Answer:
-5
Step-by-step explanation:
-16+(-27)+21+(-19)+14+(-3)/6
-30/6
=-5
Answer:
The ratio of pounds of chicken to cups of rice is 2 to 3.
Step-by-step explanation:
3 rice: 2 chicken
3:2 ratio
can be written either number first
a. Does her equation make sense?
If so, explain why her equation must be true. If it is not correct, determine what is incorrect and rewrite the equation.
b. If you have not already done so, solve her equation, clearly showing all your steps.
What are the measures of the two angles?
c. Verify that your answer is correct.
The figure is attached below
Given : (2x+1) + (x-10) = 90
(a) Yes , the equation make sense because right angle is 90 degree. Also two angles make up 90 degree.
(b) solve for x, (2x+1) + (x-10) = 90
2x+1 + x-10 = 90 ( combine like terms)
3x -9 = 90 (add 9 on both sides)
3x = 99
x = 33
One angle is 2x+1 = 2(33) +1 = 67 degrees
Another angle = x-10 = 33-10 = 23 degrees
(c) one angle + another angle = 90
67 + 23 = 90
So verified
Answer: (a), (b), (c), and (d)
Step-by-step explanation:
Check the options
![(a)\\\Rightarrow [\sin x+\cos x]^2=\sin ^2x+\cos ^2x+2\sin x\cos x\\\Rightarrow [\sin x+\cos x]^2=1+2\sin x\cos x\\\Rightarrow \Rightarrow [\sin x+\cos x]^2=1+\sin 2x](https://tex.z-dn.net/?f=%28a%29%5C%5C%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D%5Csin%20%5E2x%2B%5Ccos%20%5E2x%2B2%5Csin%20x%5Ccos%20x%5C%5C%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D1%2B2%5Csin%20x%5Ccos%20x%5C%5C%5CRightarrow%20%5CRightarrow%20%5B%5Csin%20x%2B%5Ccos%20x%5D%5E2%3D1%2B%5Csin%202x)

![(c)\\\Rightarrow \dfrac{\sin 3x}{\sin x\cos x}=\dfrac{3\sin x-4\sin ^3x}{\sin x\cos x}\\\\\Rightarrow 3\sec x-4\sin ^2x\sec x\\\Rightarrow 3\sec x-4[1-\cos ^2x]\sec x\\\Rightarrow 3\sec x-4\sec x+4\cos x\\\Rightarrow 4\cos x-\sec x](https://tex.z-dn.net/?f=%28c%29%5C%5C%5CRightarrow%20%5Cdfrac%7B%5Csin%203x%7D%7B%5Csin%20x%5Ccos%20x%7D%3D%5Cdfrac%7B3%5Csin%20x-4%5Csin%20%5E3x%7D%7B%5Csin%20x%5Ccos%20x%7D%5C%5C%5C%5C%5CRightarrow%203%5Csec%20x-4%5Csin%20%5E2x%5Csec%20x%5C%5C%5CRightarrow%203%5Csec%20x-4%5B1-%5Ccos%20%5E2x%5D%5Csec%20x%5C%5C%5CRightarrow%20%203%5Csec%20x-4%5Csec%20x%2B4%5Ccos%20x%5C%5C%5CRightarrow%204%5Ccos%20x-%5Csec%20x)
![(d)\\\Rightarrow \dfrac{\sin 3x-\sin x}{\cos 3x+\cos x}=\dfrac{2\cos [\frac{3x+x}{2}] \sin [\frac{3x-x}{2}]}{2\cos [\frac{3x+x}{2}]\cos [\frac{3x-x}{2}]}\\\\\Rightarrow \dfrac{2\cos 2x\sin x}{2\cos 2x\cos x}=\dfrac{\sin x}{\cos x}\\\\\Rightarrow \tan x](https://tex.z-dn.net/?f=%28d%29%5C%5C%5CRightarrow%20%5Cdfrac%7B%5Csin%203x-%5Csin%20x%7D%7B%5Ccos%203x%2B%5Ccos%20x%7D%3D%5Cdfrac%7B2%5Ccos%20%5B%5Cfrac%7B3x%2Bx%7D%7B2%7D%5D%20%5Csin%20%5B%5Cfrac%7B3x-x%7D%7B2%7D%5D%7D%7B2%5Ccos%20%5B%5Cfrac%7B3x%2Bx%7D%7B2%7D%5D%5Ccos%20%5B%5Cfrac%7B3x-x%7D%7B2%7D%5D%7D%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B2%5Ccos%202x%5Csin%20x%7D%7B2%5Ccos%202x%5Ccos%20x%7D%3D%5Cdfrac%7B%5Csin%20x%7D%7B%5Ccos%20x%7D%5C%5C%5C%5C%5CRightarrow%20%5Ctan%20x)
Thus, all the identities are correct.
Answer:
B) one solution
Step-by-step explanation:
The blue line and the red line cross at only one point so there is one solution. It would be no solution if the blue line never crossed the red line and it would be two or possibly more solutions if the lines crossed more than once.