Equation for Liz:
L = 8n
Equation for Andy:
A = 8n + 35
Step-by-step explanation:
Let the no. of necklace be 'n'
Cost per necklace= $8
Equation for Liz:
L = 8n
Because Liz sells only necklace for $8 each
Equation for Andy:
A = 8n + 35
Because Andy sells each necklace for $8 and she sold the bracelets for $35
Answer:
From the graph attached, we know that 
by the corresponding angle theorem, this theorem is about all angles that derive form the intersection of one transversal line with a pair of parallels. Specifically, corresponding angles are those which are placed at the same side of the transversal, one interior to parallels, one exterior to parallels, like 
and 
.
We also know that, by definition of linear pair postulate, 
and are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.
They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that and together are 180°, because they are on a straight angle. That is, 
If we substitute for , we have 
, which means that and are also supplementary by definition.
Answer:
y2 = C1xe^(4x)
Step-by-step explanation:
Given that y1 = e^(4x) is a solution to the differential equation
y'' - 8y' + 16y = 0
We want to find the second solution y2 of the equation using the method of reduction of order.
Let
y2 = uy1
Because y2 is a solution to the differential equation, it satisfies
y2'' - 8y2' + 16y2 = 0
y2 = ue^(4x)
y2' = u'e^(4x) + 4ue^(4x)
y2'' = u''e^(4x) + 4u'e^(4x) + 4u'e^(4x) + 16ue^(4x)
= u''e^(4x) + 8u'e^(4x) + 16ue^(4x)
Using these,
y2'' - 8y2' + 16y2 =
[u''e^(4x) + 8u'e^(4x) + 16ue^(4x)] - 8[u'e^(4x) + 4ue^(4x)] + 16ue^(4x) = 0
u''e^(4x) = 0
Let w = u', then w' = u''
w'e^(4x) = 0
w' = 0
Integrating this, we have
w = C1
But w = u'
u' = C1
Integrating again, we have
u = C1x
But y2 = ue^(4x)
y2 = C1xe^(4x)
And this is the second solution
Remark
The entire trip costs 485 dollars. She has a hundred, and you are looking for the number of weeks needed to save for the trip.
Step one
Set up the basic equation.
35w + 100 ≥ 485
Step two
solve
35w + 100 ≥ 485 Subtract 100 from both sides.
35W ≥ 485 - 100
35W ≥ 385 Divide by 35
W ≥ 385 / 35
W ≥ 11 weeks.
Since we don't have choices, we can't eliminate those that are wrong.
If I had to guess I would say it was something that looked like
35W + 100 ≥ 485
