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snow_lady [41]
2 years ago
9

What is the slope function y=8x+6

Mathematics
1 answer:
Sever21 [200]2 years ago
3 0
8x is the slope .. 6 is the y-intercept
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Which shows the best use of the associative and commutative to make simplifying 3/4-5+9-2/4+2 easier
ziro4ka [17]

Answer:

(not this)  3/4-5+9-2/4+2

Step-by-step explanation:

1 1/3 instead of 3/4 and 2/4

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3 years ago
Axis of symmetry for f(x) = -2x2 + 20x -42
Ksenya-84 [330]
For the function f(x)=2x^2 +20x-42

We can use the formula for the axis of symetry, which is x= \frac{-b}{2a}

With the values substituted, we get...

\frac{-20}{2(-2)} =5

Therefore the axis of symmetry is x=5 
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3 years ago
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What is the midpoint M of that line segment?
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Answer:

Midpoint = (  (x1+x2)/2 , (y1+y2)/2 )

Step-by-step explanation:

Please upload the line segment otherwise, you can use the equation above to solve for it.

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How to write in inqvality
Kitty [74]

Answer:

If you mean "How do I write an inequality?", the answer is COEFFICIENTxVARIABLE {any symbol} COEFFICIENTxVARIABLE >/< INTEGER

In other words, you should have something like this: -3x + 4v < 63

Or this: 51x - 16v > 11

Or anything along those lines.

8 0
3 years ago
The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,
uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right).

We need to solve it and obtain an expression for P(t) in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right).

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that k=0.04 and K=500 and the initial condition P(0)=100.

Notice that this equation is separable, then

\frac{dP}{P(1-P/K)} = kdt.

Now, intagrating in both sides of the equation

\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C.

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}.

So,

\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|.

We have obtained that:

-\ln\left| \frac{K-P}{P}\right| = kt +C

which is equivalent to

\ln\left| \frac{K-P}{P}\right|= -kt -C

Taking exponentials in both hands:

\left| \frac{K-P}{P}\right| = e^{-kt -C}

Hence,

\frac{K-P(t)}{P(t)} = Ae^{-kt}.

The next step is to substitute the given values in the statement of the problem:

\frac{500-P(t)}{P(t)} = Ae^{-0.04t}.

We calculate the value of A using the initial condition P(0)=100, substituting t=0:

\frac{500-100}{100} = A} and A=4.

So,

\frac{500-P(t)}{P(t)} = 4e^{-0.04t}.

Finally, as we want the value of t such that P(t)=200, we substitute this last value into the above equation. Thus,

\frac{500-200}{200} = 4e^{-0.04t}.

This is equivalent to \frac{3}{8} = e^{-0.04t}. Taking logarithms we get \ln\frac{3}{8} = -0.04t. Then,

t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325.

So, the population of rats will be 200 after 25 months.

6 0
3 years ago
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