Find the discriminant, and determine the number of real solutions. then solve 2x^2+3x-9=0

1 answer:

7 0

Discriminant =
b² - 4ac

3² - 4(2)(- 9)
9 + 72
81

Your equation has two real solutions.

2x² + 3x - 9 = 0
2x² + 6x - 3x - 9 = 0
2x(x + 3) - 3(x + 3) = 0

(2x - 3)(x + 3) = 0

Set each equal to zero:

2x - 3 = 0
2x = 3
x = 3/2

x + 3 = 0
x = - 3

Your two solutions are x = - 3, 3/2

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Percent of turn pike is 75% and percent of parkway is 25%.

Solution:

Given, The state of New Jersey makes approximately $1.55 billion annually from tolls of the $1.55 billion

About $\frac{3}{4}$ comes from tolls on the turnpike

Remaining $\frac{1}{4}$ comes from tolls on the parkway

To find the percent of the total revenue from turnpike:

$\begin{array}{l}{\text { Percent of turnpike }=\frac{\text { amount from parkway }}{\text { total revenue }} \times 100} \\\\ {=\frac{\frac{3}{4} \text { of total revenue }}{\text { tot al revenue }} \times 100} \\\\ {=\frac{\frac{3}{4} \times \text { total revenue }}{\text { total revenue }} \times 100} \\\\ {=\frac{3}{4} \times 100=3 \times 25=75 \%}\end{array}$

To find the percent of the total revenue from parkway:

$\begin{array}{l}{\text { Percent of parkway }=\frac{\text { amount from parkway }}{\text { total revenue }} \times 100} \\\\ {=\frac{\frac{1}{4} \text { of total revenue }}{\text { total revenue }} \times 100} \\\\ {=\frac{\frac{1}{4} \times \text { total revenue}}{\text { total revenue }} \times 100} \\\\ {=\frac{1}{4} \times 100=25 \%}\end{array}$