Because when two lines intercept, the two opposite angles from the four angles that are created from the intercepted lines are always equal.
Answer:
A
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Let larger number be L
and
smaller number be S
The larger is 1 more than twice smaller, so we can write:
L = 1 + 2S
4 times larger is 9 times smaller, so we can write:
4L = 9S
Let's put 1st equation in 2nd and solve for S first:
4L = 9S
4(1 + 2S) = 9S
4 + 8S = 9S
S = 4
Now,
L = 1 + 2S
L = 1 + 2(4)
L = 9
The larger number is, thus, equal to 9
First, let's get the area of the entire triangle since we'll need it later. The area of a triangle is A=1/2*b*h
We can find the height with the Pythagorean theorem by splitting the triangle in half.
3^2+b^2=6^2
9+b^2=36
b^2=27
b=√27
Then we can find the area:
A=1/2*6*√27
A=3√27 or =9√3 or 15.59
Now we can find the area of each region in the triangle other than the shaded region because they are all portions of a circle.
Each region has an angle of 60 because this is an equilateral triangle. Therefore the area of each region other than the shaded region will be 1/6 the area of a circle with a radius of 3 because a full circle is 360 degrees.
A=pi*r^2/6
A=pi*9/6
A=4.71
So three of these regions would have an area of 14.14
We do the area of the triangle minus the area of these regions to get the area of the shaded region
15.59-14.14 = 1.45
Hope this helps!
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