<h3>
Answer: x = 30</h3>
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Explanation:
If a regular polygon has n sides, then each interior angle has the measure of
i = 180(n-2)/n
In this case, we have n = 6 sides, so,
i = 180(n-2)/n
i = 180(6-2)/6
i = 120
Each interior angle of a regular hexagon is 120 degrees.
This means the bottom-right angle of the triangle is 120 degrees. The upper-right angle of that triangle is shown to be x degrees. The remaining angle is also x due to the triangle being isosceles (recall that regular hexagons have all sides the same length). Isosceles triangles have congruent base angles, which are opposite the congruent sides.
Use the fact that for any triangle, the three angles always add to 180, and we get...
x+120+x = 180
2x+120 = 180
2x = 180-120
2x = 60
x = 60/2
x = 30
Answer:
Step-by-step explanation:
<u>Given vertices of a triangle:</u>
- A(4, 12), B(14, 6), and C(-6, 2)
Let the circumcenter is point M(x, y)
We know that the circumcenter is equidistant from each of the vertices.
<u>Use distance formula:</u>
- AM = √(x - 4)² + (y - 12)²
- BM = √(x - 14)² + (y - 6)²
- CM = √(x + 6)² + (y - 2)²
<u>All three distances are equal:</u>
- AM = BM = CM ⇒ AM² = BM² = CM² ⇒
- (x - 4)² + (y - 12)² = (x - 14)² + (y - 6)² = (x + 6)² + (y - 2)²
<u>Square of each:</u>
- AM² = x² - 8x + 16 + y² - 24y + 144 = x² + y² - 8x - 24y + 160
- BM² = x² - 28x + 196 + y² - 12y + 36 = x² + y² - 28x - 12y + 232
- CM² = x² + 12x + 36 + y² - 4y + 4 = x² + y² + 12x - 4y + 40
<u>Comparing the squares, we get following system:</u>
- -8x- 24y + 160 = -28x - 12y + 232 ⇒ 20x - 12y = 72 ⇒ 5x - 3y = 18
- - 8x - 24y + 160 = 12x - 4y + 40 ⇒ 20x + 20y = 120 ⇒ x + y = 6
<u>Solve by substitution, x = 6 - y:</u>
- 5(6 - y) - 3y = 18
- 30 - 8y = 18
- 8y = 12
- y = 1.5
<u>Find x:</u>
So the circumcenter is M(4.5, 1.5)
The answer is x^3 - 7x^2 + 5x + 21
Answer:
see the explanation in the procedure
Step-by-step explanation:
we know that
The equation of a line in standard form is
where
A is a positive integer
B and C are integers
<em>Find the intercepts</em>
<u><em>Find the y-intercept</em></u>
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
In order for C/B to be a fraction, C must not be a multiple of B
<u><em>Find the x-intercept</em></u>
The x-intercept is the value of x when the value of y is equal to zero
so
For y=0
In order for C/A to be a fraction, C must not be a multiple of A
Answer: 9y + 7 = y
Explanation:
The phrase, "nine times a number y" is "9y" in the form of an equation. When any term is by a number, they are meant to be multiplied together. So, "9y" means "9 times y".
The phrase, "plus seven" simply means to add seven.
The phrase, "equal to number y" is "= y" because "number y" refers to that term.
And so, all together, you get 9y + 7 = y.
(Brainliest would be appreciated)
I hope this helped!
Good luck <3
