Pauley graphs the change in temperature of a glass of hot tea over time. he sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. which best describes this function?

it is linear because the graph decreases over time.

it is linear because there is both an independent and a dependent variable.

it is nonlinear because linear functions are increasing functions.

it is nonlinear because linear functions increase or decrease at the same rate.

Answer with explanation:

Graph drawn by Pauley ,for the change in temperature of hot tea:

→Function Decreases Quickly first, and then decreases more slowly as time passes

If the equation of the function has been linear, there must have been constant rate of  decrease of temperature.

Here,when we compose the function,that is , f(x)=y, where,

that is , y(temperature), decreases,when time increases.

Suppose this function is linear,represented as

→ y=k x, where k is the slope of line , a fixed real umber, it shows that,y and x are directly proportional to each other,that is when time increases ,temperature increases or vice versa.

→But , here the situation is different,that is with increase in one variable(time),other variable (temperature), decreases .  

So,we can conclude that, the given function can't be linear.

Option D: It is nonlinear because linear functions increase or decrease at the same rate. is description about the situation Described.

Answer with explanation:

Graph drawn by Pauley ,for the change in temperature of hot tea:

→Function Decreases Quickly first, and then decreases more slowly as time passes

If the equation of the function has been linear, there must have been constant rate of  decrease of temperature.

Here,when we compose the function,that is , f(x)=y, where,

that is , y(temperature), decreases,when time increases.

Suppose this function is linear,represented as

→ y=k x, where k is the slope of line , a fixed real umber, it shows that,y and x are directly proportional to each other,that is when time increases ,temperature increases or vice versa.

→But , here the situation is different,that is with increase in one variable(time),other variable (temperature), decreases .  

So,we can conclude that, the given function can't be linear.

Option D: It is nonlinear because linear functions increase or decrease at the same rate. is description about the situation Described.

perimeter of the first rectangular board is 9 feet.

step-by-step explanation:

let p = perimeter of first board.

l = length of first board

w = width of first board

length of first board = 2 * width of first board - 3

l = 2w - 3

perimeter of first board = 2l + 2w

since l = 2w-3, then

p = 2*(2w-3) + 2w which equals 4w-6 + 2w which equals 6w-6

length and width of the second board are reciprocals of corresponding length and width of the first board.

length of second board = 1/(2w-3)

width of second board = 1/w

perimeter of second board is 1/5th perimeter of the first board.

perimeter of second board = p/5

perimeter of the second board = (2/(2w-3) + 2/w)

since the perimeter of the first board is 5 times the perimeter of the second board, this means that:

6w-6 = 5*(2/(2w-3) + 2/w)

which is the same as:

6w-6 = (10/(2w-3) + 10/w)

if we multiply both sides of this equation by (2w-3), we get:

(6w-6)*(2w-3) = 10 + 10*(2w-3)/w

if we multiply both sides of this equation by w, we get:

(6w-6)*(2w-3)*w = 10*w + 10*(2w-3)

we can simplify this to become:

(6w-6)*(2w-3)*w = 10w + 20w - 30

which becomes:

(6w-6)*(2w-3)*w = 30w-30

if we divide both sides of this equation by (6w-6), we get:

(2w-3)*w = (30w-30)/(6w-6)

which becomes:

(2w-3)*w = 5

this can be simplified to:

2w^2 - 3w = 5

subtract 5 from both sides of this equation to get:

2w^2 - 3w - 5 = 0

which can be factored into:

(2w-5)*(w+1) = 0

which makes:

w = 5/2

or

w = -1.

w can't be negative so the only possible answer is w = 5/2.

if w = 5/2, then

p = 2w-3 = 5-3 = 2

we have:

p = 2

w = 5/2

p = 2l + 2w gets p = 4 + 5 = 9

the perimeter of the first board is 9 feet.

since the perimeter of the second board is 1/5 the perimeter of the first board, the perimeter of the second board is 9/5.

to see if that's correct, we substitute known values for l and w into the second board.

the length of the second board is 1/l.

this becomes 1/2.

the width of the second board is 1/w

this bgecomes 1/(5/2) = (2/5)

let l2 = length of second board.

let w2 = width of second board.

l2 = (1/2)

w2 = (2/5)

let p2= perimeter of second board.

then p2 = 9/5

since p2 = 2*l2 + 2*w2, we should get p2 = 9/5 using the dimensions of l2 and w2.

2 * l2 = 2 * (1/2) = 1

2 * w2 = 2 * (2/5) = 4/5

1 is the same as 5/5

5/5 + 4/5 = 9/5

p2 checks out good.

the dimensions as given are good.

answer to the problem is:

perimeter of the first rectangular board is 9 feet.

srry idk

step-by-step explanation: