Mathematics, 15.08.2021 04:50 krystalhurst97

The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t^4 – 9t^3 + 24t^2 – 20t, where t is the number of months since the restaurant opened. How many months after the franchise opens will it begin to show a profit? 5 months
3 months
2 months
1 month

(2 months isn’t the answer btw)

Answers: 3

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Answer from: rivman10

The profitability of the restaurant is when the function gives a value greater than 0. The franchise does not make a profit after 5, 3, 2 or 1 month of opening.

Given that:

P(t) = t^4 - 9t^3 + 24t^2 - 20t

To calculate the profit, we simply substitute the values of t in the above equation.

(a) 5 months

This means t =5

So, we have:

$P(5) = 5^4 - 9\times 5^3 + 24 \times 5^2 - 20 \times 5$

P(5) = 0

(b) 3 months

This means that t=3

So, we have:

$P(3) = 3^4 - 9 \times 3^3 + 24 \times 3^2 - 20 \times 3$

P(3) = -6

This means that t = 2

So, we have:

$P(2) = 2^4 - 9 \times 2^3 + 24 \times 2^2 - 20 \times 2$

P(2) = 0

(d) 1 month

This means that t = 1

So, we have:

$P(1) = 1^4 - 9 \times 1^3 + 24 \times 1^2 - 20 \times 1$

P(1) = -4

For the restaurant to make a profit, the equation has to give a positive value. Since none of the values of t gives a positive value for P(t).

Then, we can say the franchise does not make a profit after 5, 3, 2 or 1 month of opening.

Read more about functions at:

Answer from: Quest

the length of o'p' is $1.5\times op$ .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

$k=\frac{o'p'}{op}$

the scale factor is 1.5.

$1.5=\frac{o'p'}{op}$

multiply both sides by op.

$1.5\times op=o'p'$

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is $1.5\times op$ .

Answer from: Quest

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

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