Bosco

CORRECTION to my above.  

3x + 2 = 0 which means x = –3/2   

It should have been      x = –2/3     

Which makes the final answer     x  =  (–2/3, –4) 

_.

CORRECTION to my above.   

An error has been pointed out to me. 

The answer should be 16 (x+ 5)    

Of course it should.  

Right away I knew that that lengthy discourse was not written by the real GA.  It lacks the subtlety that is much of the grace of GA's prose.  Agreed, it is entertaining, in a ham-handed sort of way, not worthy of admiration yet, but a tolerable beginning.  The author has promise, but must rid herself/himself of the bane of the amateur writer, to wit, overuse of adjectives.  And the author says "Ah" three times, way too many.  Note to the author:  I wouldn't have been so hard on you if you hadn't tried to pass yourself off as GA; register an account and log in, to receive the measure of acclaim you deserve.     

_.

Simplify    

                           (2x + 10)⁴      

                          ––––––––      

                             (x + 5)³          

Factor the (x + 5)'s out of the numerator   

so you can cancel out the denominator.  

I'll write it out real simple.  Actually, I have to,   

if I'm going to keep those exponents straight.  

                           (2)(x + 5) • (2)(x + 5) • (2)(x + 5) • (2)(x + 5)   

                          –––––––––––––––––––––––––––––––—–––     

                                (x + 5)   •   (x + 5)   •   (x + 5)             

                          Which leaves      8 (x + 5)    

_.

All members of our painting team paint at the same rate. If 20 members can paint a 2000 square foot wall in 30 minutes, then how long would it take the  members to paint a 2000 square foot wall, in minutes?   

You mean another 2000 square foot wall?   

Maybe the opposite side of the same wall?   

Well, since it took 30 minutes to paint the first wall,  

then, to paint the second wall, another 30 minutes.  

_.

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 36, QR = 16, and MY = 50, then find the area of triangle PQR    

Those are the lengths of the sides of the triangle, which is all you need to find the area using Heron's Formula.   

if a, b, and c are the lengths of the sides: Area = square root of s(s - a)(s - b)(s - c) where s is half the perimeter.   

         36 + 36 + 16            88     

s  =  ———————  =  ———  =  44     

                 2                       2            

A  =  square root of (44)(44 – 36)(44 – 36)(44 – 16)    

A  =  square root of (44)(8)(8)(28)    

A  =  square root of 78,848     

A  =  280.8 square units    

_.

I drove to the beach at a rate of 40 miles per hour.  If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later.  How many miles did I drive?   

You mean 45 minutes earlier.  Obviously, if you drive faster, you get there faster.  

This problem makes use of

the following relationship:                   Distance = Velocity x Time 

                                                           D  =  V • T  

case 1                                                 D  =  (40) • (T)  

case 2                                                 D  =  (50) • (T – 45)  

Since the Distance, D, is the  

same for both cases, let's set       

the "V•T"s equal to each other.             (50)(T – 45)  =  (40)(T)  

                                                               50T – 2250  =  40T  

Subtract 40T from both sides                  10T – 2250  =  0  

Add 2250 to both sides                                       10T  =  2250  

Divide both sides by 10                                           T  =  225   (this is in minutes)  

Divide minutes by 60 to get hours                           T  =  225 min / 60 min/hr  =  3.75 hours  

Plug this T back into original equation                     D  =  (40 mi/hr) • (3.75 hr)  =  150 miles  

_.

>>> people who can't be bothered to look up their question <<<    

But the OP is looking up their answer.  They're looking them up right here.  

I didn't tell them anything that their math instructor wouldn't have told them.  

I didn't reveal exactly what the values of those trigonometric functions are.  

just how to find them.  I did what the teacher should have done, or maybe    

the instructor did try to teach this, but the student couldn't grasp it then.      

At least you said "please" which is courteous versus some of these trolls.  

.

I didn't check the imaginary numbers, but the real       

numbers check out right on the money.  Good work.     

_.

how do you find the exact values for sin 0, cos 0, and tan 0    

You can look them up in the trig tables    

You can find them on a scientific calculator  

You can google each one as a question   

Or, my favorite, you can draw, or visualize, a right triangle.   

And then knowing the ratios   

sine  =  opposite leg over hypotenuse             

cosine  =  adjacent leg over hypotenuse   

tangent  =  opposite leg over adjacent leg   

edited to add ~  In this context, "over" means "divided by".  

_.