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Margaret [11]
3 years ago
8

Pls help me. rlly need help. question in picture. pls hurry​

Mathematics
1 answer:
Goshia [24]3 years ago
7 0

Answer:

(x-9)(x-6)

Step-by-step explanation:

Factor x^2-15x+54

Find two numbers that add up to -15 and multiply to 54 (hint hint, two negatives makes a positive hint hint):

-9, -6

Rewrite the expression:

(x-9)(x-6)

<em>Finito.</em>

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Age Problem. Please help. I suck at these.
eimsori [14]
Let Cynthia's age be C, then Abigail's age A

since Abigail is 8 years older, her age A = C+8.

20 years ago Cynthia's she was C-20 and Abigail was A-20=3(C-20)

A-20=3C-60
A=3C-40
but we just said A=C+8
so 3C-40=C+8
2C=48
C=24
A=24+8=32

Cynthia's age is 24 and Abigail's age is 32
7 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
At a dog park , there are 10 black dogs, 5 brown dog, 2 white dog, and 12 multi color dogs​
Sophie [7]
What question are you trying to ask?
5 0
3 years ago
Read 2 more answers
Which of the below descriptions shows a possible HAMILTON PATH?
Vadim26 [7]

Option B: FECBAD is the Hamilton path

Explanation:

Given that ABCDEF is a graph with vertices A,B,C,D,E and F

We need to determine the Hamilton path.

Since, we know that a Hamilton path is a path that touches every vertex in a graph exactly once.

Option A: EFADECBA

The path touches the vertices E and A twice.

Hence, the path EFADECBA is not a Hamilton path.

Therefore, Option A is not the correct answer.

Option B: FECBAD

The path touches every vertex in the graph exactly once.

Hence, the path FECBAD is a Hamilton path.

Therefore, Option B is the correct answer.

Option C: ADEFBD

The path touches the vertex A twice because when the path travels from F to B the only way to travel through A.

Hence, the path ADEFBD is not a Hamilton path.

Therefore, Option C is not the correct answer.

Option D: ADECBAFE

The path touches the vertices E and A twice.

Hence, the path ADECBAFE is not a Hamilton path.

Therefore, Option D is not the correct answer.

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3 years ago
What is the circumference of the circle?
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Step-by-step explanation:

What is the circumference of the circle?

f) 52 cm2

e) 2610 cm2

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3 years ago
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