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Katen [24]
2 years ago
13

Find x and y can someone pls help

Mathematics
2 answers:
kodGreya [7K]2 years ago
8 0

Answer:

x = 25, y = 10

Step-by-step explanation:

I'll add a drawing of my own so that it's easier for me to explain, and for you to understand.  

Since line BC and line DE are parallel and line AE is being shared, angle ACB and angle CED will be the same. So the square will also be 3y.

Since line AB and line CD are parallel and line AE is being shared, angle CAB and angle ECD will be the same. So the heart will be 2x.

Now that we figured out two unknown angles, we can see that the two triangles share two angles with the same value. Since angles in a triangle add up to 180 (Added angles in every triangle are the same), the triangle shape (I drew) will be 4x.

We have a few clues to find the value of x and y.

1) 2x + 4x + 3y = 180 (all angles in a triangle add up to 180)

2) 3y + 2x = 180 - 100 (If you look near point C, we can see that 3y + 100 + 2x equals a flat line. A flat line equals 180)

We can use substitution. 3y + 2x can be replaced with 80.

So our new equation will be: 4x = 100

x = 25.

Now we can replace x with 25 in our second clue.

3y + 2(25) = 80

3y + 50 = 80

3y = 30

y = 10.

We can conclude that x = 25, and y = 10

Afina-wow [57]2 years ago
6 0

Answer:

x = 25 and y = 10

Step-by-step explanation:

The <u>arrows</u> on the line segments mean the lines are parallel.

Therefore, the diagram shows two similar triangles, which means their <u>interior angles</u> are the <u>same size</u>.  (Refer to the attached diagram).

<u>Interior angles of a triangle sum to 180°</u>:

⇒ 2x + 4x + 3y = 180

⇒ 6x + 3y = 180

⇒ 3(2x + y) = 180

⇒ 2x + y = 60

⇒ 2x = 60 - y

<u>Angles on a straight line sum to 180°</u>:

⇒ 3y + 100 + 2x = 180

⇒ 2x + 3y = 80

⇒ 2x = 80 - 3y

<u>Substitute</u> the first equation into the second equation, and <u>solve for y</u>:

⇒ 60 - y = 80 - 3y

⇒ 60 + 2y = 80

⇒ 2y = 20

⇒ y = 10

<u>Substitute</u> the found value of y into one of the equations and <u>solve for x</u>:

⇒ 2x = 60 - 10

⇒ 2x = 50

⇒ x = 25

Therefore, x = 25 and y = 10.

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<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

x\approx 2.9ft

<h2>Explanation:</h2><h2 />

First of all, let's calculate the area of the original rectangular garden:

A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2

Jake wants to increase the area by 50%, so the new area would be:

A'=168(1.5) \\ \\ A'=252ft^2

He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:

(12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives

Finally:

<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

x\approx 2.9ft

<h2>Learn more:</h2>

Dilation: brainly.com/question/10945890

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Answer:

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It is usually said that the mood in which you wake up is largely dependent on the type of sleep you have been in. This, in itself, is proof of the importance of sleep in our lives. While sleeping, our body finally gets its share of rest, and it also gets ample time to rejuvenate from all the wear and tear that it went through during the entire day. Not only this, the body is in its own working condition when we are sleeping, as this is the time when it supports the healthy functioning of the brain as well as physical attributes of our body. How many times have you been suffering from a headache, and then you slept for some time and found the pain to have vanished? This is the effect that a sound sleep session has on your mind as well as body.

Sleep is not only important for grown-up individuals and people who go to work, but it is also very essential for small babies and children in their growing-up years, as well. In small children, sleep supports the growth as well as development of their minds and bodies, and hence is a non- negotiable activity necessary for all human beings.

Sleep is undoubtedly one of the most essential requirements for the human body to function properly. It plays a very important role in ensuring the wellness of the human body, both physically as well as mentally. In fact, the importance of sleep is clear from the fact that it helps you with maintaining a good lifestyle throughout your entire lifetime. Not only does it help you maintain your physical and mental health, it also helps in maintaining a decent and healthy lifestyle along with ensuring safety from a number of fatal diseases.

It is usually said that the mood in which you wake up is largely dependent on the type of sleep you have been in. This, in itself, is proof of the importance of sleep in our lives. While sleeping, our body finally gets its share of rest, and it also gets ample time to rejuvenate from all the wear and tear that it went through during the entire day. Not only this, the body is in its own working condition when we are sleeping, as this is the time when it supports the healthy functioning of the brain as well as physical attributes of our body. How many times have you been suffering from a headache, and then you slept for some time and found the pain to have vanished? This is the effect that a sound sleep session has on your mind as well as body.

Sleep is not only important for grown-up individuals and people who go to work, but it is also very essential for small babies and children in their growing-up years, as well. In small children, sleep supports the growth as well as development of their minds and bodies, and hence is a non- negotiable activity necessary for all human beings.

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(C) \frac{1}{3} fraction of the marbles now in the bag is blue.

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To find what fraction of the marbles now in the bag is blue:

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Know more about fractions here:

brainly.com/question/17220365

SPJ4

Complete question:

A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?

(A) 1/5

(B) 1/4

(C) 1/3

(D) 2/5

(E) 1/2

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