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ON the left side it started off 4 and is now 12 which is a 300%increase

6*3= 18 

18-6= 12 

x=12

To find the population 10 years from now, first you have to find how much the population increases in a year. 

5% of 22,000 is how much the population would increase in a year, which is 1100 per year. Now you have how much the population increases in a year, so all you have to do is multiply it by 10, and add it to 22,000 to find the total population.

1100*10=11000

11000+22000= 33,000

nah, that was perfect!

Thank You!

WLOG, let the vertical height of ABCD be 1 (the trapezoid will then obviously be way more squashed than the image). 

Notice that triangles ABO and ODD are similar. Therefore, the ratio of the length of CD to the length of AB is $36:25$ , so the height of triangle ABO is $\frac{25}{36+25} = \frac{25}{61}$. 

The height of OXY is then just $\frac{1}{2}-\frac{25}{61}=\frac{11}{122}$. Since OXY and ABO are similar, the length of xy is just $\frac{11}{122}\cdot61 = \boxed{5.5}$

(i am not completely sure of this answer as I submitted this very late at night and I am not extremely good at these particular problems)

Q is the incenter of the triangle, which means that it has the same distance to the three sides of the triangle. QM, QP, and QN are line segments perpedicular to the sides and so their measure indicates that distance. So PQ must also be 6 units long.

LQ is an angle bisecto, so the measure of PLN is 2(22)= 44 degrees.

Measure of PJM is 180-(44+ 34) = 102 degrees, so PJQ has measure (1/2)(102) = 51 degrees since JQ is an angle bisector.

Guest answerer:

How would you get 0?

I assume you mean prime factor 270.

270/2 = 135

135/3 = 45

45/3 = 15

15/3 = 5

5/5 = 1

Therefore: 270 = 2 * 3 * 3 * 3 * 5

This Q was posted a little while ago.....and it had a diagram...

     you might try to search for it and see if it was ever answered....

Not sure of this

1   2    16    17    18   32    33  

Thanks mate!

The graph of is shown in red below. Find

https://latex.artofproblemsolving.com/d/9/f/d9fbbcb6f385be51bfae50bf03b220b3c7909ba9.png

(Assume grid lines are spaced 1 unit apart.)

Look at the value of the red line (the function) where x = 2    you should see  f(2) = 2  

The graph of is a parabola whose vertex is at . The graph of is also a parabola. Where is the vertex of the graph of ?

Write your answer as an ordered pair.

  Will be shifted 3 to the RIGHT   to  4,-2

Two ways at least to do this...

   here is one      in the first equation where 'x' is    put in the second equation (-1/4x + 1/4)   and simplify

      if the result is just 'x'   theya re inverses.....try it ......let us know if ya need more help....

second method     y =  -4x+1     switch x's and y's

                              x = -4y + 1    solve for 'y'  to see if it matches the second equation.....if it does, they are inverses....

The possible angles of DBE are 14 and 20.

Edit: I shortly found out that i had flipped the y coordinate, not the x coordinate. The answer is (2, -7) btw

tysm!

5 out of (1+5= 6)   are yellow

5/6 = 20     so there are  24 total ....meaning  4 are  red

if you add  x red marbles to the 4    they become 1/3 of the total

     (4+x)/ (24+x) =1/3    cross multiply

12 + 3x = 24+x

   2x = 12

     x = 6 ===== reds added       now there are 10 out of 30 reds   20 out of 30 are yellow    ratio   1:2

There might be a better way to determine those angles – there probably is a better way to determine those angles – but here's what I thought of. 

Move to the left of the angle marked 3y and draw a perpendicular between lines e and f.  

This creates a five sided figure.  The sum of the interior angles of a polygon of n sides is (n – 2) • 180^o  

The sum of the interior angles of the pentagon is 540^o  

Note that one of the interior angles is the supplementary angle of 2x so its value is (180^o – 2x)    

The five angles:  

90^o  - one of the angles newly created with the perpendicular line  

90^o  - the other angle newly created with the perpendicular line  

3y  -  another angle

(180^o – 2x)  -  another angle  

a  -  the angle we want to find

a  =  540^o minus all the other angles    

a  =  540^o – 90^o – 90^o – 3y – (180^o – 2x)  

a  =  540^o – 180^o – 3y – 180^o + 2x  

a  =  2x – 3y + 180^o  

_.

Allowed obviously but not encouraged... you will not often get answers to all of your Q's when you post them this way....

Cross multiply:

5(a-b) = 3(a+b)

5a - 5b = 3a+3b

2a = 8b

a/b = 8/2   =   4:1

2 x 135

2 x 3 x 45

2 x 3 x 3 x 15

2 x 3 x 3 x 3 x 5     ( IhaveOBJD put one too many 3's in there .....but nice try !)

maybe use pick's theorem

I believe you could just substitute and solve. I am achieving (5 - sqrt3, 5 + sqrt3) and (5 + sqrt3, 5 - sqrt3).

note that 7-24-25 is a pythagorean triple