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Nat2105 [25]
4 years ago
14

Which table represents a linear function ?

Mathematics
1 answer:
telo118 [61]4 years ago
5 0

Answer:

table D

Step-by-step explanation:

the value in the y axis moves by the same amount each time.

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Help please solve by factoring
marta [7]

Answer:

x = −1/6,−3

Step-by-step explanation:

Hope this helps

5 0
4 years ago
The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of
Alexandra [31]

Answer:

Population of mosquitoes in the area at any time t is:

P(t) =504,943.26  -104,943.26e^{0.693t}

Step-by-step explanation:

assume population at any time t = P(t)

population increases at a rate proportional to the current population:

⇒dP/dt ∝ P

 \implies \frac{dP}{dt} =kP----(1)

where k is constant rate at which population is doubled

solving (1)

ln|P(t)|=kt +C\\P(t)= e^{kt+C}\\P(t)=Ce^{kt}

t=0\\P(0) = P_{o}\\\implies C= P_{o}\\P(t) =P_{o}e^{kt}\\ ---- (2)

initial population = 400,000

population is doubled every week

                                                 ⇒P(1)=2P(0)

Using (2)

                                 P_{o}e^{k(1)} = 2P_{o} e^{k(0)}\\

                                            e^{k} =2\\k=ln|2|\\

In presence of predators amount is decreased by 50,000 per day

Then amount decreased per week = 350,000

In this case (1) becomes

\frac{dP}{dt}=kP-350,000\\\frac{dP}{dt} - kP=-350,000\\ ---(3)

solving (3) by calculating integrating factor

                                          I.F=e^{\int-k dt}

Multiplying I.F with all terms of (3)

e^{-kt}\frac{dP}{dt} - ke^{-kt}P =-350,000 e^{-kt}\\\frac{d}{dt}(e^{-kt}P) =  -350,000 e^{-kt}

Integrating w.r.to t

                         e^{-kt}P(t)= \frac{350,000e^{-kt}}{k} +C

                         P(t) =\frac{350,000}{k} +Ce^{kt}\\

                                          k=ln|2| =0.693

                          P(t) =504,943.26 + Ce^{0.693t}\\

at t=0

                        P(0) =504,943.26 + Ce^{0.693(0)}

                        400,000 =504,943.26 + C

                           C = -104,943.26

So, population of mosquitoes in the area at any time t is

                  P(t) =504,943.26  -104,943.26e^{0.693t}

6 0
3 years ago
|x|-5 what does the vertical bar means?​
Masja [62]

Answer:

it means absolute valuen so anything inside becomes a positve.

Step-by-step explanation:

6 0
3 years ago
What is the factored form of 8x^24-27y^6
zalisa [80]

Factoring:  8x^{24}-27y^6  


Theory : A difference of two perfect cubes,  a^3-b^3 can be factored into

             (a-b)*(a^2+ab+b^2)


Proof :  (a-b)*(a^2+ab+b^2)=

           a^3+a^2b+ab^2-ba^2-b^2a-b^3=

           a^3+(a^2b-ba^2)+(ab^2-b^2a)-b^3=

           a^3+0+0+b^3=

           a^3+b^3


Check :  8  is the cube of  2  


Check :  27  is the cube of   3  

Check :   x^{24} is the cube of    x^8


Check :  y^6 is the cube of    y^2


Factorization is :

            (2x^8 - 3y^2)*(4x^{16} + 6x^8y^2 + 9y^4)

5 0
4 years ago
If f(x)=x+4 and g(x)=x2-1 what is (gof)(x)?
Tema [17]

Answer:

x^2+8x+15

Step-by-step explanation:

This is g(f(x)), or g(x+4). x+4 squared is x^2+8x+16, and taking 1 away from that is x^2+8x+15.

5 0
3 years ago
Read 2 more answers
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