Question

5.Find the roots of the parabola given by the following equation.

2x2+ 5x - 9 = 2x

6.Solve the inequality and graph the solution on a number line.
–3(5y – 4) ≥ 17

Answer 1

Part 5) The roots are x=-3 and x=1.5

Part 6) The solution on a number line is the shading area below of the line y=-1/3 (close circle)

Explanation:

Part 5) Find the roots of the parabola given by the following equation

`2x^(2) +5x-9=2x`

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`2x^(2)+5x-2x-9=0`

`2x^(2)+3x-9=0`

so

`a=2\\b=3\\c=-9`

substitute in the formula

`x=\frac{-3(+/-)\sqrt{3^(2)-4(2)(-9)}} {2(2)}`

`x=\frac{-3(+/-)√(81)} {4}`

`x=\frac{-3(+/-)9} {4}`

`x=\frac{-3(+)9} {4}=1.5`

`x=\frac{-3(-)9} {4}=-3`

therefore

The roots are x=-3 and x=1.5

Part 6) Solve the inequality and graph the solution on a number line.

`-3(5y-4)\geq 17`

Solve for y

`-15y+12\geq 17`

Subtract 12 both sides

`-15y\geq 17-12`

`-15y\geq 5`

Multiply by -1 both sides

`15y\leq -5`

Divide by 15 both sides

`y\leq -1/3`

The solution is the interval -----> (-∞, -1/3]

All real numbers less than or equal to negative one third

The solution on a number line is the shading area below of the line y=-1/3 (close circle)

The graph in the attached figure