Answer:
4/5
Step-by-step explanation:
Wow! There so much extra stuff on this drawing, naturally it's hard to see
what's going on.
First, do you remember "vertical angles" ? They're the pair of opposite angles
that form where lines cross, and they're equal.
-- It says that angle-1 is 55 degrees.
Angle-1 and angle-7 are vertical angles, so angle-7 is also 55 degrees.
-- It says that angle-4 is 60 degrees.
Angle-4 and angle-6 are vertical angles, so angle-6 is also 60 degrees.
Now you can forget about all that stuff that's outside of the triangle in the middle,
and just look at the triangle. They want you to find angle-10.
See the angles at the top of the triangle ... angle-7 and angle-6 ?
We know what both of those are. Angle-7 is 55 degrees, and angle-6 is 60 degrees.
Do you remember what the 3 angles inside a triangle always add up to ?
They always add up to 180 degrees.
Add angle-7 and angle-6 together . . . 55 + 60 = 115 degrees.
So angle-10 is just the rest of the 180 degrees inside the triangle.
Angle-10 = 180 - (115) = 65 degrees
Answer:
I am pretty sure this statement is false so it'd be: x= 0
Step-by-step explanation:
Answer: ![14*\sqrt[3]{x^{10}}](https://tex.z-dn.net/?f=14%2A%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%7D)
Step-by-step explanation:
First, let's remember the rules:
![x^{1/n} = \sqrt[n]{x}](https://tex.z-dn.net/?f=x%5E%7B1%2Fn%7D%20%3D%20%5Csqrt%5Bn%5D%7Bx%7D)
such that:
![\sqrt[n]{x^m} = x^{m/n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5Em%7D%20%3D%20x%5E%7Bm%2Fn%7D)
Now we have the equation:
![4*\sqrt[3]{x^{10}} + 5*x^3*\sqrt[3]{8*x}](https://tex.z-dn.net/?f=4%2A%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%7D%20%2B%205%2Ax%5E3%2A%5Csqrt%5B3%5D%7B8%2Ax%7D)
First, let's rewrite the roots as we saw above:
![4*x^{10/3} + 5*x^3*\sqrt[3]{8}*x^{1/3} = 4*x^{10/3} + 5*\sqrt[3]{8}*x^{3 + 1/3}](https://tex.z-dn.net/?f=4%2Ax%5E%7B10%2F3%7D%20%2B%205%2Ax%5E3%2A%5Csqrt%5B3%5D%7B8%7D%2Ax%5E%7B1%2F3%7D%20%3D%204%2Ax%5E%7B10%2F3%7D%20%2B%205%2A%5Csqrt%5B3%5D%7B8%7D%2Ax%5E%7B3%20%2B%201%2F3%7D)
We also know that: ![\sqrt[3]{8} = 2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%20%3D%202)
and that: 
Replacing those two things in our equation, we get:
![4*x^{10/3} + 5*\sqrt[3]{8}*x^{3 + 1/3} = 4*x^{10/3} + 5*2*x^{10/3} = (4 + 5*2)*x^{10/3}](https://tex.z-dn.net/?f=4%2Ax%5E%7B10%2F3%7D%20%2B%205%2A%5Csqrt%5B3%5D%7B8%7D%2Ax%5E%7B3%20%2B%201%2F3%7D%20%3D%204%2Ax%5E%7B10%2F3%7D%20%2B%205%2A2%2Ax%5E%7B10%2F3%7D%20%3D%20%284%20%2B%205%2A2%29%2Ax%5E%7B10%2F3%7D)
![(4 + 10)*x^{10/3} = 14*\sqrt[3]{x^{10}}](https://tex.z-dn.net/?f=%284%20%2B%2010%29%2Ax%5E%7B10%2F3%7D%20%3D%2014%2A%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%7D)
Where in the final step, I returned to the cubic root form.
