Hello from MrBillDoesMath!
Answer:
@ = pi/3 (or 60 degrees) or @ = 7 pi/3 (or 420 degrees)
Discussion:
Let "@' denote the angle "theta". We are asked to find @ in the interval [0, 4 pi)
where
4cos(@) - 2 = 0. Adding 2 to both sides
4 cos(@) - 2 +2 = 2 =>
4 cos(@) = 2 Divide both sides by 4
cos(@) = 2/4 = 0.5
This implies that @ = pi/3 (or 60 degrees) or @ = (pi/3 + 2pi) = 7 pi/3 (or 420 degrees)
Thank you,
MrB
Answer:
8 one-dollar bills
3 five-dollar bills
2 ten-dollar bills
Step-by-step explanation:
Let x = # of one-dollar bills, y = # of five-dollar bills, and z = # of ten-dollar bills. Total amount in the wallet is $43, so the first equation would be 1x + 5y + 10z = 43. Next, there are 4 times as many one-dollar bills as ten-dollar bills, so x = 4z. There are 13 bills in total, so x + y + z = 13
x + 5y + 10z = 43
x = 4z
x + y + z = 13
x + 5y + 10z = 43
x + 0y - 4z = 0
x + y + z = 13
5y + 14z = 43
-y - 5z = -13
5y + 14z = 43
-5y - 25z = -65
-11z = -22
z = 2
x = 4z
x = 4*2 = 8
x + y + z = 13
8 + y + 2 = 13
10 + y = 13
y = 3
Try to get the u’s on one side so for this to happen, you would subtract the four from both sides.
u - 4u = 7 - 4
combine like terms
-3u = 3
divide by -3
u = -1
Answer:
k=6,912
Step-by-step explanation:
5678+1234=6912
40mph for Car B I think. 45mph for Car A. 45(mph) times 4(h) is 180(distance) and 40 times 4.5 is also 180. Sorry if I'm wrong.
