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5*5=25

5*3=15

15/2=7.5

so 

7.5+25=32.5   

Wow I cant Belive thanks curiousdude for laying that out and thanks everyone else for laying it out to but I think curiousdude really made clear of it and Cphill becasue he was going step by step..... 

Thanks Dimitristhym for your private tutoring and offering time to help me! 

Thankyou all!

~Nickolas 

Thanks Rom, I might just do that  

Find the area of each shape, then add them up.

Area of square=5\(\cdot\)5

Area of right triangle=5\(\cdot\)3 /2

Figure that out

I think hectictar answered something like this a few days ago.....mine isn't as exquisite as hers

Area  =  (1/2)  (a) (b) sin C       (1)

And

   a            b                              a sin B

____  =  ____      so   b  =      ______           (2)

sinA       sin B                            sin A

Sub (2) into (1)     and we have that

Area  =  (1/2) (a) (a sin B) sin C             a^2 sin B sin C

             ___________________    =     ______________

                           ( sin  A)                             2  sin  A

You should be able to do the other two  using

Area =  (1/2) (b) (c) sin A           and   noting that          c  = b sin C /sin B

And

Area  = (1/2) (a) (c) sin B              and noting that   a  = c sin A / sin C

The total number of coins is  65

x + y  =  65       ←This is equation 1

The total value of the coins is $3.80

the total number of cents  =  380

5x + 10y  =  380       ←This is equation 2

From equation 1 we know...

x + y  =  65

x  =  65 - y

From equation 2 we know...

5x + 10y  =  380

                                         We know  x  =  65 - y  so we can substitute  65 - y  in for  x

5( 65 - y ) + 10y  =  380

                                         Distribute  5  to the terms in parenthesees.

325 - 5y + 10y  =  380

                                         Subtract  325  from both sides.

-5y + 10y  =  380 - 325

                                         Combine like terms.

5y  =  55

                                         Divide both sides by  5

y  =  11

Again from equation  1  we know....

x  =  65 - y

                           And we just determined that  y = 11

x  =  65 - 11

x  =  54

x + y  = 65    ⇒  y = 65 - x      (1)

5x + 10y = 380      (2)

Sub (1) into (2)  for  y    and we have that

5x + 10 ( 65 - x)  = 380    simplify

5x + 650 - 10x = 380

-5x + 650 = 380        subtract 650 from each side

-5x = -270       divide both sides by -5

x = 54 = the number of 5 cent coins

And 65 - x  =  65 - 54  = 11 = the number of 10 cent coins

S = F/ [1 - R], where S = sum of infinite series, F = First term, R = Common ratio

S = 4 / [1 - 6/7]

S = 4 / (1/7)

S = 4 x 7

S = 28 =7 + 6 + 5 + 4 + 3 + 2 + 1 + 0

4.)$A,B,C,D,$ and $E$ are points on a circle of radius $2$ in counterclockwise order. We know $AB=BC=DE=2$ and $CD=EA.$ Find $[ABCDE]$.

Call the center of the circle , O

If AB + BC + DE = 2

Then triangles  AOB, BOC and DOE   must be equilateral.....and their combined area  =

3 (1/2) (2)^2 * √3/2  =

3√3  units^2

Since angles AOB, BOC and DOE  = 60°

And CD = EA

Then angles COD and EOA  must   each equal  [ 360 - 3(60)]  / 2  =  180/ 2  = 90°

So....the total area of triangles COD and DOE  =   2 (1/2) * 2^2  =  4 units^2

So....the total area of  ABCDE  =   4+ 3√3  units^2

Nice, hectictar   !!!!

Start by finding the equation of the red line.

The red line passes through the points  (1, -2)  and  (3, 1)

slope of red line  =  \(\frac{\text{rise} }{ \text{run} }\ =\ \frac{1--2}{3-1}\ =\ \frac{3}{2}\)

Using the point  (1, -2)  and the slope  \(\frac32\) ,  the equation of the red line in point-slope form is:

y + 2  =  \(\frac32\)(x - 1)

                                 Multiply both sides of the equation by  2 .

2(y + 2)  =  3(x - 1)

                                 Distribute.

2y + 4  =  3x - 3

                                 Subtract  3x  from both sides and add  3  to both sides.

-3x + 2y + 7  =  0

And the red line is dotted, so it is not included in the inequality. So the liner inequality of the graph is either

-3x + 2y + 7  >  0       or       -3x + 2y + 7  <  0

To determine which one, pick a point which we know should make the inequality true and test that point.

We know that the point  (0, 0)  should make the inequality true.

Is it true that     -3(0) + 2(0) + 7  >  0       ?  Yes, it is true that  7 > 0 .

So the linear inequality of the graph is     -3x + 2y + 7  >  0

\((\sqrt{2}+\sqrt{3})^3\)        ⇒     \( a\sqrt{2} + b\sqrt{3} + c\sqrt{6}\)

( √2 + √3)^3  = 

(√2)^3 + 3*(√2)^2 *(√3) + 3 * (√2) *(√3)^2  + ( √3)^3  =

2√2 + 3*2*√3 + 3*3*√2 + 3√3  =

2√2 + 9√2 + 6√3 + 3√3  =

11√2 + 9 √3  + 0 √6

a + b + c  =

11 + 9 + 0  =

20

Actually, due to Pythagoras, AD=8 & AB=17. So the answer is 8/17. (For #2)  

Let  a  and  b  be the measures of the two other angles of the triangle.

the sum of the interior angles in a triangle  =  180°

a + b + (a + b)  =  180°

2(a + b)  =  180°

a + b  =  90°

the measure of the smallest exterior angle  =  180° - the measure of the largest interior angle

the measure of the smallest exterior angle  =  180° - ( a + b )

the measure of the smallest exterior angle  =  180° - 90°

the measure of the smallest exterior angle  =  90°

Yes, you and CPhill gave him six replies and he made progress at every step. He was learning how to do this.  Nickolas is none too bright, but he’s not a retardo. The kid wants to learn. In his final attempt, he used the formula for the area of a right triangle on the square. If you pointed this out, he would have solved it himself. Along with a sense of accomplishment, he’d likely remember the difference.   

You are right but we try with 6 answers to help him.I solve it because mabe understand the consept of the exercise for this reason I write tit like this Area = area1 + area2 and if understand the consepm will understand and the operations.

I was student and I have students I know how it is.

Have a nice day/night.

What I suggest is you continue to help him solve it –not do it for him.

Would you have learned math if someone always did the problems for you?  

Every number appears Pascals' Triangle at least once, so the answer is a hundred(100).

I solve it step by step we told him its (side)^2 side=5 and he told 5^2 = 12.5...

Be more polite and also I talk with him in p.m.

After all instead my answer and all this answers of CPhill what will suggested you as an answer?

There are a theorem witch say:

An exterior angle of a triangle is equal to the sum of the other two angles of the triangle.

So the measure of the smallest exterior angle of the triangle equals to the sum of the other two angles of the triangle.

See answer No. 2 here: https://web2.0calc.com/questions/please-emergency-details-please

Aha ok thank you I was wandering if it was a mathematical symbol witch I didn't know.