Answer:
A
Step-by-step explanation:
We are given:
![\displaystyle \cos(\theta)=-\frac{12}{13},\,\theta\in\text{QIII}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%28%5Ctheta%29%3D-%5Cfrac%7B12%7D%7B13%7D%2C%5C%2C%5Ctheta%5Cin%5Ctext%7BQIII%7D)
Since cosine is the ratio of the adjacent side over the hypotenuse, this means that the opposite side is (we can ignore negatives for now):
![o=\sqrt{13^2-12^2}=\sqrt{25}=5](https://tex.z-dn.net/?f=o%3D%5Csqrt%7B13%5E2-12%5E2%7D%3D%5Csqrt%7B25%7D%3D5)
So, the opposite side is 5, the adjacent side is 12, and the hypotenuse is 13.
And since θ is in QIII, sine/cosecant is negative, cosine/secant is negative, and tangent/cotangent is positive.
Cosecant is given by the hypotenuse over the opposite side. Thus:
![\displaystyle \csc(\theta)=\frac{13}{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccsc%28%5Ctheta%29%3D%5Cfrac%7B13%7D%7B5%7D)
Since θ is in QIII, cosecant must be negative:
![\displaystyle \csc(\theta)=-\frac{13}{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccsc%28%5Ctheta%29%3D-%5Cfrac%7B13%7D%7B5%7D)
Our answer is A.
<span>A. Calculate the value of x.</span>
Answer:
All A. B. C. D.
Step-by-step explanation:
Answer:
(-6,9,-3)
Step-by-step explanation:
-3x -y +z=6
-3x-y+3z =0
x-3z =3
Multiply the second equation by -1
-1 *(-3x-y+3z) =0*-1
3x +y -3z =0
Add this to the first equation
-3x -y +z=6
3x +y -3z =0
----------------------
0 + 0 + -2z = 6
Divide by -2
-2z/-2 = 6/-2
z = 6/-2
z=-3
Take the third equation to find x
x-3z=3
x-3(-3) = 3
x+9=3
Subtract 9 from each side
x+9-9 =3-9
x=-6
Now we need to find y
3x +y -3z =0
3(-6) +y -3(-3) =0
-18 +y +9=0
-9+y =0
Add 9 to each side
-9+9+y = 0+9
y=9
(-6,9,-3)
There is a 2 in 4 chance for a red shirt
there is a 1 in 2 chance for blue pants
There is (I think) a 1 in 6 chance for the chosen pain to be worn.