12 cookies= 1 dozen.
12*4 (dozens) =48
48/ 4= 12
12 cookies is a 1/4 or 25% of the whole amount of cookies.
48- 12= 36
He brings 36 cookies to school.
Answer:
The solution proves that the equation has a non-trivial solution.
Step-by-step explanation:
We want to show that the equation has nontrivial solutions for which 
Let 
be a set of non-zero numbers such that that 
Because T is a linear solution:
= 
= 
= 
= 
= 0
This shows that 
are linearly independent with the mapping resulting in a non-trivial solution.
Answer:
- rate of the boat in still water = 6.5 miles / hour
- rate of the current = 2.5 miles / hour.
Explanation:
<u>1) Name the two variables:</u>
- b: rate of the boat in still water:
With that, the net rates of the boat down the river and upstrean are:
<u>2) Now set the equations for the distance as a function of the times and the rates:</u>
- downstream: 18 miles = (b + c) × 2 hours
- upstream: 18 miles = (b - c) × 4.5 hours
<u>3) Set the system of equations:</u>
- 18 = 2(b + c) ⇒ 9 = b + c . . . Equation (1)
- 18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)
<u>4) Solve the system by </u><u>elimination</u><u>:</u>
- Add equations (1) and (2): 9 + 4 = 2b
- Divide both sides by 2: 13/2 = b
- Replace b with 6.5 in equation (2) and solve:
4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5
<u>5) Results:</u>
- b = rate of the boat in still water = 6.5 miles / hour
- c = rate of the current = 2.5 miles / hour.
You need to use the angle sum of a triangle in triangle CAD to express y in term of x
for triangla CAD , y = (180 -x) /2
180 = 3x + [ (180-x)/2]
x = 36
hope this helps
