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3 years ago

5

7. The graph of part of linear function g is shown on the grid. Which inequality best represents the domain of the part shown?

1 answer:

PSYCHO15rus [73]3 years ago

3 0

Answer:

a

Step-by-step explanation:

Domain means the change in x.

so the domain will be which values of x the fn goes through.

you can see the black line goes from -9 to 2 in x values.

the -9 isn't filled in, but the 2 is. filled in means it will be with an equals instead of without.

so x is between -9 and 2, 2 is with equals -9 is without,

so the first one.

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galben [10]

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2 years ago

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Tashia ate 1/3 of a pizza, and Jay ate 3/8 of the same pizza. What fraction of the pizza was eaten?

Sauron [17]

This is basically saying how much of the pizza did Tashia and Jay both ate, thus combining their portions together.

1/3 + 3/8 = fraction of pizza eaten

To add fractions, you must have a common denominator. Which is 24 in this case because 3*8 = 24.

So you multiply 1/3 with 8 and multiply 3/8 with 3.

1/3*8= 8/24
3/8*3= 9/24

Now you add the fractions.
8/24+9/24= 17/24. You add the numerator, the denominator stays the same.

17/24 of the pizza was eaten.

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3 years ago

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katen-ka-za [31]

Answer:

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3.a,e

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Step-by-step explanation:

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3 years ago

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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

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

$1000 = 300e^{24r}$

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

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

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

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

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

$r = 0.05$

So

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

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

2 years ago

The perimeter of a square is 66.8 cm. What is the side lengh of the square

mylen [45]

Side length = 16.7 cm

Solution:

Perimeter of a square given = 66.8 cm

In a square four sides are equal.

The perimeter of a square = 4 × side

⇒ 4 × side = 66.8 cm

Divide both sides of the equation by 4 to equal the expression.

⇒ side = 66.8 ÷ 4

⇒ side = $\frac{66.8}{4}$

⇒ side = 16.7 cm

Hence, the side length of the square is 16.7 cm.

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2 years ago