If given the equation, you need to take the number beside the x and y and change their signs to get your point:
x - 8 (Take the -8 and make it +8)
y + 2 (Take the +2 and make it -2)
Your point is (8, -2)
If the 5 scores have a mean of 8, then their total sum would be 8*5 = 40
Now if one score if added (let's call this score x), there are 6 scores and the mean changes to 9, thus:
(40 + x)/6 = 9
40 + x = 54
x = 14
Answer:
y = 2(x - 1)² + 1
Step-by-step explanation:
The equation of a quadratic function in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, 1), thus
y = a(x - 1)² + 1
To find a substitute (4, 19) into the equation
19 = a(4 - 1)² + 1
19 = 9a + 1 ( subtract 1 from both sides )
18 = 9a ( divide both sides by 9 ), thus
a = 2
y = 2(x - 1)² + 1 ← in vertex form
If we let m₁, m₂, and m₃ be the measures of the angles of the triangle, the equation that would relate them to each other is,
m₁ + m₂ + m₃ = 180
Given the measures of the first two angles, the measure of the third angle is calculated through the equation,
m₃ = 180 - (m₁ + m₂)
Substituting the known expressions,
m₃ = 180 - (-3x⁵ + 2x²)
Simplifying,
<em> m₃ = 180 + 3x⁵ - 2x²</em>
