The endpoints of a line are (10, 4) and (-2, 8). Find the slope of
the line.

Answers

Answer 1

Answer: your answer would be m= -1/3

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Limit of x^2-81/x+9
As x goes toward -9

Answers

Hello,

Use the factoration

a^2 - b^2 = (a - b)(a + b)

Then,

x^2 - 81 = x^2 - 9^2

x^2 - 9^2 = ( x - 9).(x + 9)

Then,

Lim (x^2- 81) /(x+9)

= Lim (x -9)(x+9)/(x+9)

Simplity x + 9

Lim (x -9)

Now replace x = -9

Lim ( -9 -9)

Lim -18 = -18
_______________

The second method without using factorization would be to calculate the limit by the hospital rule.

Lim f(x)/g(x) = lim f(x)'/g(x)'

Where,

f(x)' and g(x)' are the derivates.

Let f(x) = x^2 -81

f(x)' = 2x + 0
f(x)' = 2x

Let g(x) = x +9

g(x)' = 1 + 0
g(x)' = 1

Then the Lim stay:

Lim (x^2 -81)/(x+9) = Lim 2x /1

Now replace x = -9

Lim 2×-9 = Lim -18

= -18

Please help me out with the below question

Answers

Answer:

Step-by-step explanation:

this is only what I know correct me if I'm wrong thank you

What is the determinant of an elementary row replacement matrix? An elementary n xn row replacement matrix is the same as the n x n identity matrix with__________ of the_____________replaced with some number k.This means this is the ___________and so its determinent is ___________.of its diagnol enteries. Thus, the determinant of an elementary row replacement matrix is______________.
1. Exactly one,atleast one
2. 1's or 0's
3. Identity matrix,invertible matrix, triangular matrix or zero matrix.
4. Product or sum
5. A number

Answers

Answer:

Step-by-step explanation:

Recall that an elementary matrix of a matrix operation is obtained by applying the matrix operation to the identity matrix. In this case, by replacement, it means changing the whole row of a matrix and replacing it with a the same row multiplied by a number k.

In this case, the solution is

What is the determinant of an elementary row replacement matrix?

An elementary n xn row replacement matrix is the same as the n x n identity matrix with Exactly one of the 1's replaced with some number k.This means this is the triangular matrix and so its determinent is product of its diagonal entries. Thus, the determinant of an elementary row replacement matrix is a number. Especifically, the number k we used to replace the one

1. Exactly one,atleast one

2. 1's or 0's

3. Identity matrix,invertible matrix, triangular matrix or zero matrix.

4. Product or sum

5. A number

For this line 3x−4y−12=0, which statement is true? 1- The x-intercept is 4, and the y-intercept is 3. 2-The x-intercept is 4, and the y-intercept is -3 3-The x-intercept is 3, and the y-intercept is -4. 4-The x-intercept is 3, and the y-intercept is 4.

Answers

9514 1404 393

Answer:

2. The x-intercept is 4, and the y-intercept is -3

Step-by-step explanation:

The given equation is in general form. I find it easier to see the intercepts when the equation is written in standard form:

3x -4y = 12

Setting y=0 and solving for x, we have the x-intercept:

3x = 12 ⇒ x = 12/3 = 4

Setting x=0 and solving for y, we have the y-intercept:

-4y = 12 ⇒ y = 12/-4 = -3

The x-intercept is 4; the y-intercept is -3.

Suppose you are a chemist who is trying to synthesize a specific compound. You have been working with a new technique and you think that this process can turn 60% of the input compounds into the desired synthesized compound, and want to attempt the process enough times to get an estimate that is within .04 of the true proportion that is converted. How many times should you execute the process to get the desired precision

Answers

Answer:

The sample size 'n' = 576

576 times should you execute the process to get the desired precision

Step-by-step explanation:

Explanation :-

Step(i)

Given data the process can turn 60% of the input compounds into the desired synthesized compound.

Sample proportion ' p' = 60% = 0.60

Given data the estimate within 0.04 of the true proportion that is converted

The margin of error of the true population proportion

M.E = 0.04

Step(ii)

The margin of error of the true population proportion is determined by

$M.E = ( Z_(0.05) √(p(1-p)) )/(√(n) )$

$0.04 = ( 1.96 √(0.60(1-0.60)) )/(√(n) )$

$√(n) = ( 1.96 √(0.60(1-0.60)) )/(0.04 )$

on calculation, we get

$√(n) = 24$

squaring on both sides ,we get

n = 576

Final answer:-

The sample size 'n' = 576

576 times should you execute the process to get the desired precision

The United Van Lines moving company has a truck filled for deliveries to five different sites. If the order of the deliveries is randomly selected, what is the probability that it is the shortest route?

Answers

Answer:

0.8333%

Step-by-step explanation:

Assuming that there is only one possible shortest route, the probability that a randomly selected route is given by one divided by the permutation of the order of five different sites:

$P=(1)/((5!)/((5-5)!))=(1)/(5*4*3*2*1)\n P=0.008333=0.8333\%$