Answer:
B
Step-by-step explanation:
![\sqrt[4]{2x^2} *\sqrt[4]{2x^3} =(2x^2)^{1/4}*(2x^3)^{1/4}\\= 2^{1/4}*(x^2)^{1/4} *2^{1/4} * (x^3)^{1/4}\\](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2x%5E2%7D%20%2A%5Csqrt%5B4%5D%7B2x%5E3%7D%20%3D%282x%5E2%29%5E%7B1%2F4%7D%2A%282x%5E3%29%5E%7B1%2F4%7D%5C%5C%3D%202%5E%7B1%2F4%7D%2A%28x%5E2%29%5E%7B1%2F4%7D%20%2A2%5E%7B1%2F4%7D%20%2A%20%28x%5E3%29%5E%7B1%2F4%7D%5C%5C)
combine like terms
these steps use exponent laws
a few key ones i used:
(x^y^z) = x^(y*z)
x^y * x^z = x^(y+z)
let me know if you have any questions!
So our ratio is 2:3, therefore we are looking for a multiple of 2 and a multiple of 3 that are proportional to this ratio. We can start by multiplying the ratio by 2, which gets us 4:6, which, since 4+6 is ten, is not a correct answer. If you continue the pattern of multiplying the ration with different numbers, you would eventually discover that, if you multiply the ratio by 5, you get 10:15. Since 10+15 is equal to 25, we know that this is the correct answer
The midpoint formula is (x1+x2/2, y1+y2/2
so you would do (-5+14)/2=4.5. (-2+12)/2=5
(4.5, 5)
Answer:
3/5
Step-by-step explanation:
We need to use the trig identity that cos(2A) = cos²A - sin²A, where A is an angle. In this case, A is ∠ABC. Essentially, we want to find cos∠ABC and sin∠ABC to solve this problem.
Cosine is adjacent ÷ hypotenuse. Here, the adjacent side of ∠ABC is side BC, which is 4 units. The hypotenuse is 2√5. So, cos∠ABC = 4/2√5 = 2/√5.
Sine is opposite ÷ hypotenuse. Here, the opposite side of ∠ABC is side AC, which is 2 units. The hypotenuse is still 2√5. So sin∠ABC = 2/2√5 = 1/√5.
Now, cos²∠ABC = (cos∠ABC)² = (2/√5)² = 4/5.
sin²∠ABC = (sin∠ABC)² = (1/√5)² = 1/5
Then cos(2∠ABC) = 4/5 - 1/5 = 3/5.
