Answer:
p = ½ (x₁ + x₂)
q = a (x₁x₂ − ¼ (x₁ + x₂)²)
Step-by-step explanation:
y = a (x − x₁) (x − x₂)
Expand:
y = a (x² − x₁x − x₂x + x₁x₂)
y = a (x² − (x₁ + x₂)x + x₁x₂)
Distribute a to the first two terms:
y = a (x² − (x₁ + x₂)x) + ax₁x₂
Complete the square:
y = a (x² − (x₁ + x₂)x + ¼(x₁ + x₂)²) + ax₁x₂ − ¼ a(x₁ + x₂)²
y = a (x − ½ (x₁ + x₂))² + a (x₁x₂ − ¼ (x₁ + x₂)²)
Therefore:
p = ½ (x₁ + x₂)
q = a (x₁x₂ − ¼ (x₁ + x₂)²)
Answer:
59
Step-by-step explanation:
Let c and b represent the scores of Colin and Brian respectively. Then
c + b = 59. Since brian scored 59 more points than Colin, that means c = 0 and b = 59. Their combined score is 0 + 59 = 59.
35/100 = x/300
10500 = 100x
105 students play the trumpet
The sum of the interior angles in a triangle is 180 degrees. Therefore, if we add up all of these angles, they must be equal to 180.
64 + 85 + (4x + 27) = 180
176 + 4x = 180
4x = 4
x = 1
Let's check our answer!
4(1) + 27 = 31
31 + 85 + 64 = 180
180 = 180
Hope this helps!! :)