Consider the line y =2/3x-4.

Mathematics

1 answer:

ladessa [460]2 years ago

6 0

Answer:

1.) a line parallel to the line will have slope 2/3

2.) a line perpendicular to the line will have slope -3/2

Step-by-step explanation:

The slope of parallel lines must always be the same. Therefore, if a line is parallel to y = 2/3x - 4, the other line must have slope 2/3 and not have the same y-intercept (otherwise it would represent the same line).

The slope of perpendicular lines are reciprocals with opposite signs. Basically, if you have one slope of one equation, to find the perpendicular slope you would simply flip the slope over and change the sign.

For example: if the slope was 2/3, the perpendicular slope is flipping 2/3 upside down to get 3/2 and changing the sign from positive to negative = -3/2

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a certain number of two digit is three times the sum of its digit and if 45 added to it the digit will be reversed find the numb

bogdanovich [222]

· Author has 184 answers and 67.6K answer views
Let the number be (10 x + y)

Then, 10 x + y = 3 * (x + y) (given)

Or, 10 x + y = 3 x + 3 y

Or, 10 x - 3 x = 3 y - y

Or, 7x = 2 y

Or, x = 2 y / 7 ( Eq. 1)

Also, 10 x + y + 45 = 10 y + x ( given)

Or, 10 x - x = 10 y - y - 45

Or, 9 x = 9 y - 45 ( Eq. 2)

Substituting the value of x from (Eq. 1) in (Eq. 2), we have:

9 * 2 y / 7 = 9 y - 45

Or, (9 y ) - (18 y / 7) = 45

Or, 63 y - 18 y = 315

Or, 45 y = 315

Or, y = 7

From (Eq. 1),

x = 2 * 7 / 7 = 2

So, the number is 10 x + y = (10 * 2) + 7 = (20 + 7) = 27

Answer

Check:

Sum of the digits = 2 + 7 = 9

9 * 3 = 27 ✓

Adding 45 to the number 27, we get 72. So, the digits get reversed.

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