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3 years ago

Calculate the slope of the line passing through the two colored points below (-1 , 1) (1, 1)

1 answer:

algol133 years ago

3 0

Slope is defined as the change in y with respect to the change in x.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Plug in the values.

$\frac{1 - 1}{1 - (-1)} = \frac{0}{2}$

So, the slope is equal to 0. Which means its a horizontal line.

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To play the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying a $1 for each five-number s

defon

There are 45 numbers out of which 5 numbers are required to win an enormous sum of money

No of ways in which 5 numbers can be selected out of 45 numbers.

$C_{45}^5=\frac{45!}{40!5!} =1221759$

out of which there is only combination foe contest winning

$P=\frac{1}{1221759}$

When 100 different tickets are bought then

Probability of winning: $\frac{100}{1221759}$

Probably of winning≈0,000082

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P.S. Hello from Russia :^)

4 0

3 years ago

Jeremy claims that if a linear function has a slope of the same steepness and the same y-intercept as the linear function in the

andre [41]

Here, we have to examine the equation of the straight line which is denoted by: y = m x +c where "m" is the slope which represents the steepness and c is the y-intercept

Here, the two linear functions have the same slope "m" and the same y-intercept "c". When both these are the same, the two linear functions are representing the same straight line.

Therefore, Jeremy is correct in his argument.

7 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

A slice is made perpendicular to the base of a right rectangular pyramid as shown.

Katena32 [7]

To find the area of a triangle, you will times height by base and divide by then divide by two. In this case the height is 22 and the base is 10. 22 times 10 is 220. You then would divided 220 by two, making your answer 110 cm squared.

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3 years ago

it takes Liam 1 hour 20 minutes to get ready and get to the train. if he start getting ready at 7:15a.m. will he be able to catc

BlackZzzverrR [31]

Yes, he will make it in time.

3 0

4 years ago

Read 2 more answers