Answer:
x = 55
Step-by-step explanation:
Draw a line parallel to the top and bottom parallel lines so this new line goes through the pointed end of x.
Draw another line parallel to the top and bottom lines through the pointy end of 45.
The bottom angle of the line through 45 is 15 degrees (alternate interior angles.
The top angle is 45 - 15 = 30
The bottom angle of the line going to x is 150 degrees. It and the 30 degree angle make 180. 30 + 150 = 180
One final observation The top angle of made by the line going through x is 180 - 25 = 155
What you have now is
155 + 150 + x = 360
305 + x = 360
x = 360 - 305
x = 55
The second attachment I solved in your another question.You may refer to that.
#1
Apply Pythagorean theorem
x²=10²-6²
Answer:
complementary angles
Step-by-step explanation:
it's a 90 degree angle added together (notice the square in the corner?) hope this helps!
Answer:
1. -1/2
2. 3/-2
3. 1/2/2
4. 7/2
Step-by-step explanation:
Hope it helped
You can use the root test here. The series will converge if
![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}](https://tex.z-dn.net/?f=L%3D%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cfrac%7B%284-x%29%5En%7D%7B4%5En%2B9%5En%7D%7D%3C1)
You have
![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}=|4-x|\lim_{n\to\infty}\frac1{\sqrt[n]{4^n+9^n}}](https://tex.z-dn.net/?f=L%3D%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cfrac%7B%284-x%29%5En%7D%7B4%5En%2B9%5En%7D%7D%3D%7C4-x%7C%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac1%7B%5Csqrt%5Bn%5D%7B4%5En%2B9%5En%7D%7D)
Notice that
![\dfrac1{\sqrt[n]{4^n+9^n}}=\dfrac1{\sqrt[n]{9^n}\sqrt[n]{1+\left(\frac49\right)^n}}=\dfrac1{9\sqrt[n]{1+\left(\frac49\right)^n}}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%5Csqrt%5Bn%5D%7B4%5En%2B9%5En%7D%7D%3D%5Cdfrac1%7B%5Csqrt%5Bn%5D%7B9%5En%7D%5Csqrt%5Bn%5D%7B1%2B%5Cleft%28%5Cfrac49%5Cright%29%5En%7D%7D%3D%5Cdfrac1%7B9%5Csqrt%5Bn%5D%7B1%2B%5Cleft%28%5Cfrac49%5Cright%29%5En%7D%7D)
so as

, you have

, which means you end up with

This is the interval of convergence. The radius of convergence can be determined by finding the half-length of the interval, or by solving the inequality in terms of

so that

is the ROC. You get