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:
the scale factor is 4 to 1, or just 4.
Step-by-step explanation:
Length = x + 2 (because it is 2 cm more than x)
Width = 2x - 5 (5 cm lest than 2x)Area = 54 cm2 this is the formula to find the area Length × Width = Area (x + 2)(2x - 5) = 542x2 - x - 10 = 54 (this is you area)
Subtract 54 on both sides of equation to make the right side zero. 2x2 - x - 64 = 0 then use the quadratic formula x = (-b ± √(b2 - 4ac)) / 2a where:a = 2b = -1c = -64 Plug in these values into the formula. x = (1 ± √(1 - 4(-128))) / 4 x = (1 ± √(513)) / 4 x = (1 ± 22.65) / 4 x = (1 + 22.65) / 4 and x = (1 - 22.65) / 4 x = 5.91 and x = -5.41 Check the validity of the x values by adding them to the length and width. If the length or width should be a negative value, then that value of x is not acceptable. Now x = 5.91 Length = 5.91 + 2 (positive value.)Width = 2(5.91) - 5 ( positive value.) x = 5.91 If we look at this -- x = -5.41, Both length and width will be negative values. We reject this value of x. The answer is x = 5.91
Hope I helped and sorry it was really long
Answer:
Step-by-step explanation:
Given:
Two points are given
x = number of minutes
y = length of the lin
⇒ (0, 6)
⇒ (20, 17)
We need to find the equation that represents the relationship between x, y.
Solution:
Using slope formula to find the slope of the equation of the line.
Substitute = (0, 6) and = (20, 17) in above equation.
So, slope of the line 
Using point slope formula.
------------(1)
Where, m = slope of the line
Substitute ⇒ (0, 6) and in equation 1.
Add 6 both side of the equation.
Therefore, the equation that represents the relationship between x and y is written as:
