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3 years ago

How many solutions does the following equation haves? -3x+9-2x=-12-5x

Mathematics

1 answer:

Mashcka [7]3 years ago

4 0

Answer:

no solution

Step-by-step explanation:

-3x+9-2x=-12-5x\

-5x+5x=-12-9

0=-21

which is impossible.

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A house cost $120,000 when it was purchased. The value of the house increases by 10% each year. Find the rate of growth each mon

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Help with this question anyone?

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3 years ago

A tank initially contains 60 gallons of brine, with 30 pounds of salt in solution. Pure water runs into the tank at 3 gallons pe

adoni [48]

Answer:

the amount of time until 23 pounds of salt remain in the tank is 0.088 minutes.

Step-by-step explanation:

The variation of the concentration of salt can be expressed as:

$\frac{dC}{dt}=Ci*Qi-Co*Qo$

being

C1: the concentration of salt in the inflow

Qi: the flow entering the tank

C2: the concentration leaving the tank (the same concentration that is in every part of the tank at that moment)

Qo: the flow going out of the tank.

With no salt in the inflow (C1=0), the equation can be reduced to

$\frac{dC}{dt}=-Co*Qo$

Rearranging the equation, it becomes

$\frac{dC}{C}=-Qo*dt$

Integrating both sides

$\int\frac{dC}{C}=\int-Qo*dt\\ln(\abs{C})+x1=-Qo*t+x2\\ln(\abs{C})=-Qo*t+x\\C=exp^{-Qo*t+x}$

It is known that the concentration at t=0 is 30 pounds in 60 gallons, so C(0) is 0.5 pounds/gallon.

$C(0)=exp^{-Qo*0+x}=0.5\\exp^{x} =0.5\\x=ln(0.5)=-0.693\\$

The final equation for the concentration of salt at any given time is

$C=exp^{-3*t-0.693}$

To answer how long it will be until there are 23 pounds of salt in the tank, we can use the last equation:

$C=exp^{-3*t-0.693}\\(23/60)=exp^{-3*t-0.693}\\ln(23/60)=-3*t-0.693\\t=-\frac{ln(23/60)+0.693}{3}=-\frac{-0.959+0.693}{3}= -\frac{-0.266}{3}=0.088$

5 0

3 years ago

Find the value of x. Give reasons to justify your solution. D ∈ AC

miskamm [114]

Answer:

x = 13

Step-by-step explanation:

Find the diagram attached

From the diagram, the sum of angle of the straight line BCD is 180°. Hence;

<BCE+<ECF<90 = 180

<BCE+64+90=180

<BCE+154 = 180

<BCE = 180-154

<BCE = 26°

Next is to get x.

The sum of interior angles <BCE and <BEC is equal to exterior angle <ABE

<BCE + <BEC = <ABE

26+x = 3x

Collect like terms

26 =3x-x

26=2x

x = 26/2

x = 13

Hence the value of x is 13

7 0

3 years ago