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3 years ago

The lines below are perpendicular if the slope of the green line is 3/2 what is the slope of the red line

Mathematics

2 answers:

shepuryov [24]3 years ago

8 0

Answer:

The perpendicular line has a slope of -2/3

Step-by-step explanation:

Perpendicular lines have a slope that multiplies to -1

3/2 * m = -1

Multiply each side by 2/3

3/2 * 2/3 *m = -1 * 2/3

m = -2/3

Whitepunk [10]3 years ago

6 0

Answer: -2/3

Step-by-step explanation: The key to understanding this problem is to understand what it means when slopes are perpendicular.

To most students, perpendicular lines are simply

lines that meet at a 90 degree angle.

However, when dealing with these kinds of problems, it's important

to think about perpendicular lines in terms of their slopes.

As a rule, the slopes of two perpendicular

lines are always negative reciprocals.

So if we know that the slope of one line is 3/2, we can find the slope of the other line by finding the negative reciprocal of 3/2.

So we take the fraction and flip it, then we change the sign.

So the negative reciprocal of 3/2 is -2/3.

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fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

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$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

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