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max2010maxim [7]

3 years ago

10

Write the equation of the line that passes. Throught the point (-2,1)and (0,8)put your aswer in fully reduce point slope form un

less it is a vertical or horizontal line

1 answer:

Soloha48 [4]3 years ago

6 0

Answer:

Step-by-step explanation:

first, we need to find the slope

slope = (y2 - y1) / (x2 - x1)

(-2,1)...x1 = -2 and y1 = 1

(0,8)...x2 = 0 and y2 = 8

now sub

slope = (8 - 1) / (0- (-2) = 7/(0 + 2) = 7/2

point slope form : y - y1 = m(x - x1)

using point (-2,1)....x1 = -2 and y1 = 1

slope(m) = 7/2

now sub

y - 1 = 7/2(x - (-2) =

y - 1 = 7/2(x + 2) <==== here is one answer

y - y1 = m(x - x1)

using point (0,8)...x1 = 0 and y1 = 8

slope(m) = 7/2

now sub

y - 8 = 7/2(x - 0) <===== another possible answer

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Solve the system of equations. 5x y = 9 3x 2y = 4 (−2, 5) (1, 4) (2, −1) (4, −4)

kobusy [5.1K]

The solution of the system of equations that is given is (2,-1).

Given a system of equations are 5x+y=9 and 3x+2y=4.

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied.

The given equations are

5x+y=9 ......(1)

3x+2y=4 ......(2)

Here, the substitution method is used to solve the system of equations.

Find the value of y from equation (1) by subtracting 5x from both sides.

5x+y-5x=9-5x

y=9-5x

To find the value of x substitute the value of y in equation (2).

3x+2(9-5x)=4

Apply the distributive property a(b+c)=ab+ac as

3x+2×9-2×5x=4

3x+18-10x=4

Combine the like terms on the left side as

-7x+18=4

Subtract 18 from both sides and get

-7x+18-18=4-18

-7x=-14

Divide both sides by -7 and get

(-7x)÷(-7)=(-14)÷(-7)

x=2

Substitute the value of x in equation (1) and get

5(2)+y=9

10+y=9

Subtract 10 from both sides

10+y-10=9-10

y=-1

Hence, the solution of system of equations 5x+y=9 and 3x+2y=4 is (2,-1).

Learn more about system of equations from here brainly.com/question/13729904

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6 0

2 years ago

If a function is odd, then which statement is true?

jolli1 [7]

By definition, a function is odd if f(-x) = -f(x) for all x in the domain. The answer is choice C

Side note: a function is even if f(-x) = f(x) for all x in the domain

4 0

2 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

What is the value of the expression below? 3/8+(-4/5)+(-3/8)+5/4

Crazy boy [7]

It will help you!

=-17/40+-3/8+5/4

= -4/5+5/4

= 9/20

And the answer is 9/20 or decimals (0.45)

4 0

3 years ago

Read 2 more answers

One of the legs of a right triangle measures 7 cm and its hypotenuse measures 12 cm.

Oksana_A [137]

Answer:

AC ≈ 9,7sm

Step-by-step explanation:

AB=7 One side of a right triangle

BC=12 Hypotenuse of a right triangle

AC=?=x The other side of a right triangle

x²+7²=12²

x²=144-49

x²=95

x=√(95) ≈ 9,7

AC ≈ 9,7sm

3 0

2 years ago