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Lisa [10]
2 years ago
8

HELPP URGENT!!! NOWW!!!!!!!! 30 POINTS!!!!!!!!!!

Mathematics
1 answer:
vesna_86 [32]2 years ago
6 0

Answer:

y= 6x

Step-by-step explanation:

Slope is 6

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What are the solutions of x2 = 8 - 5x?
jonny [76]

Answer:

That can be re-written:

x^2 + 5x -8 = 0

We use the Quadratic Formula

a=1

b = 5

c = -8

x = [-b +- sq root (b^2 - 4ac) ] / 2a

x = [-5 +- sq root (25 - - 32)] / 2

x1 = [-5 + sq root (57)] / 2

x1 = 1.27491722

x2 = [-5 - sq root (57)] / 2

x2 = -6.2749172176

Step-by-step explanation:

5 0
3 years ago
Solve for x<br> −4(x−7)=36
Ipatiy [6.2K]
-4(x-7)=36
-4x+28=36
-4x=8
x=-2
5 0
2 years ago
Read 2 more answers
Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.
Tju [1.3M]
Hello : 
<span>the nth term of a geometric sequence is : 
Un = Up ×r^(n-p)    .   r is the common ratio 
for : p=5 and n= 2
U5 = U2 ×r^3
16 = -2 r^3
r^3 = -8
but : -8 = (-2)^3
so :  r = -2
Un = U2 × r^(n-2)
Un = -2 ×(-2)^(n-2)= (-2)^(n-2+1)

</span><span>the nth term of a geometric sequenceis : Un = (-2)^(n-1)</span>
4 0
3 years ago
Read 2 more answers
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
30 POINTS FOR ANSWER!!<br> 2 numbers sum 120 and product 400<br> INSTANT ANSWER NEEDED
OLga [1]
I think the problem is
2X+20=400
You just have to answer I think X and X equals that two numbers I’m not 100% sure but I’m trying to help
4 0
3 years ago
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