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3 years ago

What is the solution to the equation 1/4x - 1/8 = 7/8 + 1/2x ?

Mathematics

1 answer:

lyudmila [28]3 years ago

7 0

Hey there! I'm happy to help!

We want to get all of the variables on the left side and all of the numbers on the right side. This will allow our variable to be isolated so we can see what it is equal to.

1/4x - 1/8 = 7/8 + 1/2x

We add 1/8 to both sides.

1/4x=1+1/2x

We subtract 1/2x from both sides.

-1/4x=1

We divide both sides by -1/4 (same thing as multiplying -4).

B. x=-4

Have a wonderful day and keep on learning! :D

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During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

3 years ago

What’s the solution to the system of equations

sesenic [268]

Answer:

The answer to the system of equations is 4, -4

5 0

3 years ago

Read 2 more answers

Liz wants to drink 1.5 litres of water each day. She buys the water in packs of 6 bottles. Each bottle contains 0.5 litres of wa

DochEvi [55]

(0.5 liter/bottle) x (6 bottles/pack) = 3 liters/pack

(10 days) x (1.5 liter/day) / (3 liter/pack) = 5 packs

8 0

4 years ago

Read 2 more answers

Please answer this, 25 points and will give brainliest!!!

Gekata [30.6K]

Answer:

Step-by-step explanation:

The median of a triangle is a line that from the vertex touches the middle lets eliminate options

a=ab starts at a vertex but doensn't touch a the middle of a line X

b=cd starts at a vertex and touches the middle of a line Ye

C= ce stars at a vertex but doesn't end at the middle of a line X

d=mb starts in the middle of the triangle and and ends a vertex X

SO THE CORRECT ANSWER IS B

-hope this helps :)

8 0

3 years ago

(1 ÷ x- 1)+(2÷ x+2)=(3÷2) solve and check for extraneous solutions

Sliva [168]

$\frac{1}{x-1}+ \frac{2}{x+2}= \frac{3}{2}$
$\frac{1(x+2)}{(x-1)(x+2)}+ \frac{2(x-1)}{(x+2)(x-1)}= \frac{3(x-1)(x+2)}{2}$
$\frac{x+2+2(x-1)}{(x-1)(x+2)}= \frac{3(x-1)(x+2)}{2}$
$\frac{x+2+2x-1}{(x-1)(x+2)}= \frac{3(x-1)(x+2)}{2}$
$\frac{3x+1}{(x-1)(x+2)}= \frac{3(x^2+x-2)}{2}$
$\frac{}{(x-1)(x+2)}= \frac{3x^2+3x-6)}{2}$
$\frac{3x+1}{(x^2+x-2)}= \frac{3x^2+3x-6)}{2}$
$\frac{2(3x+1)}{2(x^2+x-2)}= \frac{3x^2+3x-6)(x^2+x-2)}{2(x^2+x-2)}$
$\frac{2(3x+1)}{2(x^2+x-2)}-\frac{3x^2+3x-6)(x^2+x-2)}{2(x^2+x-2)}=0$
$\frac{2(3x+1)-3x^2+3x-6}{2(x^2+x-2)}=0$

this will be continued

5 0

4 years ago