The sum of the inner angles of any triangle is always 180°, i.e. you have
In the particular case of an equilater triangle, all three angles are the same, so
and the expression becomes
which implies 
So, if you rotate the triangle with respect to its center by 60 degrees, the triangle will map into itself. In particular, if you want point A to be mapped into point B, you have to perform a counter clockwise rotation of 60 degrees with respect to the center of the triangle.
Of course, this is equivalent to a clockwise rotation of 120 degrees.
Finally, both solutions admit periodicity: a rotation of 60+k360 degrees has the same effect of a rotation of 60 degrees, and the same goes for the 120 one (actually, this is obvisly true for any rotation!)
Answer:
your answer should be 15%
Answer:
a
The null hypothesis is 
The alternative hypothesis 
b
The 95% confidence interval is 
Step-by-step explanation:
From the question the we are told that
The population mean is 
The sample size is n = 30
The sample mean is 
The standard deviation is 
Given that the confidence level is 
then the level of significance is mathematically represented as
=> 
Next we obtain the critical value of 
from the normal distribution table
The value is 
Generally the margin of error is mathematically represented as
substituting values
The 95% confidence interval confidence interval is mathematically represented as
substituting values
Answer:
The solution is x = 0, y = -2.
Step-by-step explanation:
5x - 3y = 6
6x - 5y = 10
If we multiply the first equation by 5 and the second by - 3 we get:
25x - 15y = 30
-18x + 15y = -30 Adding these 2 equations eliminates y, we get:
7x + 0 = 0
x = 0.
Substituting x = 0 in the first equation:
5(0) - 3y = 6
y = 6/-3 = -2.
Answer:
121°
Step-by-step explanation:
<B = 9x - 5°
<D = 10x - 19°
<B = <D ( being opposite angles of parallelogram)
9x - 5° = 10x - 19°
10x - 9x = 19° - 5°
x = 14°
Now
<B = 9x - 5°
= 9 * 14° - 5
= 121°
