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 In triangle ABC, AB = 3, BC = 4, and angle B = 90 degrees.

Square DEFG is inscribed in triangle ABC such that D and G are on side AC, E is on side AB and F is on side BC

Find the side length of the square.

\(\begin{array}{|rclrclrcl|} \hline \tan(A) &=& \dfrac{x}{p} & && & \tan(A) &=& \dfrac{4}{3} \\ &&& \dfrac{x}{p} &=& \dfrac{4}{3}& \\ && &\dfrac{p}{x} &=& \dfrac{3}{4}& \\ && &\mathbf{p} &=& \mathbf{\dfrac{3x}{4}}& \\ \hline \end{array} \)

\(\begin{array}{|rclrclrcl|} \hline \tan(C) &=& \dfrac{x}{q} & && & \tan(C) &=& \dfrac{3}{4} \\ &&& \dfrac{x}{q} &=& \dfrac{3}{4}& \\ && &\dfrac{q}{x} &=& \dfrac{4}{3}& \\ && &\mathbf{q} &=& \mathbf{\dfrac{4x}{3}}& \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline p+x+q &=& 5 \\\\ \dfrac{3x}{4}+x+\dfrac{4x}{3} &=& 5 \\\\ x*\left( \dfrac{3}{4}+1+\dfrac{4}{3} \right) &=& 5 \\ x* \dfrac{37}{12} &=& 5 \\\\ x &=& 5*\dfrac{12}{37} \\\\ x &=& \dfrac{60}{37} \\\\ \mathbf{x} &=& \mathbf{1.\overline{621}} \\ \hline \end{array}\)

There is a lot of incidental (unneeded) information here.

Here is the pic that goes with EP's working.

First one:

6a^2 + 5a + 4 = 3,

6a^2 +5a +1 = 0      Now use Quadratic Formula to find the two values of a  ....use the smaller one to calculate   2a + 1

25^x-9^y=18

5^x-3^y=3          Multiply this equation by -4      add it to the first equation ...and see what you get !

2(3-i)+i(2+i).    expand

6 - 2i  + 2i  + i^2        =    ????      (remember  i^2 = - 1)

sin 53 = 400 ft / (swim distance)                         sin 53 = .7986

         Solve for swim distance  

                              then    time   =   distance/ rate          (rate is given as 150 ft/min)

# Chaperones = C    

#Students =  S =    7C -13        added together must equal 107

C   +   7C-13     = 107                            Solve for C    then     S = 7C-13

The rows must hold    450 -60 people 

26 rows

(450-60) people / 26 rows   =  ?       people/row

Not sure this is possible.....    for every distance Achilles runs the turtle should be   12/13 behind him

Achilles  13

Turtle     1

A  26

T   2

39

3

thanks!!

Thank you so much for explaning that problem to me!!!

Each number is a multiple of 3, or 1 more than a multiple of 3, or one less than a multiple of 3.  These number we will call x's, y's, and z's.

If we add x + y + z, then we get x, because y and z will even each other out, since y is 1 more than multiple of 3 and z is one less.

Because of this, we can conclude that we have to arrange the numbers in a repeating pattern, like x, y, z, x, y, z, ... or z, y, x, z, y, x, ...

In this set 1, 2, 3, ..., 9, there are 3 x's, 3 y's, and 3 z's.

To fill up a pattern, there are 3 choices for the first x, y, z, 2 choices for second, then 1 choice.

3^3 * 2^3 * 1^3 = 27*8*1 = 216

This is equal for both patterns, so there are 216 * 2 = 432 ways to arrange the numbers.

https://web2.0calc.com/questions/help-quick_12

and

https://web2.0calc.com/questions/help-pls-fast_2

and

https://web2.0calc.com/questions/help-please_22649

The domain will be all t  > 0

The range will be from the starting point y =  100 grams ...and gets smaller and smaller as t increases until y = 0 (eventually....when there is no more plutonium-239 to decay)

J = John age now                     five years ago   j-5

S = Sam age now = J+12         five years ago  5 (j-5)

J + 12      - 5    = 5 (J-5)

J + 7 = 5J - 25

4J = 32

J = 8                       Sam now = J + 12 = 20    y/o

I'm not entirely sure about this answer, but I'll try it.

As pentagons have 5 vertices, this means they can have four diagonals to the other side of the pentagonal prism. Each diagonal is independent of the four others, so the answer would just be 5*4 = 20.

92% water weight   means 8 % grapefruit meat  (or 8 pounds)

At 90% water weight    10% is meat

10% x = 8

.1x=8

x= 80 pounds

First, let's find the number of people rather than percentages.

65% of 600 is 390.

49% of 600 is 294

7% of 600 is 42.

The total amount of people that use the facilities is 600 - 42 = 558.

To find the number of people who use both, we add the two together and then subtract the actual amount of people, or 600.

390 + 294 = 684

684 - 600 = 84.

To find the probability, divide it by 600 to get 84/600 = 42/300 = 21/150 = 7/50.

Ok, so if it ends with a zero, that means it is divisible by ten. This means the number is divisible by both 5 and 2.

The sum of the digits is also divisible by 3, so that means it is divisible by 3. 

Because it is divisible by 3 and 2, it is also divisible by 6.

6, 3, 5, 2, are the only ones that can necessarily divide it, so your answer is 4.

If you feel the need to provide the means for a totally lazy person to cheat then by all means answer.

Is it your desire to be the answer board for a rude and lazy cheat?

This person has asked many questions and has NEVER thanked anyone.  

Should I try answering Melody?

Let X be the starting weight of the grapefruit, which is 100 pounds. Let W be the amount of water evaporated. Let the amount of water at start be A. 92% of X is A, and 90% of X-W is A - W. Equation is 23X/25 = A, 9(X-W) /10 = A - W. The first equation is 23X = 25A, the second is expanded into 9X-9W = 10A - 10W, or 9X + W = 10A. Remember that we want to find X - W, so we substitute A for X using the first equation. (5/2)(9X + W) =23X.

45X/2 + 5W/2 = 23X. 45X + 5W = 46X. X = 5W. We know X was 100, so 5W = 100, or W = 20. Thus, the final answer is 100-20 = 80. We can check the answer by seeing 90% of 80 is 9/10 * 80 = 72, which is 20 less than 92% of the start.

Do lots ot practice homework.

If you are being honest and nothing makes any sense then...

If your family can aford it, find yourself a good one to one tutor.

Hast to be a good one (maybe not expensive, just good)

If you go to one it will not take long to decide it if its a good one or not.

However, it is a mistake to think all maths is suppose to make sense. 

When you are first learning something, nothing makes much sense. A lot of it is memory work.

Practice over and over again. That is how to memorise tihngs. If you are lucky, understanding witll follow.

Thanks EP.

It is hard to read.

My real complaint though is that if a person is too lazy to write their question properly then they will be too lazy to put the effort needed into understanding any answer they are given.

So why bother answering.