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I hope this helps have a good life.

Andrew has 22.5 cause 45 divided by 2 equals 22.5 and divided by 2 is saying that it is being put in half 

How many square units are in the area of the convex quadrilateral with vertices

\(P_1(0, 0), P_2(3, 0), P_3(2, 2)\ and\ P_4(0, 3)?\)

Hello Guest!

\(A=A_{tra}+A_{tri}\)

\(A_{tra}=\frac{1}{2}\cdot (y_2+y_3)\cdot x_3=\frac{1}{2}\cdot(3+2)\cdot 2=\color{blue}5\)

\(A_{tri}=\frac{1}{2}\cdot y_3\cdot (x_4-x_3)=\frac{1}{2}\cdot 2\cdot (3-2)=\color{blue}1\)

\(A=A_{tra}+A_{tri}=5+1=\color{blue}6\)

The area of the convex quadrilateral has 6 square units.

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Yellow squares have area 1 so the sides  =  1  

Which makes the purple squares sides     =  2  

Which makes the brown squares sides      =  5   

Area of brown squares .... 2 squares with area 5²  each  =  2 • 25  =  50  

Area of purple squares .... 2 squares with area 2²  each  =  2 • 4   =    8  

Area of yellow squares ....  2 squares with area 1²  each  =  2 • 1   =    2  

Add up all six areas ....                                                    total area  =   60 square units  

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The largest positive integer n that works is 6.

1. The product of the diagonals is 12.

2. The longest is the median.

3. The radius of the inscribed circle is 2.

Call the side  of the square, S

Area of largest blue  triangle  =   (S)^2 / 2   =  S^2 /2

Area of  next largest blue triangle =   (S/2)^2 / 2 =  S^2  / 8

This  infinite series  continues   as  S^2 /32  ,etc. (each successive  square has 1/4  the area of the previous one = the  common  ratio )

So  the sum of the areas  is  S^2 (1/2  +  1/8   + 1/32  + ....... )

The sum of the series inside the parentheses is given  as     first term  /( 1 - common ratio )

(1/2)  / ( 1  -1/4)   =    (1/2) / (3/4)  =  (1/2) (4/3)  =  4 / 6  = 2/3

So

The fraction of the square  covered =    2/3

1. Let f(x)=3x+2 and g(x)=x^2   -5x-1. Find f(g(x)). 

We are putting   g into f  

3 ( x^2 - 5x  - 1) + 2   =   

3x^2 -15x  - 3  +  2   =

3x^2  - 15x  - 1

Thank you so much, have a good life CPhill

Let's suppose  that the band has 100  members

(1/5)  * 100 =   20 play percussion

(1/2) (20)  =10  play snare

10  /100    = 1  /10     CORRECT, Alston  !!!

f ( x)  - g(x)  =

(2x^2 + 3x  -9 )  - ( 5x + 11)  =      2x^2 - 2x  -20

Add h(x)

(2x^2 - 2x  - 20 )  +  (3x^2  + 1)   =    5x^2  -2x  - 19

7 mi / 10.5 m/hr = .66667 hr = 40 minutes

train 13  + 6 min later start   + walk 5 = 24 min         40 -24 = 16 min to bagel on

Side   opp  the 60° angle =   hypotenuse  * ( sqrt 3/2)  =  6.5 sqrt 3= 11.258 cm

30-60-90 triangle   hyp = 13 cm

one leg is 13 sin 30 = =6.5 cm

other leg is 13 sin 60 = 11.258 cm

1/2 b h = area = 1/2* 6.5 * 11.258 = 36.58 cm²

Let b = boys and g = girls

b = g-1     the number of boys is one less than the number of girls

g = 2(b-1)     a brother has b-1 brothers.and twice as many sisters

You now have two equations for two unknowns.  Can you take it from here?

As follows:

******

Those aren't negative signs. 

The problem says: 

The hypotenuse of a 30° 60° 90° triangle is 13 cm. Find the area of the triangle in square centimeters.

Thank you so much, have a good life and thank you for futher explaining it.

Let's say this table is Ila's working space. If half of the working space paper.

 Next, a third of the paper is sticky notes...

So, we end up getting only 1/6 of the working space is covered in sticky notes. We use 1/2x1/3 to get this.

Thank you so much, have a great life 

1/2*1/3 = 1/6

Let  18 = z

Let  x =   z + a          and       y =   z + b

So  we have

1/ (z + a) +  1/ (z + b)  =   1   /  z                

(2z + a + b)  /  [ (z + a) (z + b) ] =     1  / z           cross-multiply

(2z  +  a  +  b)  z =   (z + a) ( z + b)

2z^2  + az + bz  =  z^2  + az + bz   +  ab

z^2  =   ab

Which  means that   18^2 =   ab   =    324

a      b                 x =  z + a             y =  z  +  b

1    324                 19                         342

2    162                  20                        180

3    108                  21                         126

4     81                   22                         99

6    54                    24                         72

9    36                    27                         54

12  27                    30                         45

Smallest  value  of x  +  y =   30  +  45   =  75

nice diagram