Definition of an exterior angle
At each vertex of a triangle, an exterior angle of the triangle may be formed by extending ONE SIDE of the triangle. See picture below.
Calculating the Angles
We can use equations to represent the measures of the angles described above. One equation might tell us the sum of the angles of the triangle. For example,
x + y + z = 180
When Brooks painted more he used 6/12 of what was left(1/2 of what was left)
Answer:
x-intercepts are (0, 0) and (-6, 0)
Step-by-step explanation:
equation of a parabola in vertex form: y = a(x - h)² + k
where (h, k) is the vertex
Substituting the given vertex (-3, -18) into the equation:
y = a(x + 3)² - 18
If the y-intercept is (0, 0) then substitute x=0 and y=0 into the equation and solve for a:
0 = a(0 + 3)² - 18
⇒ 0 = a(3)² - 18
⇒ 0 = 9a - 18
⇒ 9a = 18
⇒ a = 2
Therefore, y = 2(x + 3)² - 18
To find the x-intercepts, set the equation to 0 and solve for x:
2(x + 3)² - 18 = 0
Add 18 to both sides: 2(x + 3)² = 18
Divide both sides by 2: (x + 3)² = 9
Square root both sides: x + 3 = ±3
Subtract 3 from both sides: x = ±3 - 3
so x = 3 - 3 = 0
and x = -3 - 3 = -6
So x-intercepts are (0, 0) and (-6, 0)
Answer: 3.6 feet per year
Pick any column and divide the feet over the years
eg: 7.2/2 = 3.6 (column 1)
You can think of it as the ratio
7.2 feet: 2 years
and then divide both sides by 2 to get "1 year" on the right side
7.2 feet: 2 years
7.2/2 feet: 2/2 years
3.6 feet: 1 year
