sin(x+y)=sin(x)cos(y)-cos(x)sin(y)
also, remember pythagorean rule,
given that sin(Θ)=4/5 and cos(x)=-5/13
find sin(x) and cos(Θ)
sin(x)
cos(x)=-5/13
using pythagorean identity
(sin(x))^2+(-5/13)^2=1
sin(x)=+/- 12/13
in the 2nd quadrant, sin is positve so sin(x)=12/13
cos(Θ)
sin(Θ)=4/5
using pythagrean identity
(4/5)^2+(cos(Θ))^2=1
cos(Θ)=+/-3/5
in 1st quadrant, cos is positive
cos(Θ)=3/5
so sin(Θ+x)=sin(Θ)cos(x)+cos(Θ)sin(x)
sin(Θ+x)=(4/5)(-5/13)+(3/5)(12/13)
sin(Θ+x)=16/65
answer is 1st option
A is 14 total
B is yes because the gained 11 and lost 3 which means they gained 8 after taking away the ones lost and they are still on the positive side so they keep th ball.
We have 60 gallons of 20% antifreeze.
How much 70% antifreeze do we add to get 60% antifreeze?
We'll make "x" the gallons of 70% we must add.
.20 * 60 + .70 x = .60 * (60 + x)
12 + .70x = 36 + .60x
.10x = 24
x = 240 gallons of 70% antifreeze.
Source
1728.com/mixture.htm (see example B)
Answer:
x=-3, and y=2
Step-by-step explanation:
Since both equations are equal to y, set them equal to each other and solve for x, that way you can solve for y:
x+5=-2x-4
3x+5=-4
3x=-9
x=-3
Plugging in x=-3 into one of the original equations:
y = x + 5
y = -3 + 5
y = 2
Therefore, x=-3 and y=2. You can also write as the ordered pair (-3,2) since that's where the two equations would intercept on a graph.