What is the slope of the line between (-3,6) and (-5,9)?

Please help me 30 points Show you work

GenaCL600 [577]

Answer:

(a) A translation is a rigid transformation. How does this statement support line s being parallel to line r?

Because ALL of the points of line r move the same distance in the same direction, then the inclination of the line s doesn't change with respect line r.

(b) Write and expression for the slope of line r:

(k-n)/(j-m)

(c) Write and expression for the slope of line s:

(k-n)/(j-m)

(d) Line q is a vertical is a vertical translation of line s 3 units down. P'' is the image of P'. What are the coordinates of P''?

The coordinates of P'' are:

P''=(m,n+ϴ-3)

Step-by-step explanation:

(a) A translation is a rigid transformation. How does this statement support line s being parallel to line r?

Because ALL of the points of line r move the same distance in the same direction, then the inclination of the line s doesn't change with respect line r.

(b) Write and expression for the slope of line r.

Line r goes through the points:

P=(m,n)=(xp,yp)→xp=m, yp=n

Q=(j,k)=(xq,yq)→xq=j, yq=k

Slope of line r is:

mr=(yq-yp)/(xq-xp)

Replacing the coordinates, the expression for the slope of line r is:

mr=(k-n)/(j-m)

(c) Write and expression for the slope of line s.

Line s goes through the points:

P'=(m,n+ϴ)=(xp',yp')→xp'=m, yp'=n+ϴ

Q'=(j,k+ϴ)=(xq',yq')→xq'=j, yq'=k+ϴ

Slope of line s is:

ms=(yq'-yp')/(xq'-xp')

Replacing the coordinates, the expression for the slope of line s is:

ms=[(k+ϴ)-(n+ϴ)]/(j-m)

Eliminating the parentheses in the numerator:

ms=[k+ϴ-n-ϴ]/(j-m)

Simplifyng:

ms=(k-n)/(j-m)

(d) Line q is a vertical is a vertical translation of line s 3 units down. P'' is the image of P'. What are the coordinates of P''?

3 units down, then change only the ordinate y:

P''=(xp',yp'-3)

Replacing xp' and yp':

P''=(m,n+ϴ-3)

7 0

3 years ago

Read 2 more answers

(3 points)

Snezhnost [94]

Answer:

The exponential Function is $20+12h=200$ .

Farmer will have 200 sheep after 15 years.

Step-by-step explanation:

Given:

Number of sheep bought = 20

Annual Rate of increase in sheep = 60%

We need to find that after how many years the farmer will have 200 sheep.

Let the number of years be 'h'

First we will find the Number of sheep increase in 1 year.

Number of sheep increase in 1 year is equal to Annual Rate of increase in sheep multiplied by Number of sheep bought and then divide by 100.

framing in equation form we get;

Number of sheep increase in 1 year = $\frac{60}{100}\times20 = 12$

Now we know that the number of years farmer will have 200 sheep can be calculated by Number of sheep bought plus Number of sheep increase in 1 year multiplied by number of years is equal to 200.

Framing in equation form we get;

$20+12h=200$

The exponential Function is $20+12h=200$ .

Subtracting both side by 20 using subtraction property we get;

$20+12h-20=200-20\\\\12h=180$

Now Dividing both side by 12 using Division property we get;

$\frac{12h}{12} = \frac{180}{12}\\\\h =15$

Hence Farmer will have 200 sheep after 15 years.

6 0

3 years ago

A laptop company claims up to 11.0 hours of wireless web usage for its newest laptop battery life. However, reviews on this lapt

emmainna [20.7K]

Answer:

Step-by-step explanation:

given that a laptop company claims up to 11.0 hours of wireless web usage for its newest laptop battery life. However, reviews on this laptop shows many complaints about low battery life. A survey on battery life reported by customers shows that it follows a normal distribution with mean 10.5 hours and standard deviation 27 minutes.

convert into same units into hours.

X is N(10.5, 0.45)

a) the probability that the battery life is at least 11.0 hours

$P(X\geq 11)\\\\=1-0.8667\\=0.1333$