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By similar triangles, HC/JE = 7/5.

(10+x)/2   * 4  = 38

x = 9 units

Rememger   sin^ + cos^2 =1        cos will be negative for angles > 90 degrees    (and less than 270)

  1-  25/36 = cos ^2      cos = - sqrt11/6 

tan = sin/cos     <====== you can finish..... 

It will be the same x distance on the OTHER side of the vertex    12,0

(1, 4, 8, 9, 16, 25, 27, 36, 49, 64, 81, 100, 121, 125)==14 such numbers.

Alright, I'll give the link a try. I've been having a hard time with everything related to matrices, lol. I'm never gonna use it in my future anyways, thankfully.

https://web2.0calc.com/questions/help-please-thx_4#r4

Important:  triangle WXY can be any type of triangle and the result will be the same!!!

I used the right triangle, and I got this answer:  YZ = 9.428571429

I'll let you convert that decimal into a fraction. 

Continued here.

Yes I understand that, I was not accusing you of leaving anything out.

I just wonder if the original asker of the question left something out.

I assume you copied and pasted the question?

"A total of 420 green marbles and red marbles were put into Box A

and Box B respectively. There were 1 1/2 times as many red marbles as 

green marbles. Some yellow marbles were put into Box B. For every 

3 green marbles in Box A, 16 blue ones were added into Box A.

Box A then had four times as many marbles as Box B. What was the 

ratio of the number of yellow marbles to the number of blue marbles?"

I learnt Cramer's rule before I learn other methods but it is horrible.

I guess it is easy enough once you memorise all the steps but the steps make little sense to an ordinary person like me.

Matrices are brilliant for solving equations but Cramer's rule is far less intuitive than normal matrix elimination method.

Anyway.....

I suppose you have to learn Cramer's rule.

Here is a You Tube clip that is extremely well presented.

That is what the question says.

I am far from convinced that the question is answerable.

I have looked at this question and I do not think that there is enough information given.

When you get the answer (preferably with working) can you please share it with this forum.

Do you know how to sum an arithmetic sequence ?

   d = 2   n = 17    a1=20

c+ a = 207      or     c = 207-a

c+12 = 1/2 (a-12)     sub in the red equation

207-a + 12 = 1/2 a - 6

225 = 1 1/2 a

a = 150 

k + d = 200       or   k= 200 - d

Then     k - 2/7 k = 1/4   (d + 2/7 k)

               5/7 k - 2/28 k = 1/4 d

               18/28 k = 1/4 d                 sub in the red equation

               18/28 (200 - d) = 1/4 d

                   d = 144

Let initially Kevin had x dollars and Danny had y dollars. The initial sum of money is $200 therefore,

x + y = 200     (1)

Kevin gave 2/7 of his money to Danny. So, amount of money Kevin gave to Danny is 2x/7. The Danny total money was y + 2x/7

dollars and Kevin's money was x - 2x/7 = 5x/7 dollars.

The amount of money Danny had = y + 2x/7 (2)

After taking money from the Kevin the Danny had 4 times as much money as Kevin therefore the Danny had 4 (5x/7) dollars.

The amount of money Danny had = 4(5x/7) (3)

Combining both (2) and (3)

It gives,

y + 2x/7 = 4(5x/7) 

Solve the equation for x 

2x/7 = 20x/7 - y

2x = 20x - y ⋅ 7

  x = 7y/18

Substitute x = 7x/18 in (1) and solve for y.

                      7y/18 + y = 200

7y/18 ⋅ 18 + y ⋅ 18=200 ⋅ 18

                                25y=3600

                                    y=144

The Danny had $144 at first.
 

One question per post thanks.

Notice how we have 3 right triangles. 

Use the pythagorean theorem to set up 3 equations. 

How can we manipulate 2 of the equations to find the hypotenuse of the triangle?

I hope this helps. :))

=^._.^=

27 pounds = 12.25 kg

12.25 kg * 5 mg/kg = __________ mg

  cos 243        -sin 243

-sin243          -cos 243                  Rotation is 242.928 clockwise    ( I rounded to 243 degrees) 

The smallest side length is 18*sqrt(2) + 6.