Answer:
B. (2a +3b)(4a -c)
Step-by-step explanation:
Group the terms pairwise, then factor each pair.
... (8a² -2ac) +(12ab -3bc)
2a is a common factor in the first pair of terms; 3b is a common factor in the second pair of terms. We can factor those out.
... = 2a(4a -c) +3b(4a -c)
Then we see that (4a-c) is a common factor in the result. We can factor that out.
... = (2a +3b)(4a -c) . . . . matches selection B
1) C is because it’s exactly double the size in both width and length while the others are only gaining one or the other. For example - the a length of the squares is 5 and the length on c is 10, the base on a is 3 long, the base on c is 6. The width on a is 1 and the width on c is 2. You can put these into fractions 5/10 3/6 1/2 but they all equal 1/2. So it’s double the size of a.
Answer:
I got this. Use the order PEMDAS search Up if you don’t know what it means.
Step-by-step explanation:
Start with What’s inside the parentheses
(X - 3) = 3x
(X + 5) = 5x
The divide.
How to divide it - The number coefficients are reduced the same as in simple fractions. When dividing variables, you write the problem as a fraction. Then, using the greatest common factor, you divide the numbers and reduce. You use the rules of exponents to divide variables that are the same — so you subtract the powers.
Step-by-step explanation:
Let x represent theta.
![\sin( \frac{\pi}{4} - x )](https://tex.z-dn.net/?f=%20%5Csin%28%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20-%20x%20%29%20)
Using the angle addition trig formula,
![\sin(x - y) = \sin(x) \cos(y) - \cos(x) \sin(y)](https://tex.z-dn.net/?f=%20%5Csin%28x%20-%20y%29%20%20%3D%20%20%5Csin%28x%29%20%20%5Ccos%28y%29%20%20-%20%20%5Ccos%28x%29%20%20%5Csin%28y%29%20)
![\sin( \frac{\pi}{4} ) \cos(x) - \cos( \frac{\pi}{4} ) \sin(x)](https://tex.z-dn.net/?f=%20%5Csin%28%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%29%20%20%5Ccos%28x%29%20%20-%20%20%5Ccos%28%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%29%20%20%5Csin%28x%29%20)
![( \frac{ \sqrt{2} }{2}) \cos(x) - (\frac{ \sqrt{2} }{2} )\sin(x)](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B2%7D%29%20%20%5Ccos%28x%29%20%20-%20%20%28%5Cfrac%7B%20%5Csqrt%7B2%7D%20%7D%7B2%7D%20%20%29%5Csin%28x%29%20)
Multiply one side at a time
Replace theta with x , the answer is
![\frac{ \sqrt{2} \cos(x) }{2} - \frac{ \sin(x) \sqrt{2} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B2%7D%20%5Ccos%28x%29%20%20%7D%7B2%7D%20%20-%20%20%5Cfrac%7B%20%5Csin%28x%29%20%5Csqrt%7B2%7D%20%20%7D%7B2%7D%20)
2. Convert 30 degrees into radian
![\frac{30}{1} \times \frac{\pi}{180} = \frac{\pi}{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B30%7D%7B1%7D%20%20%5Ctimes%20%20%5Cfrac%7B%5Cpi%7D%7B180%7D%20%20%3D%20%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20)
Using tangent formula,
![\tan(x + y) = \frac{ \tan(x) + \tan(y) }{1 - \tan(x) \tan(y) }](https://tex.z-dn.net/?f=%20%5Ctan%28x%20%2B%20y%29%20%20%3D%20%20%5Cfrac%7B%20%5Ctan%28x%29%20%20%2B%20%20%5Ctan%28y%29%20%7D%7B1%20-%20%20%5Ctan%28x%29%20%5Ctan%28y%29%20%20%7D%20)
![\frac{ \tan(x) + \tan( \frac{\pi}{6} ) }{1 - \tan(x) \tan( \frac{\pi}{6} ) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Ctan%28x%29%20%2B%20%20%5Ctan%28%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%29%20%20%7D%7B1%20-%20%20%5Ctan%28x%29%20%5Ctan%28%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%29%20%20%7D%20)
Tan if pi/6 is sqr root of 3/3
![\frac{ \tan(x) + ( \frac{ \sqrt{3} }{3} ) }{1 - \tan(x) (\frac{ \sqrt{3} }{3} ) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Ctan%28x%29%20%2B%20%20%28%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B3%7D%20%29%20%20%7D%7B1%20-%20%20%5Ctan%28x%29%20%20%28%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B3%7D%20%29%20%20%7D%20)
Since my phone about to die if you later simplify that,
you'll get
![\frac{(3 \tan(x) + \sqrt{3} )(3 + \sqrt{3} \tan(x) }{3(3 - \tan {}^{2} (x) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%283%20%5Ctan%28x%29%20%2B%20%20%5Csqrt%7B3%7D%20%29%283%20%2B%20%20%5Csqrt%7B3%7D%20%20%5Ctan%28x%29%20%20%7D%7B3%283%20-%20%20%5Ctan%20%7B%7D%5E%7B2%7D%20%28x%29%20%7D%20)
Replace theta with X.