<p>Hey, an explanation on any of these problems would be great. thanks.
P.776 #5
P.779 #15
P.779 #16</p>
<h1>5 - since there is a right triangle and the two legs are the same length, the triangle must be a 45-45-90 triangle. You know (or hopefully know) that in a 45-45-90 triangle the hypotenuse is equal to sqrt2 times the length of one of the legs, in this case xsqrt2. So the perimeter of the triangle is 2x+xsqrt2, and you can set this equal to 4+2sqrt2. This should make it clear that x is equal to 2.</h1>
<h1>15</h1>
<p>2^x+2^x+2^x+2^x=2^7
4(2^x)=2^7
2^x=(2^7)/4
2^x=(2^7)/(2^2)
2^x=2^(7-2)
2^x=2^5
x=5</p>
<h1>16 To maximize the value of one of the cards, the values of the other cards need to be as low as possible so that together they can average out to 15. What’s the lowest possible positive integer? 1. So the other four cards need to have a value of 1. Now you can use the equation of averages:</h1>
<p>(1+1+1+1+x)/5=15</p>
<p>Solve this and you get x=71.</p>