Please explain how to do this and still get the answer 16. Thank you!

valentinak56 [21]

In simplest form it is 3 over 4

8 0

3 years ago

A. Show that the vector v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of v is the negative

pishuonlain [190]

Answer:

Part A:

$m_1m_2=-1$

$\frac{b}{a}(\frac{-a}{b})=-1\\-1=-1$

Hence proved that Vector= ai + bj is perpendicular to the line ax + by = c.

Part B:

Slope of vector = $\frac{b}{a}$

Step-by-step explanation:

Condition for perpendicular is:

$m_1m_2=-1$

Part A:

Consider the vector v = ai + bj

x component of vector=a

y component of vector=b

Slope of vector= $m_1=\frac{y}{x}=\frac{b}{a}$

Consider the line ax + by = c:

Rearranging the equation:

ax+by=c

by=c-ax

y= $\frac{-ax}{b}+\frac{c}{b}$

According to general equation of line: $y=mx+c$

Where m is the slope

In our case the slope of above line is:

$m_2=\frac{-a}{b}$

According to the condition of perpendicular:

$m_1m_2=-1$

$\frac{b}{a}(\frac{-a}{b})=-1\\-1=-1$

Hence proved that Vector= ai + bj is perpendicular to the line ax + by = c.

Part B:

Slope of vector is also calculated above.

Since the slope of vector is negative reciprocal of the slope of the given line:

According to equation of line ax + by = c

y= $\frac{-ax}{b}+\frac{c}{b}$

According to general equation of line: $y=mx+c$

Where m is the slope

Slope of given line=m= $\frac{-a}{b}$

negative reciprocal of the slope of the given line = $\frac{b}{a}$

Slope of vector = $\frac{b}{a}$

5 0

3 years ago

What is the domain and range of the quadratic function given by the equation /(x) = 2(x-4)] - 2

Ray Of Light [21]

The domain of the function is the set of all real numbers and the range of the function is the set of all values greater than -2

<h3>How to determine the domain and the range?</h3>

The function is given as:

f(x) = 2(x -4)^2 - 2

A quadratic function can take any real number as its input.

So, the domain of the function is the set of all real numbers

The vertex of the above function is:

Vertex = (4, -2)

And the leading coefficient is:

a = 2

The y value of the vertex is;

y = -2

Because the value of a is positive, then the vertex is a minimum.

This means that the range of the function is the set of all values greater than -2

Read more about domain and range at:

brainly.com/question/10197594

#SPJ1

8 0

2 years ago

Please help.....................................................................

yarga [219]

The mean is every number added, then divided by the amount of numbers. range is the number that occurred most often. What does that get you?

7 0

3 years ago

Write the equation of the line that contains the given point and has the given slope. (15, 31), slope is 0.5

Anna11 [10]

Y=.5x+23.5 is your answer :D

7 0

4 years ago