4.

Mathematics

1 answer:

valkas [14]2 years ago

4 0

Answer: $\boxed{y=\frac{4}{5}x-2}$

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so as the slope of the given line is -5/4, the slope of the perpendicular line is 4/5.

Substituting into point-slope form,

$y-6=\frac{4}{5}(x-10)\\\\y-6=\frac{4}{5}x-8\\\\\boxed{y=\frac{4}{5}x-2}$

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A line passes through the point (0, 2) and has a slope of -1/4 What is the equation of the line?

maw [93]

Answer:

The required equation is x + 4y = 8 !!

Step-by-step explanation:

Given :-  the line passes through the point ( 0 , 2 ) and the slope of the line is ( -1/4 )

• Also, to form an equation when a point through which line passes and slope of line is given we use the formula ;

( y - y1 ) = m ( x - x1 )

Where , y and x are variables

and ( x1 , y1 ) are the points through which line passes

also, m = slope of the required line

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[ Refer to the attached file for further process ]

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By [n][n] we denote the set {1,…,n}. A function f:[m]→[n] is called monotone if f(i) \leq f(j)f(i)≤f(j)whenever i < ji

Dafna11 [192]

Answer:

There are a total of ${ 6 \choose 3} = 20$ functions.

Step-by-step explanation:

In order to define an injective monotone function from [3] to [6] we need to select 3 different values fromm {1,2,3,4,5,6} and assign the smallest one of them to 1, asign the intermediate value to 2 and the largest value to 3. That way the function is monotone and it satisfies what the problem asks.

The total way of selecting injective monotone functions is, therefore, the total amount of ways to pick 3 elements from a set of 6. That number is the combinatorial number of 6 with 3, in other words

${6 \choose 3} = \frac{6!}{3!(6-3)!} = \frac{720}{6*6} = \frac{720}{36} = 20$