Answer:
9/16 of the students
Step-by-step explanation:
first you can simplify 15/20 to 3/4
you can simplify 12/16 to 3/4
3/4*3/4=9/16
Answer: 9
Step-by-step explanation:
Add 6m on both sides. Then divide by 3 on both sides. m=9
Answer:
sin θ/2=5√26/26=0.196
Step-by-step explanation:
θ ∈(π,3π/2)
such that
θ/2 ∈(π/2,3π/4)
As a result,
0<sin θ/2<1, and
-1<cos θ/2<0
tan θ/2=sin θ/2/cos θ/2
such that
tan θ/2<0
Let
t=tan θ/2
t<0
By the double angle identity for tangents
2 tan θ/2/1-(tanθ /2)^2 = tanθ
2t/1-t^2=5/12
24t=5 - 5t^2
Solve this quadratic equation for t :
t1=1/5 and
t2= -5
Discard t1 because t is not smaller than 0
Let s= sin θ/2
0<s<1.
By the definition of tangents.
tan θ/2= sin θ/2/ cos θ/2
Apply the Pythagorean Algorithm to express the cosine of θ/2 in terms of s. Note the cos θ/2 is expected to be smaller than zero.
cos θ/2 = -√1-(sin θ/2)^2 = - √1-s^2
Solve for s.
s/-√1-s^2 = -5
s^2=25(1-s^2)
s=√25/26 = 5√26/26
Therefore
sin θ/2=5√26/26=0.196....
Answer:
Choice C. sin 105 = sin(60 + 45) = sin 60 cos 45 + cos 45 sin 60
Step-by-step explanation:
sin(A + B) = sin A cos B + cos A sin B
sin(105) = sin(60 + 45) = sin 60 cos 45 + cos 45 sin 60
Answer: choice C
I guess you want the roots of the equation.
We can factor that as
(x-6) * (x + 10)
The roots of the equation are
6 and -10
