cos (2x) = cos x
2 cos^2 x -1 = cos x using the double angle formula
2 cos ^2 x -cos x -1 =0
factor
(2 cos x+1) ( cos x -1) = 0
using the zero product property
2 cos x+1 =0 cos x -1 =0
2 cos x = -1 cos x =1
cos x = -1/2 cos x=1
taking the arccos of each side
arccos cos x = arccos (-1/2) arccos cos x = arccos 1
x = 120 degrees x=-120 degrees x=0
remember you get 2 values ( 2nd and 3rd quadrant)
these are the principal values
now we need to add 360
x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer
Answer:
y = 3x + 1
Step-by-step explanation:
If two lines are parallel to each other, they have the same slope.
The first line is Y = 3X - 5. Its slope is 3. A line parallel to this one will also have a slope of 3.
Plug this value (3) into your standard point-slope equation of y = mx + b.
y = 3x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (0, 1). Plug in the x and y values into the x and y of the standard equation.
1 = 3(0) + b
To find b, multiply the slope and the input of x (0)
1 = 0 + b
Now, add 0 to both sides to isolate b.
1 = b
Plug this into your standard equation.
y = 3x + 1
This equation is parallel to your given equation (y = 3x - 5) and contains point (0, 1)
Hope this helps!
If you round up the 27.64 to 28 and then multiply it bye 3 it eaquals 84
Answer:
6 clown fish and 4 angel fish
Step-by-step explanation:
<u>lets say he bought 8 clown fish. </u>
12*8 = 96
the last 4 dollars wont be used.
<u>lets say he bought 7 clown fish-</u>
12*7 = 84
100 - 84 = 16. 16 is not a multiple of 7.
<u>lets say he bought 6 clown fish,</u>
12*6 = 72
100 - 72 = 28
28/7 = 4
If David has $100 dollars to spend and wants to spend every dollar, he can buy 6 clown fish and 4 angel fish.
