Write a two-column proof of the Alternate Exterior Angles Theorem. (Theorem 3.3)

The size of the segment in the scale drawing using a drawing scale factor of 5 meters to one box is 30 meters.

A scale factor is a value with which the dimensions of an original two dimensional geometric figure or a three dimensional solid can be multiplied to obtain an image.

Scale factors are used in maps and drawings to represent a large geographic area, or a life sized object on paper, such that the relative sizes of the sides of the original figure are maintained

Solution;

Using the height of the arc in the drawing as the reference, we have;

50 m is equivalent to 10 boxes

Therefore;

The length of one box = (50 m)/10 = 5 m

The scale of the drawing is therefore;

The length of the given segment = 6 box length

The length, L, of the segment is too therefore;

L = 6 box × 5 m/box = 30 m

The length of the segment is L = 30 meters

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i) cost of oil change = $29.99

ii) Balance on December 1 = $252.009

iii) Difference between the two balance = $85.79

According to the question we have been that

           Total balance on November 1 = $337.88

i) We need to find how much did the oil change cost.

  For that we will first calculate how much balance was left after depositing after pay check.

Balance after spending in groceries= $337.88 - $ 42.59 = $295.29

Balance after depositing from savings account = $295.29 + $125.00 = $420.29

Balance after spending in electric bill = $420.29 - $35.67 = $384.62

Balance after depositing from paycheck = $415.00 + $384.62 = $799.62

Therefore, Cost of oil changing = $799.62 - $769.63 = $29.99

ii) For the balance on December 1 after rent had paid, we will first calculate the balance after spending for birthday present.

Balance after spending for birthday present = $769.63 - $17.54 = $752.09

Therefore the balance on December 1 = $752.09 - $500.00 = $252.09

iii) Difference in the two balance is

                                    = balance on November 1 - Balance on December 1

                                    = $337.88 - $252.09

                                    = $85.79

Hence the difference in the two balances is $85.79

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Answer: 50x+30y+5z= 690

              40x+15y+5z= 620

              45x+10y+5z= 510        

Step-by-step explanation: The first equation to find units of wood, the second is for the units of fabric, and the third is for the units of stuffing.

assuming 2x= 3x-42,

x=42

2x= 84

and 3x-42= 84

The equation that represents the cost C for membership for m months is:99.90+24.95m

The cost of a 2-year membership is $698.70

What makes up the total cost for membership for m months?

The fact that each member has to pay an enrollment fee and purchase key card for $79.95  and $19.95 respectively, means that the total fixed charge which is sum of both amounts is computed as shown below:

fixed charge=$79.95+$19.95

fixed charge=$99.90

variable cost per month=$24.95

total variable cost of m months=24.95m

C=99.90+24.95m

m=24(24 months=2 years)

cost of a 2-year membership=99.90+(24.95*24)

cost of a 2-year membership=$698.70

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The common difference d is 2.2 and the first term a1 is -9.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the two terms of arithmetic sequence,

a4 = -2.4 and a6 = 2.

now, find the common difference d.

a(n) = a1 + (n - 1)d

Let take a(n) = a6 and a1 = a4.

a6 = a4 + (6 - 4)d

a6 = a4 + 2d

now substitute the values of a6 and a4

2 = -2.4 + 2d

2 + 2.4 = 2d

d = 4.4/2

d = 2.2

so, the common difference d is 2.2.

then, find the term a1.

take the formula

a(n) = a1 + (n - 1)d

now, substitute a(n) = a4 and d = 2.2.

-2.4 = a1 + (4-1)d

-2.4 = a1 + 3d

-2.4 = a1 + 3(2.2)

-2.4 = a1 + 6.6

a1 = -6.6-2.4

a1 = -9.

so, the first term a1 is -9.

Hence, the common difference d is 2.2 and the first term a1 is -9.

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Answer:

4 or 1

Step-by-step explanation:

100%

u got this hope it helps

Answer:

The answer is -3

Step-by-step explanation:

f(-3)=3(-3)+6

f(-3)=-9+6

f(-3)=-3

Answer:the answer is -3, the first option (top to bottom)

Step-by-step explanation:

Find f(-3) as shown below

the answer is -3, the first option (top to bottom).

Answer:

10 24 32 are the answers

Step-by-step explanation:

My mom is a teacher lol

Answer:

Step-by-step explanation:

4.5 in

Divide the area of the triangle by the height.

The true statements are

The original statement is given as:

If a number is negative, the additive inverse is positive

This can be represented as

If p, then q

i.e. if p → q

So, (a) is correct

For the inverse, we simply negate the hypothesis and the conclusion

i.e. if ¬p → ¬q ----(b) is correct

For the converse, we simply switch the hypothesis and the conclusion

i.e. if q → p ----(e) is correct

Hence, the true statements are (a), (b) and (e)

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Answer:

6

Step-by-step explanation:

To find the GCF by factoring, list out all of the factors of each number and select the largest that both have in common.

Percentages greater than 100% can be expressed as x% where x is any real number

As a general rule, percentages are represented by %

Take for instance

x% is pronounced x percentage

Where x is any real number

Whether x is greater than 100 or not, the format of the expression remains the same

i.e. 150 percent is written as 150% and 25 percent is written as 25%

Hence, percentages greater than 100% can be expressed as x% where x is any real number

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The percentage of $99 to $70 is -29.29.The percentage change of $99 to $70 is decreases.

given that

the Andy's bank account went from $99 to $70.

The previous value is $99.

The new value is $70.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is generally represents by the percent sign, "%."

The most reliable indicator of percent change is the percent of growth or decrease. Calculations are frequently used to determine how much something has changed,

so the

change = original - new = $99 - $70 = -29

[tex]percentage = \frac{ - 29}{99} \times 100[/tex]

percentage = -29.29.

Hence,The percentage change of $99 to $70 is decreases.

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Answer:

answer is =3

Step-by-step explanation:

2*100000000+10000000/7*10000*1000

=210000000/70000000

=3

Answer:

Price after first increase:

Price after second increase:

The two steps above can be combined as:

Points lines and plane together are the undefined teerms that provide the base for geometry . the definition must be a word whose meaning is accepted as intiutively clear as that meaning is accepted without definition this words are called undefined terms . Although these terms are not defined in a broad way it is used for defining other terms but a small description is needed .

POINTS is the most fundamental object in geometry just like cell is the basic unit of life . A point just looks like a dot and is named by a variable the objecive of the point is to represent a position only .It has zero size .

LINES A straight line can be a medium connecting a set of infinetly many points . it extends infinitely in opposite direction . It has infinte lenght , no widht , no height .The symbol ↔  denotes that line , a line can also be denoted with a smaller letter .

PLANES It is considered as a set of infinite points joining to form a flat surface extending in all directions infinetly it has undefined lenght widht and no height . A single capital letter is used to denote a plane .

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Answer:

y=2x-7

Step-by-step explanation:

[tex]2x-y=6 \\ \\ -2x+y=-6 \\ \\ y=2x-6[/tex]

Parallel lines have the same slope, so we want the line with a slope of 2 through (3, -1).

This line is y=2x-7.

Answer:

f(x):f(x)=2/7x-9

Step-by-step explanation:

If it is wrong than i am sorry

Using proportions, it is found that:

a. There are 2736 calories in the fudge recipe.

b. There are 42.75 calories in a 1-inch by 1-inch piece of fudge.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, the recipe is composed by:

Hence the number of calories in the recipe is given by:

6 x 99 + 0.5 x 12 + 4 x 389 + 4 x 145 = 2736.

There are 2736 calories in the fudge recipe.

For item b, the areas are given as follows:

Hence the piece of fugde is 1/64 of the recipe, thus:

1/64 x 2736 = 42.75 calories.

There are 42.75 calories in a 1-inch by 1-inch piece of fudge.

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Answer:The marble that is farthest from the target is the pink marble.

Step-by-step explanation:

Answer:

Step-by-step explanatio                                                                                                     -3/8d-1 3/8

The expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or (-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.

(-3 1/4d + 3/5) - (2 7/8d + 7/10)

⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10

⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10

⇒ (-13/4 - 23/8)d + 6/10 - 7/10

⇒ (-26/8 - 23/8)d - 1/10

⇒ -49/8 d - 1/10

Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

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Answer: m<JKM=70 degrees

Step-by-step explanation:

JKM=JKL+LKM

JKM=42+28

JKM=70

m<JKM=70 degrees

According to the given statement the perpendicular distance form the point  (-4,4)  is 66.3.

Coordinate Geometry can be used to define points in space. The primary axis labeled a x- and y-axes is defined first, and then the points were measured and labelled in relation to these points. Furthermore, numerous geometric forms such as a line, curve, circle, ellipse, and hyperbola can be plotted inside the coordinate axes and their attributes studied.

the equation for line ℓ.

Begin by finding the slope of the line through the given points,(0,-2) and (1,3):

m = (Y₂ - Y₁)/(x₂ - x₁)

  = (3 - (-2))/(1 - 0)

  = 5/1

  = 5

The equation of the line using point (1,3) on the line:

Y - Y₁ = m(x - x₁)

putting value we get: (m = 5)

Y - (-2) = 5(x - 1)

Y + 2 =  5x - 5

Y  = 5x - 3

The equation of the line w perpendicular to line ℓ through P(-4,4).

The slop of line l is 5. Write the equation of the line using point P(-4,4) on the line.

Y - Y₁ = m(x - x₁)

Y - 4 = 5(x - (-4))

Y - 4 = 5x + 4

Y = 5x + 8

Solve the system of equations to determine the point of intersection. Subtract both sides of (1) and (2) to eliminate y.

5x + 8 = 5x - 3

5x + 8 - 5x + 3 = 0

x = 11

putting the value of x to find y:

Y = 5x + 8

Y = 62

Applying the formula to find the distance of a points:'

[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

d = √((11 - 4 )² + (62 + 4)²)

d = √(4405)

d = 66.3

According to the given statement the perpendicular distance form the point  (-4,4)  is 66.3.

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The height of the second person is 72 inches .

Let the height of the second person be "x"

We need to line up a relationship between 2 sets of numbers.

We are told that the connection could be a direct proportion as it is given that "a person 81 inches tall casts a shadow 94.5 inches long". therefore we will setup a magnitude relation that relates those 2 which is given by 81/94.5.

Since 81 and 94.5 are unit each in inches and that we will categorical the peak of the tree within the same units, feet, because the shadow of the tree, we do not got to worry concerning conversion of units.

81 is to 94.5 as x is to 84 is given by

81/94.5 = x / 84

0.8571 × 84 = x

      72 = x

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Answer:

In bold below.

Step-by-step explanation:

There are 12*12 = 144 square inches in a square foot.

So, there are 144 in^2 per 1 ft^2

So, we have:

               144 in^2

32 ft^2     -----------   =      4608 in^2.

                   1 ft^2

For yards it is 1 yd^2 per 9 ft^2 :-

                  1 yd^2

32 ft^2 =   ------------ =   3.56 yd^2.

                    9 ft^2