Lucinda is writing a coordinate proof to show that a diagonal of a parallelogram partitions the parallelogram into two equal areas.


A parallelogram graphed on a coordinate plane. The vertices of rectangle are labeled as K L M and N. The vertex labeled as K lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as L lies on begin ordered pair x comma 2 y end ordered pair. The coordinate of vertex M is left blank. The vertex labeled as N lies on begin ordered pair 3 x comma 0 end ordered pair. A diagonal is drawn between points K and M.



Enter your answers in the boxes to complete Lucinda's proof.

Since KLMN is a parallelogram and a parallelogram's opposite sides are parallel and congruent, the coordinates for M are (4x, 2y).


In △KMN, the length of the base is and the height is . So an expression for the area of △KMN is .


In △KLM, the length of the base is 3x and the height is 2y. So an expression for the area of △KLM is .


Comparing the area of the two triangles that are formed by a diagonal of the parallelogram shows that a diagonal of a parallelogram partitions the parallelogram into two equal areas.

The width of the door is [tex]37.8ft[/tex] and the height of the door is [tex]39.6ft[/tex]

Let

[tex]A=\text{the front area of the door}\\h=\text{the height of the door}\\w=\text{the width of the door}[/tex]

From the question

[tex]A=w\times h=1496.9\\h=w+1.8[/tex]

We are to find both the width and the height of the door. To proceed, we have to eliminate the height, and solve for the width. Later, we calculate the value of the height from the width.

Eliminate the height;

[tex]A=w\times h\\A=w\times(w+1.8)\\w^2+1.8w-A=0[/tex]

substitute the value of the front area into the equation and solve for the width

[tex]w^2+1.8w-1496.9=0\\w\approx 37.8\text{ or }w\approx-39.6[/tex]

the width can only take positive value. Now, to get the height

[tex]h=w+1.8\\=37.8+1.8\\=39.6[/tex]

the width and height of the door are [tex]37.8ft[/tex] and [tex]39.6ft[/tex] respectively.

Another example can be found in the link: https://brainly.com/question/18625465

Answer:

yes

Step-by-step explanation:

Ratios are equivalent if they are multiples or divisors of each other.

5 : 2 ( multiply both sides by 6 )

= 30 : 12

or

30 : 12 ( divide both sides by 6 )

= 5 : 2

Thus 5 : 2 and 30 : 12 are equivalent ratios

Answer:

equivalent

Step-by-step explanation: 5 x 6 = 30      2 x 6 = 12

Answer:

A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval)

Step-by-step explanation:

A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation. Examples of discrete quantitative variables are number of needle punctures, number of pregnancies and number of hospitalizations.

Answer:

x = -3

Step-by-step explanation:

1. 5 - x = 8

2.   +x    +x

3. 5 = x + 8

4. -8       -8

5. x = -3

[tex] \boxed{ \huge \bf \: Solution:—}[/tex]

[tex] \sf \longmapsto \dfrac{2}{3} \ + \dfrac{7}{15} [/tex]

[tex]\sf \longmapsto \: \dfrac{10}{15} + \dfrac{7}{15} [/tex]

[tex]\sf \longmapsto \: \dfrac{10 + 7}{15} [/tex]

[tex]\sf \longmapsto \dfrac{17}{15} [/tex]

[tex]\boxed{\huge\bf{Answer:—}}[/tex]

[tex]\bf \dfrac{17}{15} [/tex]

OR

[tex]\bf{1.13}[/tex]

Answer:

Step-by-step explanation:

Answer: The answer is c. f(n)=4n+1

Answer:1. How can you tell by looking at each graph that a proportional relationship exists between the quantities?

relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.

2. Find the constant of proportionality for each graph. Write your answer as y = kx.

y = kx or y = k/x, where k determines how the two variables are related to one another. This k is known as the constant of proportionality.

Step-by-step explanation:

Work Shown:

1 week = 7 days

3 weeks = 21 days .... multiply both sides by 3

3 weeks + 4 days = 21 days + 4 days = 25 days

Answer:

14.3%

Step-by-step explanation:

1/7=0.142857142857

round that to the nearest tenth and that is 0.143

make it a percentage and it is 14.3%

1. Value=206

2. Value=205

3. Value= 208

4. Value=207

Answer:

Step-by-step explanation:

The Mega Clean mixture with 3 1/2 per gallon has more cleaner in it. The first mixture has .75 oz per quart. The second mixture has .875 oz per qt.

HOPE THAT HELP YOU

Answer: £4,164

Step-by-step explanation: multiply 896 by 4 to get £3,584 next add 580 to 3,584 to get £4,164

Answer: 4,164

Step-by-step explanation: I am confused if the 896 is a percent or the money she owes every year, now here is the explanation.

Emily took the £580 and after the 4 years she owes 896*4 = £3,584 plus the original £580 which is £4,164

If it it without the original £580 then the answer is 896*4 = £3,584

If that is not correct then i am sorry

The survey was intended for Bill's middle school during the summer. The

survey was administered to students of other schools on a Saturday.

Reasons:

The type of error made is a non sampling error, given that the target of the

study is the number of times in a week students at his middle school

attend the beach during the summer.

The errors are; Selection bias error.

The selection bias error is a type error that is due to the researcher

chooses what to study, such that the participant have common

characteristics rather than being random.

Learn more about selection bias error here:

https://brainly.com/question/13727092

Answer:

code is 4163

Step-by-step explanation:

x-35=27;x=64

-96=-8x;x=12

6=x/4 +2;x=16

76-3x=-29; x=31

code is 4163

Answer:

at least 8

Step-by-step explanation:

im from k12

Answer:

6.67%

Step-by-step explanation:

5 / 75 = 0.066667

(0.066667)(100) = 6.67%

Answer:

800 shrimp

Step-by-step explanation:

100 plates of shrimp

8 shrimp on each plate

100 × 8 = 800

= 800 shrimp were prepared by the chef

Hope this helps.

Answer:

54

Step-by-step explanation:

okay so the method it sounds like is multiplication so first you would skip count by 3's like this 3, 6, 9,12,15,18,21,24,27,30  and while your doing that count on a paper or anything you can wright on because you don't have 18 fingers anyway when you mark your 18th tali mark then if you remember or if you wrote down the numbers  then that's your answer

Answer:

Hola

tengo una pregunta

de que país

eres? ._.

Answer:

3

just because

Answer:

See below

Step-by-step explanation:

[tex]\sqrt[3]{9}=9^{\frac{1}{3}}[/tex]

[tex](\sqrt[3]{9})^3=(9^{\frac{1}{3}})^3[/tex]

[tex]9=9^{\frac{1}{3}*3[/tex]

[tex]9=9^\frac{3}{3}[/tex]

[tex]9=9^1[/tex]

[tex]9=9[/tex]

Remember that [tex](a^b)^c=a^{b*c}[/tex]

Answer:

-2x

Step-by-step explanation:

the answer for the question is -2x

Answer: the 20 ounce box cost less per ounce

Step-by-step explanation:

Answer:

Step-by-step explanation:

If I am not mistaken the equation is [tex]S(t) = 2 + 31t - 16t^{2}[/tex]

Then in that case V(t) = S'(t) = 31 - 32t

V(t)=0 gives the time when the stone hits the ground.

31 - 32t = 0

32t = 31

t = 31/32 = 0.96875s

Answer:

...

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Cumulative Exam 2021

Merry Christmas <3

P.S. Have a good winter break :)

Answer:

67 hamburgers

Step-by-step explanation:

In order to find the answer to this question, you must do the following equation:

44÷2/3. The answer to this is 66.

Then, you add 1 to 66, because 2/3 divided by 2/3 = 1!

So, the cook can make 67 hamburgers.

Answer:

x = 18

Step-by-step explanation:

Answer: multiply 6 by 3 and 10 by 3

Step-by-step explanation:

G = 10.8

creds to sqdancefan