CPhill

If ZAX is equilateral and has a perimeter of 30, then each side is 10.  So XA = ZA = 10....

And note that  ZL = 1/2 of XA  = 5

So....using the Pythagorean Theorem, LA  =

√[ZA^2 - ZL^2]  = √[10^2 - 5^2] = √[100 - 25] = √75 = √[25 * 3] =  5√3 = LA

So...the area of the quadrilateral = B*H = XA * LA  = 10 * 5√3  =  50√3  =  about 86.6 sq units

The altitude in an isoceles right triangle creates two congruent triangles whose base and height are each = 6.

So .... 2 (1/2) b * h   =   2 (1/2) 36 = 36 sq units

Let y  be the years between the time you were 48 and the time when you will be three times as old as your daughter ... (2021).....so we have

48 + y  = 3(y + 2)

48 + y  = 3y + 6

42 = 2y    

y= 21

So you will  be 69  in 2021.....so you're 6 years younger now  = 63

Check....

Your daughter will be 23 in 2021.....so she was born in 1998

When she was 2   (in 2000), you were 15 years younger than you are now....so 63 - 15 = 48....and this was 24 times her age in 2000....!!!! 

Am I correct????

3(2y+3) = 5y+9       distribute the "3" across the terms in the parentheses

6y + 9   = 5y + 9      subtract 9 ftom both sides

6y = 5y                     subtract 5y from both sides

6y - 5y = 0               factor out y

y(6 - 5)  = 0

y*1  = 0

y = 0

s = 2 [(3/4)pi ]  = 3/2pi  = about 4.71 in

Could you explain this one more in detail, Melody (or Nauseated)....???....I'm afraid I'm not seeing where you got these combinatoric formulas from.....

Sign me, 

Confused   !!!

1 / [1 +sin Θ] + 1 / [ 1 - sin Θ ]   get a common denominator

[ 1 - sin Θ + 1 + sin Θ ]  /  [ 1 - sin^2 Θ]  =

2 / [1 - sin^2 Θ ]  =

2 / cos^2 Θ  =

2 sec^2  Θ

 x³ + 4x² = 150

The hour hand moves 1/12 x 360°  in every hour = 30° every hour or 30/3600 = 1/120°  every second.....at 4AM it had advanced 120° since midnight.

But, since 7 minutes and 19 seconds = 439  seconds....it has advanced an additional 439/120 =  3.6583°  since 4AM .....so it has advanced 123.8583°  since midnight

The minute hand advances 360° every hour = 6°  every minute. So, in 7 minutes it has advanced 42° since the top of the hour plus another 19/60 x 6°  = 1.9°....so it has advanced 43.9°  since 4AM

So...the angle between the hands is  [ 123.8583 - 43.9  ]°  = about 79.7583°  {I assume you might want the negative of this iif we're measuring clockwise  ???}