Let's look at the first equation.

3y = 5x - 1

y = 5/3 y - 1/3

This line has slope 5/3. A line perpendicular to it has slope -3/5.

The second line is y = -3/5 x + 9.
Its slope is indeed -3/5, so the second line is perpendicular to the first one.

There is an infinite number of lines perpendicular to any given line. You concluded correctly that the two lines in this problem are perpendicular based on the fact that their slopes are negative reciprocals. The second line, y = -3/5 x + 9, is only one line that is perpendicular to the first line. There is an infinite number of lines perpendicular to the first line. All the perpendicular lines have the slope -3/5 and different y-intercepts. The +9 here is just the y-intercept of this specific perpendicular line. Since there is an infinite number of y-intercepts, there is an infinite number of perpendiculars.

7 0

4 years ago

the perimeter of a rectangle is 192 ft. the ratio of its length to its width is 7:5 what are dimensions of the rectangle?

Jobisdone [24]

Answer: Hence the dimensions are 56 ft and 40 ft.

Step-by-step explanation:

Alright, lets get started.

The ratio of sides of rectangle is given as 7:5.

It means, the length of rectangle is : $7x$

It means, the width of rectangle is : $5x$

So the perimeter of rectangle will be : $2(length + width)$

Plugging the value of sides length and width,

the perimeter of rectangle will be : $2\times(7x+5x)$

the perimeter of rectangle will be : $2\times 12x$

the perimeter of rectangle will be : $24x$

As per question, the given perimeter is 192, so

$24x=192$

Dividing 24 in both sides,

$x=\frac{192}{24}$

$x=8$

Hence the length of rectangle will be : $7\times 8 =56$

Hence the width of rectangle will be : $5\times 8 =40$

Hence the dimensions are 56 ft and 40 ft. : Answer

Hope it will help :)

6 0

3 years ago

Determine the equation of the line that passes through the given points. (3,18) and (8,33)

vampirchik [111]

Work out the gradient:
Change in Y/ Change in X
15/5 = 3
Plug this into linear equation of a line : Y=mx + c
Y=3x + c
To work out c plug in known point: 18 = (3)(3) + c
18 - 9 = c
C= 9
Therefore Y= 3x + 9

7 0

3 years ago

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