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gladu [14]
2 years ago
14

Determine whether the graph of the equation is increasing or decreasing. Write the correct answer before the number. Show your s

olutions.
5y = x - 2​​
Mathematics
1 answer:
KATRIN_1 [288]2 years ago
5 0

Answer:

Increasing

Step-by-step explanation:

We are given the function:

\displaystyle \large{5y = x - 2}

Since y is the function of x; we isolate y by dividing both sides by 5.

\displaystyle \large{ \frac{5y}{5}  =  \frac{x - 2}{5} }

Thus:

\displaystyle \large{ y =  \frac{x - 2}{5} }

Simplify the expression, separating the fraction.

\displaystyle \large{ y =   \frac{x}{5}   -  \frac{2}{5} }

Familiar with this equation? This function is a linear function.

Now to the increasing and decreasing part. There are several ways to find whether if the graph is increasing.

  1. By substituting values
  2. Graph Visualization (Or look at the graph)

I will demonstrate the first method. Start from substituting negative to positive, if we keep substituting higher numbers and we get higher y-value then the graph is increasing.

If we substitute higher numbers but we get lower y-value then the graph is decreasing.

<u>S</u><u>u</u><u>b</u><u>s</u><u>t</u><u>i</u><u>t</u><u>u</u><u>t</u><u>i</u><u>o</u><u>n</u>

y = -1/5 - 2/5 = -3/5

y = 0-2/5 = -2/5

y = 1/5-2/5 = -1/5

y = 2/5-2/5 = 0

y = 3/5-2/5 = 1/5

y = 4/5-2/5 = 2/5

y = 5/5-2/5 = 3/5

y = 6/5-2/5 = 4/5

...

As so on, as we see, when x keeps increasing, y increases too.

Therefore, the graph is increasing.

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love history [14]
SAS only. The 3rd side cannot be proven. 
8 0
3 years ago
I WILL GIVE BRAINLIEST!! PLEASE HURRY
crimeas [40]

Answer:

B. It rejects the concept of social class in the American system.

Explanation:

The Enlightenment of the American Colonies was a period in time where the people were encouraged to become their own nation. This period was represented by many speeches and pieces of writing that boasted freedom of speech, equality, freedom of the press, and religious tolerance.

This specific piece of writing focuses on the aspect of all people in the nation of America having protected freedoms and rights to become their own people.

5 0
3 years ago
Let represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of is as follows.
Sindrei [870]

Answer:

a) P(X=3) = 0.1

b) P(X\geq 3) =1-P(X

And replacing we got:

P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4

c) P(X=4) = 0.3

d) P(X=0) = 0.2

e) E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2

f) E(X^2)= \sum_{i=1}^n X^2_i P(X_i)

And replacing we got:

E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4

And the variance would be:

Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4

And the deviation:

\sigma =\sqrt{2.4} = 1.549

Step-by-step explanation:

We have the following distribution

x      0     1     2   3   4

P(x) 0.2 0.3 0.1 0.1 0.3

Part a

For this case:

P(X=3) = 0.1

Part b

We want this probability:

P(X\geq 3) =1-P(X

And replacing we got:

P(X \geq 3) = 1- [0.2+0.3+0.1]= 0.4

Part c

For this case we want this probability:

P(X=4) = 0.3

Part d

P(X=0) = 0.2

Part e

We can find the mean with this formula:

E(X)= \sum_{i=1}^n X_i P(X_i)

And replacing we got:

E(X) =0*0.2 +1*0.3+2*0.1 +3*0.1 +4*0.3= 2

Part f

We can find the second moment with this formula

E(X^2)= \sum_{i=1}^n X^2_i P(X_i)

And replacing we got:

E(X^2) =0^2*0.2 +1^2*0.3+2^2*0.1 +3^2*0.1 +4^2*0.3= 6.4

And the variance would be:

Var(X0 =E(X^2)- [E(X)]^2 = 6.4 -(2^2)= 2.4

And the deviation:

\sigma =\sqrt{2.4} = 1.549

4 0
3 years ago
Two number add to 336 and the first is bigger that the second. What are the two numbers?
makvit [3.9K]
336 divided by 2 is 168.

so just change it up. 

the two numbers can be 166+170


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
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