Please help.........

A line segment has endpoints A(4, 8) and B(2, 10). The point M is the midpoint of AB. What is an equation of a line perpendicula

Vera_Pavlovna [14]

I)

The Midpoint M of the line segment AB is found using the Midpoint formula:

$M=( \frac{4+2}{2} , \frac{8+10}{2})=(3, 9)$

ii)

the slope of the line through A and B is found by the slope formula:

$m= \frac{y_1-y_2}{x_2-x_1}= \frac{10-8}{2-4}= \frac{2}{-2}=-1$

iii)

the product of the slopes of 2 perpendicular lines is -1, so the slope of the line perpendicular to the line through A and B is -1/(-1)=1

iv)

the equation of the line with slope 1, which contains point M(3, 9) is found by the slope point form equation of a line:

y-9=1(x-3)

y-9=x-3

y=x+6

Answer: y=x+6

7 0

3 years ago

What is the slope of this line?

Talja [164]

Answer:

-1

Step-by-step explanation:

Slope= rise/run

Since the line is decreasing, it will be negative.

6 0

3 years ago

Convert the given radian measure to a degree measure. 1.1 pi a. Negative 99 degrees b. Negative 198 degrees c. 99 degrees d. 198

irina1246 [14]

d is the right ancer

7 0

3 years ago

A soccer ball has an interior

AnnZ [28]

Answer:

5575 cm³

Step-by-step explanation:

The volume of a sphere is V = (4/3)πr³. If we substitute r = (d/2 where r is the radius and d the diameter), this formula becomes:

πd³

V = (4/3)π·d³/8, or V = -------------

6

and so, if d = 22 cm, the volume is:

π(22 cm)³

V = ------------------- = 5575 cm³

6

4 0

2 years ago

Read 2 more answers

For integers a, b, and c, consider the linear Diophantine equation ax C by D c: Suppose integers x0 and y0 satisfy the equation;

Dmitrij [34]

Answer:

a.

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

b. x = -8 and y = 4

Step-by-step explanation:

This question is incomplete. I will type the complete question below before giving my solution.

For integers a, b, c, consider the linear Diophantine equation

$ax+by=c$

Suppose integers x0 and yo satisfy the equation; that is,

$ax_0+by_0 = c$

what other values

$x = x_0+h$ and $y=y_0+k$

also satisfy ax + by = c? Formulate a conjecture that answers this question.

Devise some numerical examples to ground your exploration. For example, 6(-3) + 15*2 = 12.

Can you find other integers x and y such that 6x + 15y = 12?

How many other pairs of integers x and y can you find ?

Can you find infinitely many other solutions?

From the Extended Euclidean Algorithm, given any integers a and b, integers s and t can be found such that

$as+bt=gcd(a,b)$

the numbers s and t are not unique, but you only need one pair. Once s and t are found, since we are assuming that gcd(a,b) divides c, there exists an integer k such that gcd(a,b)k = c.

Multiplying as + bt = gcd(a,b) through by k you get

$a(sk) + b(tk) = gcd(a,b)k = c$

So this gives one solution, with x = sk and y = tk.

Now assuming that ax1 + by1 = c is a solution, and ax + by = c is some other solution. Taking the difference between the two, we get

$a(x_1-x) + b(y_1-y)=0$

Therefore,

$a(x_1-x) = b(y-y_1)$

This means that a divides b(y−y1), and therefore a/gcd(a,b) divides y−y1. Hence,

$y = y_1+r(\frac{a}{gcd(a, b)})$ for some integer r. Substituting into the equation

$a(x_1-x)=rb(\frac{a}{gcd(a, b)} )\\gcd(a, b)*a(x_1-x)=rba$

or

$x = x_1-r(\frac{b}{gcd(a, b)} )$

Thus if ax1 + by1 = c is any solution, then all solutions are of the form

$x = x_1+r(\frac{b}{gcd(a, b)} )\\y=y_1-r(\frac{a}{gcd(a, b)} )$

In order to find all integer solutions to 6x + 15y = 12

we first use the Euclidean algorithm to find gcd(15,6); the parenthetical equation is how we will use this equality after we complete the computation.

$15 = 6*2+3\\6=3*2+0$