All Answers 358093 Answers

Equilateral triangle APQ is inscribed inside square ABCD. Find the area of square ABCD.    

cosine of angle BAP = BA/PA    

cosine of angle DAQ = DA/QA     

BA = DA                             both being sides of a square     

PA = QA                             both being sides of an equilateral triangle    

therefore angle BAP = angle DAQ   

angle PAQ = 60^o                 being an angle of an equilateral triangle    

therefore angle BAP = (1/2)(90^o – 60^o) = 15^o       

cosine BAP = BA/PA   

cosine 15^o  = 0.9659                     from the tables        

therefore    BA/PA = 0.9659   

                         BA = (PA)(0.9659)    

                         BA = (4)(0.9659)

                         BA = 3.8637   

                         Area of the square = (3.8637)²  =  14.928 square units    

I did some rounding on each decimal fraction that I wrote down above,       

but as I was doing the calculations I left the entire fraction.       

_.

It is pretty clear you aren't smart enough to make up that joke.

(3^3-2^4)*6    

I assume you want this multiplied out    

                                                                     (3³ – 2⁴) • 6    

Perform the exponent operations                 (27 – 16) • 6    

                                                                             (11) • 6    

                                                                                 66   

_.

That's funny right there.      

_.

Solve the quadratic equation using the square root property. 25=(x+8)^2  

Definition from online:  "the square root property states that if we have an equation with a perfect square on one side and a number on the other side, then we can take the square root of both sides and add a plus or minus sign to the side with the number and solve the equation"   

                                                                                 25  =  (x + 8)²    

Take the square root of both sides                             5  =  x + 8     

Add a plus or minus side to the number                   +5  =  x + 8    

Subtract 8 from both sides                                         x  =  (–3, –13)    

_.

Note that \(x=1+\frac1{1+x}\), so \(x^2+x=1+x+1 \implies x=\pm \sqrt 2\). However, since \(x\) is obviously positive, the answer is \(\sqrt 2\).

Correct

Our badminton team has finished 75% of its season.  So far, we have won 20% of the games we played.  What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?  

You've played 75% of the season.  So, you've played   

75% of the total number of games in the whole season.   

You've won 20% of 75% of the total number of games    

in the season.  That means you've won 15% of the total    

number of games in the season.  

To achieve that 50% winning season, you will need to win   

another 35% of the total number of games in the season.  

However, since there's only 25% of the season left, then   

there are only 25% of the total number of games in the  

season left to play.  There are not enough games left.    

It's impossible to achieve your 50% winning season.    

_.

So if you have won about 15% of the games this season, you can't achieve a 50% win rate....