All categories

3 years ago

The lines represented by the equations y - x = -8 and y = -x – 6 are

Mathematics

1 answer:

ziro4ka [17]3 years ago

7 0

Answer:

Perpendicular

Step-by-step explanation:

Here, the slopes of the lines are 1 & -1

( they are same with opposite symbols) so, the lines are perpendicular

You might be interested in

A (sin 40)/ 24( sin 118)

Svetradugi [14.3K]

Where is the rest of the question?

3 0

3 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:

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

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

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

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

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.

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

Therefore gcd(6,15) = 3. Since 3|12, the equation has integral solutions.

We then find a way of representing 3 as a linear combination of 6 and 15, using the Euclidean algorithm computation and the equalities, we have,

$3 = 15-6*2$

Because 4 multiplies 3 to give 12, we multiply by 4

$12 = 15*4-6*8$

So one solution is

$x=-8$ & $y = 4$

All other solutions will have the form

$x=-8+\frac{15r}{3} = -8+5r\\y=4-\frac{6r}{3} =4-2r$

where $r$ ∈ Ζ

Hence by putting r values, we get many (x, y)

3 0

3 years ago

|7m–56|, if m<8 write without using absolute value

Ilia_Sergeevich [38]

Answer:

56-7m

Step-by-step explanation:

l7m–56l m<8

so lets replace m with something smalller then 8, how about 7

so then it would be...

l 7 * 7 - 56 l=

l 49-56 l = l -7 l

but the absulute value of -7 is 7, so how does this help us? well lets see

56-49= 7 this proves that all we have to do is switch the order giving us the solution 56-7m

hope this helped :)

4 0

3 years ago

Anna opens two savings accounts at the beginning of the year. She deposits $5,000 in an account that earns 2% interest each year

xenn [34]

As we know she wont be depositing or withdrawing that means that the total money remaining in the bank would be static and would just add up the interest their is.

SO 2 per cent of 5000 is 100 $. So she will earn a 100 $ from her first account.

And 2.5 % from 10000 is around 250 $ so she earn a total of 250 $ from her second account.

Now adding up the complete money that she will earn at the end of the year would be around 350 $.

5 0

3 years ago

Which statement is correct regarding independent events?

Aleks04 [339]

Answer:

first of all

Step-by-step explanation:

TWO PLUS TWO = four

6 0

3 years ago