Answer:
Yes
Step-by-step explanation:
3:9 in their lowest forms are 1:3 which is the same for 6:18
Answer:
D (-3, 5)
Step-by-step explanation:
270 counter clockwise is the same as 90 clockwise.
For a 90° clockwise or 270° counter clockwise, take the opposite of the x coordinate then switch the coordinates.
(-5, -3) -----> (5, -3) ------> (-3, 5)
You can also rotate your screen 90° clockwise to see the new coordinates for A.
Straight line:
y = mx + c
m is the slope of the graph and c is the y-intercept
In this case, m = 5 as stated in the question, so...
y = 5x + c
By substituting the given co-ordinates (-2,-1) into this equation, we can find c
-1 = 5(-2) + c
-1 = -10 + c
-1 + 10 = -10 + c + 10 (Add 10 to both sides)
9 = c
c = 9
Put c = 9 into the equation:
y = 5x + 9
Answer:
x = {nπ -π/4, (4nπ -π)/16}
Step-by-step explanation:
It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:
cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)
= cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)
= sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))
= (sin(x) +cos(x))·(sin(4x) +cos(4x))
Each of the sums in this product is of the same form, so each can be simplified using the identity ...
sin(x) +cos(x) = √2·sin(x +π/4)
Then the given equation can be rewritten as ...
cos(3x) +sin(5x) = 0
2·sin(x +π/4)·sin(4x +π/4) = 0
Of course sin(x) = 0 for x = n·π, so these factors are zero when ...
sin(x +π/4) = 0 ⇒ x = nπ -π/4
sin(4x +π/4) = 0 ⇒ x = (nπ -π/4)/4 = (4nπ -π)/16
The solutions are ...
x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n
Answer:
yes
Step-by-step explanation:
