Translate the following into algebraic expressions: If a number is three less than five times m, what is the number?

What is the equation in standard form of a perpendicular line that passes through (5,-1)

arlik [135]

Y = (-1/2)x + (3/2)

is a line that will pass through (5, 1), though I have no idea what you want it to be perpendicular to, as you have no provided any other equation.

4 0

4 years ago

2. Suppose 27 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 80% a month.

Marta_Voda [28]

Explanation

The question indicates we should use a logistic model to estimate the number of plants after 5 months.

This can be done using the formula below;

$\begin{gathered} P(t)=\frac{K}{1+Ae^{-kt}};A=\frac{K-P_{0_{}}}{P_0}_{} \\ \text{From the question} \\ P_0=\text{ Initial Plants=27} \\ K=\text{Carrying capacity =140} \end{gathered}$

Workings

Step 1: We would need to get the value of A using the carrying capacity and initial plants that started growing in the yard.

This gives;

$\begin{gathered} A=\frac{140-27}{27} \\ A=\frac{113}{27} \end{gathered}$

Step 2: Substitute the value of A into the formula.

$P(t)=\frac{140}{1+\frac{113}{27}e^{-kt}}$

Step 3: Find the value of the constant k

Kindly recall that we are told that the plants increase by 80% after each month. Therefore, after one month we would have;

$\begin{gathered} P(1)=27+(\frac{80}{100}\times27) \\ P(1)=\frac{243}{5} \end{gathered}$

We can then have that after t= 1month

$\begin{gathered} \frac{140}{1+\frac{113}{27}e^{-k\times1}}=\frac{243}{5} \\ Flip\text{ the equation} \\ \frac{1+\frac{113}{27}e^{-k}}{140}=\frac{5}{243} \\ 243(1+\frac{113}{27}e^{-k})=700 \\ 243+1017e^{-k}=700 \\ 1017e^{-k}=700-243 \\ 1017e^{-k}=457 \\ e^{-k}=\frac{457}{1017} \\ -k=\ln (\frac{457}{1017}) \end{gathered}$

Step 4: Substitute -k back into the initial formula.

$\begin{gathered} P(t)=\frac{140}{1+\frac{113}{27}e^{\ln (\frac{457}{1017})t}} \\ =\frac{140}{1+\frac{113}{27}(e^{\ln (\frac{457}{1017})})^t} \\ P(t)=\frac{140}{1+\frac{113}{27}(\frac{457}{1017}^{})^t} \\ \end{gathered}$

The above model is can be used to find the population at any time in the future.

Therefore after 5 months, we can estimate the model to be;

$\begin{gathered} P(5)=\frac{140}{1+\frac{113}{27}(\frac{457}{1017}^{})^5} \\ P(5)=\frac{140}{1.07668} \\ P(5)=130.029\approx130 \end{gathered}$

Answer: The estimated number of plants after 5 months is 130 plants.

8 0

1 year ago

What is a artafart and a Earth quack?

bekas [8.4K]

Aftershocks occur after the most major part of an earth quake happens. Earthquakes occur at fault lines near the tectonic border. They occur because of the sudden movement for staying rigid while they were edging closer and closer. So the sudden movement releases a large amount of tension buried deep below the earth creating or resulting in an earthquake.

3 0

3 years ago

2s + 36 > 50 do fractional solutions make sense in this context? Why or why not

Arisa [49]

Answer:

There may be fractional solutions in this context.

Step-by-step explanation:

We are given an inequality equation and we have to get a solution to that.

It is, 2s + 36 > 50

⇒ 2s > 50 - 36 {Subtracting 36 from both the sides}

⇒ 2s > 14

⇒ s > 7 {Dividing both sides by 2}

Therefore, solution of this given inequality is s > 7.

Now, the value of s is greater than 7 which may be an integer or a fraction.

So, there may be fractional solutions in this context. (Answer)

6 0

4 years ago

The domain of y = cot x is all real numbers such that _______.

Artyom0805 [142]

Answer:

Step-by-step explanation:

x≠ n*π, where n is an integer

because x/π can not be an integer

4 0

3 years ago