Answer/Step-by-step explanation:
Factor this. GCF=2
2(2cos2x+cos x-1)=0
2(2cos x -1)(cos x+1)=0 Set each factor equal to zero and solve
2cos x -1=0 Add 1 to both sides
2cos x =1 Divide by 2
cos x =1/2
x=π/3
x=5π/3
cos x+1=0 Subtract 1 from both sides
cos x=-1
<u><em>x = π</em></u>
<u><em></em></u>
Volume of a rectangular prism=Base*Height
Area is 48 meters squared and height is 2 meters
V=48*2
V=96 cubic meters
Answer:
x = 1/3
Step-by-step explanation:
3(x – 1) – 2(2x + 1) = 8(x – 1)
Distribute
3x-3 -4x-2 = 8x-8
Combine like terms
-x-5 = 8x-8
Add x to each side
-x+x-5 =8x+x -8
-5 = 9x-8
Add 8 to each side
-5+8 = 9x-8+8
3 = 9x
Divide by 9
3/9 =9x/9
1/3 =x
The answer is 27 because there isn't enough bars of soap to have 2 in each package
Answer:
3xy
Step-by-step explanation:
We are to determine the GCF of the expression.
![6(x^3)(y^3)+45(x^2)(y^2)+21xy](https://tex.z-dn.net/?f=6%28x%5E3%29%28y%5E3%29%2B45%28x%5E2%29%28y%5E2%29%2B21xy)
THe GCF of the expression is the term that exactly divides all the terms in the expression
<u>Step 1</u>
If we observe the expression carefully, we notice that it has a common term of 3, x and y. That is, 3,x and y divides each term.
<u>Step 2</u>
Divide by 3xy for confirmation
![3xy\left(\dfrac{6(x^3)(y^3)}{3xy} +\dfrac{45(x^2)(y^2)}{3xy}+\dfrac{21xy}{3xy}\right)\\=3xy[2(x^2)(y^2)+15xy+7]](https://tex.z-dn.net/?f=3xy%5Cleft%28%5Cdfrac%7B6%28x%5E3%29%28y%5E3%29%7D%7B3xy%7D%20%2B%5Cdfrac%7B45%28x%5E2%29%28y%5E2%29%7D%7B3xy%7D%2B%5Cdfrac%7B21xy%7D%7B3xy%7D%5Cright%29%5C%5C%3D3xy%5B2%28x%5E2%29%28y%5E2%29%2B15xy%2B7%5D)
Therefore, we can confirm that the GCF is 3xy.