Are these lines parallel, perpendicular, or neither?

In summary, for question 3, the correct solution is x = -1 +/- 2sqr34. For question 4, the first pair of lines is perpendicular and the second pair of lines is correct with a product of -1 for their slopes.
  • #1
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Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :)

PART A

3) Solve 2x^2 + 4x = 15 by using the quadratic formula.

x = -1 +/- 2sqr34

4) Determine whether the given pairs of lines are parallel, perpendicular, or neither.

a) y = -4x + 3 b) x - 4y = 4

My answer: Perpendicular
 
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  • #2
Re: Please check my answers - 2

3.) Incorrect.

We have:

\(\displaystyle 2x^2+4x-15=0\)

\(\displaystyle x=\frac{-4\pm\sqrt{(4)^2-4(2)(-15)}}{2(2)}=\frac{-4\pm\sqrt{136}}{4}=\frac{-4\pm2\sqrt{34}}{4}=\frac{-2\pm\sqrt{34}}{2}\)

We could choose to write this as:

\(\displaystyle x=-1\pm\sqrt{\frac{17}{2}}\)

4.)

a) Correct. The product of the slopes of the two lines is -1.
 
  • #3
Re: Please check my answers - 2

Thank you ! :)
 

FAQ: Are these lines parallel, perpendicular, or neither?

What is the quadratic formula?

The quadratic formula is a mathematical formula used to find the solutions to a quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The formula is x = (-b ± √(b^2-4ac)) / 2a.

How is the quadratic formula used to find the solutions to a quadratic equation?

The quadratic formula is used by substituting the values of a, b, and c from the given quadratic equation into the formula. The resulting solutions are the values of x that make the equation true.

How can the quadratic formula be used to determine whether two lines are parallel, perpendicular, or neither?

To determine whether two lines are parallel, perpendicular, or neither, you must first find the equations of the two lines in the form y = mx + b. Then, compare the values of the slopes (m) of the two lines. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular. If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.

Can the quadratic formula be used to find the distance between two parallel or perpendicular lines?

No, the quadratic formula cannot be used to find the distance between two parallel or perpendicular lines. The distance between two parallel lines can be found by finding the distance between any two points on each line. The distance between two perpendicular lines can be found by using the Pythagorean Theorem.

What happens if the discriminant (b^2-4ac) in the quadratic formula is negative?

If the discriminant is negative, the quadratic equation has no real solutions. This means that the graph of the equation does not intersect with the x-axis and the equation has no solutions. In terms of determining whether two lines are parallel, perpendicular, or neither, if the discriminant is negative, the slopes of the lines will not be able to be compared and it cannot be determined whether the lines are parallel, perpendicular, or neither.

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