Answer:
W = 16
L = 24
Step-by-step explanation:
Let's write down the information we have first
"The length of a rectangle is 8 feet longer than it is wide"
L = W + 8
"If each side is increased 8 feet, then the area is multiplied by 2."
(L + 8)(W + 8) = 2LW
Now we can solve for W first, then L
(W + 16)(W + 8) = 2W(W + 8)
W² + 24W + 128 = 2W² + 16W
0 = W²- 8W - 128
0 = (W - 16)(W + 8)
W = 16
L = 24
(This part above is solved like quadratics)
8y^3+316
divide both sides by 4 (smallest divisable number) just say you tried to factor 2 and 3 and they weren't whole numbers and then you tried 4 and gave you the answer :)
4(2y^3+79)
Answer:
B. Since Ax-b is consistent, its solution set is obtained by translating the solution set of Ax=0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax= 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.
Step-by-step explanation:
the answer to the question is answer B. and here is the explanation below
let us imagine that the equation ax = b has a solution
now our goal will be to show that the solution of ax =b when ax = 0 has only trivial solution.
ax = 0 is homogenous
if this equation was consistent for b, we define
ax = b to be a set of vector that has the form
w = m + gh(h is a subscript)
gh is a solution of ax = 0
from what we have above, ax=b is in the form ofw= m+gh
with
m = solution of ax=b
gh = soulution of ax=0
ax = 0 has only trivial solution
gh = 0
with gh = 0
ax=b is w=m
so ax = b is unique.
3 females 15 females
–––––––– = –––––––––
2 males n males
cross multiply
3n=15*2
3n=30
n=10
10 males
