Complete the coordinate proof of the theorem.


The coordinates of parallelogram ABCD are A (0, 0), B (a, 0), C ( , ), and D (0, b).

The coordinates of the midpoint of AC¯¯¯¯¯ are ( , b2).

The coordinates of the midpoint of BD¯¯¯¯¯ are (a2, ).

The midpoints of the diagonals have the same coordinates.

Therefore, AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.

Final Correct Answer:

14n - 16g + 8

Hope this helps :)

Error:

The error was that I'm the first step where they distributed -4 to the numbers - 3n, + 4g, - 2 wrong. They multiplied with the wrong integer rules.

Real answer - how to solve:

- 4 multiply by - 3n would be + 12n (Negative times Negative equals Positive).

-4 multiply by + 4g would be - 16g (Negative times Positive equals Negative).

- 4 multiply by - 2 would be + 8 (Negative times Negative equals Positive).

So that was the error.

Step-by-step explanation:

1. Distribute.

2n - 4( - 3n + 4g - 2)

2n + 12n - 16g + 8

2. Combine Like Terms (CLT).

2n + 12n - 16g + 8

14n - 16g + 8

Answer:

l = [tex]\frac{S-\pi r^2}{\pi r}[/tex]

Step-by-step explanation:

S = πr² + πrl ( subtract πr² from both sides )

S - πr² = πrl ( isolate l by dividing both sides by πr )

[tex]\frac{S-\pi r^2}{\pi r}[/tex] = l

Answer:

[tex] l = \dfrac{S - \pi r^2}{\pi r} [/tex]

Step-by-step explanation:

[tex]S = \pi r^2+\pi rl[/tex]

[tex]\pi r^2+\pi rl = S[/tex]

[tex]\pi rl = S - \pi r^2[/tex]

[tex] l = \dfrac{S - \pi r^2}{\pi r} [/tex]

Answer:

The answers to the question in reference to the graph are mentioned below.

Step-by-step explanation:

It is given that we need to find the mentioned questions alongside the graphs of the functions;

Now, let us consider the first question given herein;

Now, let us consider the second part of the question;

To know more about this topic, click here:

https://brainly.com/question/2565875

#SPJ9

The age distribution of nurses in Great Britain at the time of Florence Nightingale will be 30 - 39, 40 - 49, etc.

Age distribution, also known as age composition, is the proportion of people in each age group within a given population in population studies. The main reason why age distributions vary between nations is because of variations in fertility rates and trends.

It can be estimated by dividing the populations of those aged 0 to 14, and 65 and older, by those aged 15 to 64. Example: In a town, there are 6,800 people over the age of 65 and 41,650 children under the age of 14.

The percentages of people in a population who are a certain age have a significant impact on how quickly that population grows.

In conclusion, the age distribution of nurses in Great Britain at the time of Florence Nightingale will be 30 - 39, 40 - 49, etc.

Learn more about age distribution on:

brainly.com/question/28355249

#SPJ1

Using the Empirical Rule, the percentages are given as follows:

a) 99.7%.

b) 49.85%.

c) 0.15%.

It states that, for a normally distributed random variable:

In this problem, we have that:

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

#SPJ1

The animal is 150 inches tall .

Scale Factor = ( scale / actual )

Given : Scale Factor = ( 1 / 30 )

To find : the actual height of animal .

Let t be the actual height of animal .

Therefore Scale Factor comes out to be ( 5 / t ) .

Equating both the scale factors and hence finding the value of t ,

( 1 / 30 ) = ( 5 / t )

t = 150 inches .

Therefore , the animal is 150 inches tall .

To learn more on scale factor follow link :

https://brainly.com/question/1903243

#SPJ9

The total amount of that Harry will need for the project is nineteen and seven twentieth feet. option A

Wood 1:

Total = Length of each × Number of pieces

= 2 5/8 × 6

= 21/8 × 6

= 126 / 8

= 15 3/4 meters

Wood 2:

Total = Length of each × Number of pieces

= 1 1/5 × 3

= 6/5 × 3

= 18/5

= 3 3/5 meters

Total amount of wood needed for the project = 15 3/4 meters + 3 3/5 meters

= 126/8 + 18/5

= (630+144) / 40

= 774/40

= 19 14/40

= 19 7/20 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and seven twentieths feet. option A

Learn more about fraction:

https://brainly.com/question/11562149

#SPJ1

Answer:

we conclude that if JKL is rotated 180° clockwise about the origin, what are the new coordinates of point J(-4, 6) will be: J' (4, -6)

Hence, the answer choice (B) is correct.

Step-by-step explanation:

The rule of rotating a point 180° clockwise about the origin states that if we rotate a point P(x, y) 180° clockwise about the origin, it would take a new position with the coordinates P'(-x, y).

In other words, the sign of its x and y coordinates change.

Thus, the rule is:

P(x, y) → P'(-x, -y)

Given the triangle ΔJKL with the coordinates

J(-4, 6)

K(-1, 2)

J(-4, 2)

Thus, according to the rule:

P(x, y) → P'(-x, -y)

The new position of point J (-4, 6) will be J' (4, -6)

The new position of point K (-1, 2) will be K' (1, -2)

The new position of point L (-4, 2) will be L'  (4, -2)

Finally, we conclude that if JKL is rotated 180° clockwise about the origin, what are the new coordinates of point J(-4, 6) will be: J' (4, -6)

Hence, the answer choice (B) is correct.

Answer: 58%

Step-by-step explanation:
66.50 x 0.58 = 38.57

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

the sum is 0.

30+(-30)

= 30-30

=0

Answer:

21 dollars

Step-by-step explanation:

Cents ÷ 100 = Dollars

2100 ÷ 100 = 21

Hope this helped! (๑>◡<๑) xx

Answer: you would be paying 210$ if that’s what you’re asking

Step-by-step explanation:

Therefore, the speed of the bird is 55.44 kilometers per hour.

We know that speed is given by the formula distance travelled divided by the time taken.

Here distance = 46.2 meters and time = 3 seconds.

We are asked to find the speed in terms of kilometers per hour.

So, we need to convert the meters into kilometres and the seconds into hours.

We know that 1 kilometer is equal to 1000 meters.

⇒ 1 meter = (1/1000) kilometer

⇒ 1 meter = 0.001 kilometer

Therefore, 46.2 meters = 46.2 × (0.001) kilometers = 0.0462 kilometers

We know that 1 hour is equal to 3600 seconds.

⇒ 1 second = (1/3600) hours

⇒ 3 seconds = (3/3600) hours

Therefore the speed of the bird is equal to

speed = 0.0462 ÷ (3/3600) kilometers per hour

⇒ speed = 3600 × 0.0462 ÷ 3 kilometers per hour

⇒ speed = 3600 × 0.0154 kilometers per hour

⇒ speed = 55.44 kilometers per hour

Learn more unitary method here :

https://brainly.com/question/26046491

#SPJ9

Disclaimer:

The question is not complete.

Assuming the following as the complete question for answering.

An eagle flies 46.2 meters in 3 seconds. We need to find the speed of the eagle in kilometers per hour.

Answer: 88.4 centimeters

Step-by-step explanation:

Let's make a proportion:

412 m - 82.4 cm

442 m - x cm

Hence,

[tex]\displaystyle\\x=\frac{442*82,4}{412} \\\\x=\frac{442*82.4}{82.4*5} \\\\x=\frac{442}{5}=\\\\x=\frac{88,4*5}{5}=\\\\x=88,4\ cm[/tex]

Answer:

3x10-3

Step-by-step explanation:

9:3=3

the power 10^10 becomes the inverse so 10^-10. You need to subtract the exponents 7-10=-3 (following powers rules)

Answer: 50/100=0.5

100/10=10

Step-by-step explanation:

50/100=

1/2=0.5

100/10=

10^2 / 10^1 =

10^(2-1)=

10^1=10

50/100=0.5

100/10=10

Triangle ABC is translated 2 units right and 2 units down so that point A would be at the origin; hence the translated point B would be at B'(-2, 6)

Triangle ABC is rotated 90° clockwise about the origin to get A'(2, 2), B'(8, 4) and C'(3, 9)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

A) The vertices of triangle ABC is at A(-2, 2), B(-4, 8) and C(-9, 3). Triangle ABC is translated 2 units right and 2 units down so that point A would be at the origin; hence the translated point B would be at B'(-2, 6)

B) The vertices of triangle ABC is at A(-2, 2), B(-4, 8) and C(-9, 3). It is rotated 90° clockwise about the origin to get A'(2, 2), B'(8, 4) and C'(3, 9)

Find out more on transformation at: brainly.com/question/4289712

#SPJ1

[tex]\textit{sum of all interior angles}\\\\ S=180(n - 2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies S=180(5-2)\implies S=540 \\\\[-0.35em] ~\dotfill\\\\ 105+118+75+130+x~~ = ~~540\implies 428+x=540\implies x=112[/tex]

Answer:  Draw a straight line through (0, 16) and (1, 14)

The graph is below.

=========================================================

Explanation:

There are at least two approaches we can take

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

Method 1

Plug in x = 0 to find that....

y = -2x+16

y = -2(0)+16

y = 16

The point (x,y) = (0,16) is on the line. This is the y intercept

Repeat similar steps for x = 1

y = -2x+16

y = -2(1)+16

y = 14

The point (1, 14) is also on the line

Plot the points (0, 16) and (1, 14). Then draw a straight line through them to complete the graph for y = -2x+16

You only need 2 points at minimum to draw a linear graph.

The graph is shown below. Ignore the stuff in red.

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

Method 2

Compare y = -2x+16 to the form y = mx+b

The y intercept is where the graph crosses the y axis. In this case, it's at the location (0, 16)

Start at this point and move down 2 units and to the right 1 unit to arrive at (1, 14) which is another point on the line.

The stuff in red shows this motion of "down 2, right 1"

note that slope = -2 = -2/1 = rise/run

rise/run = -2/1

rise = -2 = go down 2

run = 1 = go to the right 1

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

Side note: You can use a graphing tool like Desmos or GeoGebra to graph quickly. I used GeoGebra to make the diagram below. Though it's handy to have practice to do it by hand.

In linear equation, n = 15 is the value of equation .

What in mathematics is a linear equation?

What is the linear equation's formula?

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).

-17 = 1/5n - 20

- 17 + 20 = 1/5n

3 = n/5

n = 15

Learn more about linear equation

brainly.com/question/11897796

#SPJ9

Answer:

candies bought = 3

price of 1 candy = $2.50

price of 3 candies =$(3*2.50)

Step-by-step explanation:

byeeee

It does not violate the law of supply.

The law of supply states that the quantity of a good supplied (i.e., the amount owners or producers offer for sale) rises as the market price rises, and falls as the price falls. Conversely, the law of demand says that the quantity of a good demanded falls as the price rises, and vice versa.

we can also say that ,The law of supply says that a higher price will induce producers to supply a higher quantity to the market. Because businesses seek to increase revenue, when they expect to receive a higher price for something, they will produce more of it.

An increase in price almost always leads to an increase in the quantity supplied of that good or service, while a decrease in price will decrease the quantity supplied.

The law of supply is a fundamental principle of economic theory which states that, keeping other factors constant, an increase in price results in an increase in quantity supplied.In other words, there is a direct relationship between price and quantity: quantities respond in the same direction as price changes.

Hence ,It does not violate the law of supply.

To learn more about law of supply

visit - https://brainly.com/question/11240536

#SPJ9

20 is the value in the given data set which have a relative frequency of 30%.

Given,

The data set as,

10, 20, 20, 50, 30, 20, 10, 50, 60, 70.

We have to find the value from the above given data set which have a relative frequency of 30%.

Relative frequency = (subgroup count / total count) × 100

Here, 20 is the most repeating value. So we can calculate with it.

There are three 20's in the set.

So, subgroup count = 3

Total count = 10

Then,

Relative frequency = (3/10) × 100 = 30

Hence, we can conclude that 20 is the value in the given data set which have a relative frequency of 30%

Learn more about relative frequency here:

https://brainly.com/question/16832475

#SPJ1

Answer:X=27

Step-by-step explanation:

(36-90)-180=54

54/2=27=x

Answer:

x = 27

Step-by-step explanation:

36 + ∠MON + 2x = 180

since ∠MON = 90

then 2x = 180 - 90 - 36

2x = 54

x = 27

Answer:-32 -0.46x is ur answer

Step-by-step explanation:

A triangle is graphed on a coordinate grid and then translated 5 units to the right and 1 unit up then the original triangle is located at (5,-4), and vertex of the new triangle after the translation is equal to = (10, -3)

A triangle is graphed on a coordinate grid and then translated 5 units to the right and 1 unit up.

If one of the vertices of the original triangle is = (5,-4)

Then the vertex of the new triangle after the translation is,

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Based on the given conditions, formulate,

A triangle is 5 units right.

That means, +5

And Triangle is 1 unit up.

That means, +1

Original triangle is located at (5,-4)

So, we can write,

⇒ (5+5 , -4+1)

⇒ (10, -3)

Therefore, the new triangle after the translation is equal to = (10, -3).

To learn more about visit Triangle translation :

brainly.com/question/8240654

#SPJ1

The equations that represent the largest number of x desks, y coffee tables, and z corner tables that can be made are

50x + 30y + 5z = 690

40x + 15y + 5z = 620

45x + 10y + 5z = 510

From the question, we are to determine the three equations that are needed to find the largest number of x desks, y coffee tables, and z corner tables that can be made

From the given information,

Desks use 50 units of wood, 40 units of fabrics, and 45 units of stuffing

Coffee tables use 30 units of wood, 15 units of fabrics, and 10 units of stuffing

Corner tables use 5 units of wood, 5 units of fabrics, and 5 units of stuffing

Also,

There are 690 units of wood, 620 units of fabric and 510 units of stuffing available to make the items

Thus,

The equations that represent the largest number of x desks, y coffee tables, and z corner tables that can be made are

50x + 30y + 5z = 690

40x + 15y + 5z = 620

45x + 10y + 5z = 510

Learn more on Writing linear equations here: https://brainly.com/question/20696003

#SPJ1

Answer: 12328 is the answer

Step-by-step explanation:

You put the 536 on top and 23 on the bottom and you multiply 3 first to get 1608 then you multiply 2 to get 10720. You add these two numbers and you get 12328 as your answer! :D

The product of 23 multiplied by 536 is 12,328.

We have,

The concept used to find the product of 23 multiplied by 536 is basic multiplication.

Start with the rightmost digit of the bottom number (536), which is 6.

Multiply 6 by the top number (23). We have 6 multiplied by 3, which equals 18.

Write down the rightmost digit of the result (8) under the line.

Carry over the remaining digit, which is 1, to the next column.

Now, multiply the carried-over digit (1) by the top number (23). We have 1 multiplied by 3, which equals 3.

Add the carried-over digit (1) to the result (3), which gives us 4.

Write down the rightmost digit of this new result (4) next to the previous digit (8), giving us 48.

Finally, multiply the leftmost digit of the bottom number (5) by the top number (23). We have 5 multiplied by 3, which equals 15.

Write down this result (15) shifted one place to the left, giving us 150.

Add the two partial products: 48 + 150 = 198.

Therefore,

The product of 23 multiplied by 536 is 198.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6

Answer:

8 13/20

Step-by-step explanation: