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3 years ago

Write an equation in point-slope form of the line that passes through the given point and with the given slope m.

1 answer:

8 0

$\text{the point:}\ (x_0,\ y_0)\\\\\text{the slope:}\ m\\\\\text{The equation of a line in point-slope form:}\\\\y-y_0=m(x-x_0)$

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) There are 8 children in Sophie's preschool class. During free time yesterday, 1 of them

Klio2033 [76]

Using it's concept, it is found that there is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.

<h3>What is a probability?</h3>

A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.

For an experimental probability, these numbers of outcomes are taken from previous trials.

In this problem, in the previous trial, one out of eight students read a book, hence:

p = 1/8 = 0.125 = 12.5%.

There is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.

More can be learned about probabilities at brainly.com/question/14398287

5 0

3 years ago

F(x) = (x - c)(x + c), find the y-intercepts of the inverse of f(x).

Allushta [10]

Answer:

what are the coordinates

Step-by-step explanation:

8 0

3 years ago

Solve these linear equations in the form y=yn+yp with yn=y(0)e^at.

WINSTONCH [101]

Answer:

a) $y(t) = y_{0}e^{4t} + 2$ . It does not have a steady state

b) $y(t) = y_{0}e^{-4t} + 2$ . It has a steady state.

Step-by-step explanation:

a) $y' -4y = -8$

The first step is finding $y_{n}(t)$ . So:

$y' - 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r - 4 = 0$

$r = 4$

So:

$y_{n}(t) = y_{0}e^{4t}$

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' -4(y_{p}) = -8$

$(C)' - 4C = -8$

C is a constant, so (C)' = 0.

$-4C = -8$

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{4t} + 2$

b) $y' +4y = 8$

The first step is finding $y_{n}(t)$ . So:

$y' + 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r + 4 =$

$r = -4$

So:

$y_{n}(t) = y_{0}e^{-4t}$

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' +4(y_{p}) = 8$

$(C)' + 4C = 8$

C is a constant, so (C)' = 0.

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{-4t} + 2$

6 0

3 years ago

The following figure is a rhombus. Find the value of m. Then, use that value to find the measure of VW

maxonik [38]

Answer:

$m=8$

The length of VW = 36 units.

Step-by-step explanation:

We know that a rhombus is a quadrilateral with four sides. All four sides have the same length.

From the diagram, it is clear that

The length of VW= 6m-12

The length of WX = 4m+4

As all the four sides of the rhombus have equal length.

So we can observe

$VW=WX$

$6m-12 = 4m+4$

Add 12 to both sides

$6m-12+12=4m+4+12$

$6m=4m+16$

$2m=16$

Divide both sides by 2

$\frac{2m}{2}=\frac{16}{2}$

$m=8$

The length of VW= 6m-12

= 6(8)-12 ∵ $m=8$

= 48-12

= 36

Thereofore, the length of VW = 36 units.

3 0

3 years ago

Help!! please answer as fast as you can

Ann [662]

Answer:

x=35

Step-by-step explanation:

Since these are straight lines, you simply reflect the 35 degrees over the other side because this is a vertical angle.

x=35

3 0

3 years ago

Read 2 more answers

Write an equation in​ point-slope form of the line that passes through the given point and with the given slope m.

Write an equation in point-slope form of the line that passes through the given point and with the given slope m.