecting a sports drink and a water bottle = (number of sports drinks / total number of bottles) x (number of water bottles / (total number of bottles - 1))

For the first cooler, the probability of selecting a sports drink and a water bottle is:

(19/39) x (20/38) = 0.2498, or about 24.98%

For the second cooler, the probability of selecting a sports drink and a water bottle is:

(14/29) x (15/28) = 0.2586, or about 25.86%

Therefore, the runner should choose the second cooler, because it has a slightly higher probability of selecting a sports drink and a water bottle.

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To find the \( x \)-intercepts of a function, we need to set the function equal to 0 and solve for \( x \). This will give us the values of \( x \) where the function crosses the \( x \)-axis. In this case, we have:

\[ f(x)=x^{2}+5 x-14=0 \]

We can solve this quadratic equation using the quadratic formula:

\[ x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a} \]

Plugging in the values of \( a=1 \), \( b=5 \), and \( c=-14 \), we get:

\[ x=\frac{-(5)\pm\sqrt{(5)^{2}-4(1)(-14)}}{2(1)} \]

Simplifying, we get:

\[ x=\frac{-5\pm\sqrt{25+56}}{2} \]

\[ x=\frac{-5\pm\sqrt{81}}{2} \]

\[ x=\frac{-5\pm9}{2} \]

This gives us two solutions for \( x \):

\[ x=\frac{-5+9}{2}=\frac{4}{2}=2 \]

\[ x=\frac{-5-9}{2}=\frac{-14}{2}=-7 \]

So the \( x \)-intercepts of the function are \( (2,0) \) and \( (-7,0) \).

Answer: \[ (2,0),(-7,0) \]

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Answer:

Step-by-step explanation:

2-Bs:  4 x 3.8 = 15.2     2 x 15.2 = 30.4 m²

2-Cs:  11.5 x 3.8 = 43.7   2 x 43.7 = 87.4 m²

Total S.A. = 92 + 30.4 + 87.4 = 209.8 m²

Answer: 2.98m squared i think im not sure im just guessing im still not fully awake yet bro.

Step-by-step explanation:

line e is parallel to line m because angle 1 + angle 2 = 180°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Represent the adjascent angle to angle 2 by x and adjascent angle to angle 1 by y

therefore ;

2 = y ( corresponding angles are equal)

1 = x ( corresponding angles are equal)

angle 1+y = 180 ( angle on a straight line)

angle 2 + x = 180

<1= 180-y

<2 = 180 -x

and both equations

< 1 +<2 = 180

therefore since < 1 +<2 = 180, then line e is parallel to line m

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