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salinasroel22
28.08.2019 •
Mathematics
Parabola a can be represented using the equation (x + 3)2 = y, while line b can be represented using the equation y = mx + 9. isabel determines one solution to the system of two equations must always pass through the vertex of parabola a. which best describes the reasonableness of her solution?
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Ответ:
line b: y = mx + 9
y = (x+3)² → (x+3)(x+3) = x² + 3x + 3x + 9 = x² + 6x + 9
y = y
mx + 9 = x² + 6x + 9 ; assume that m = 1
x + 9 = x² + 6x + 9
9 = x² + 6x - x + 9
9 - 9 = x² + 5x
0 = x² + 5x
x = -b + √(b²) - 4ac / 2a
x = [-5 + √25 - 4(1)(0)] /2(1)
x = (- 5 + √25)/2 = -5 + 5 / 2 = 0/2 = 0
x = (-5 - √25)/2 = -5 -5 /2 = -10/2 = -5
x = 0 ; y = x² + 6x + 9 → y = 0² + 6(0) + 9 → y = 9 → (0,9)
x = -5 ; y = x² + 6x + 9 → y = (-5)² + 6(-5) + 9 → y = 25 - 30 + 9 → y = 4 → (-5,4)
the points of intersection are (0,9) and (-5,4)
Ответ:
The equation is adjusted by dividing the tax amount by the percent to find the original cost. Dividing by the percent is the inverse operation of multiplying by percent.
Step-by-step explanation: