A and b are legs
a^2+b^2=c^2
lets say
a>b
so
a=13+3b
c=14+3b
a^2+b^2=c^2
(13+3b)^2+b^2=(14+3b)^2
9b^2+78b+169+b^2=9b^2+84b+196
10b^2+78b+169=9b^2+84b+196
minus 9b^2 both sides
b^2+78b+169=84b+196
minus 84b both sides
b^2-6b+169=196
minus 196 both sides
b^2-6b-27=0
factor
(b+3)(b-9)=0
set to zero
b+3=0
b=-3, false, dimentions cannot be negative
b-9=0
b=9
shorter leg is 9
a=13+3b
a=13+3(9)
a=13+27
a=40
c=14+3b
c=14+27
c=41
side legnths are
9in, 40in, 41in
AB being the longest and is opposite the right angle.
Answer (B)
Answer:He should buy the six pack.
Step-by-step explanation:
The total number of hotdogs that the shopper needs is 48.
The store sells identical hot dogs in 2 differently sized packages. They sell a six pack hot dog for $2.10, and an eight pack of hot dog for $3.12.
If the shopper buys the six pack hot dog, he would need to buy 8 of it. The total cost would be
8 × 2.10 = $16.8
If the shopper buys the eight pack hot dog, he would need to buy 6 of it. The total cost would be
6 × 3.12 = $18.72
The 6 pack is cheaper than the eight pack. Therefore,
He should buy the six pack.
O = number of oat cereal, w = number of wheat cereal, f = number of fruit cereal:
o + w + f = 4250
o = w + 715
f = 5w
The second equation tells us the value of o in terms of w, and the third equation tells us the value of f in terms of w, so we can plug in "w + 715" for o and "5w" for f in the first equation:
o + w + f = 4250
(w + 715) + w + (5w) = 4250
Then, add like terms and subtract and divide to isolate the w:
w + 715 + w + 5w = 4250
7w + 715 = 4250 Subtract 715 on both sides:
7w = 3535 Divide by 7 on each side:
w = 505
Now that we have w, we can plug it into the last equation to find f, the number of fruit cereal boxes:
f = 5w
f = 5(505)
f = 2525
Therefore, the factory packages 2525 fruit cereal boxes.
