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3 years ago

Will the ordered pairs listed in the table form a straight line when plotted? Explain your reasoning.

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

4 0

Answer:

Yes.

Step-by-step explanation:

If the slope between successive points have the same slope then they will form a straight line.

Slope = ( 3.5- -1) / (-2 - -8) = 4.5/6 = 3/4

Slope = (12.5 - 3.5) / (10 - -2) = 9 / 12 = 3/4

Slope = (20-12.5)/(20-10) - 7.5/10 = 3/4 .

So the answer is yes.

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Is 1500 ml greater than less than or equal to 1.5 l?

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Is 1500 ml greater than less than or equal to 1.5 l is equal.

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3 years ago

Find the slope of the line.

Anika [276]

The equation for working out the slope of a linear line is: $\frac{y_2 - y_1}{x_2 - x_1}$ , where x and y are the coordinate pairs.

So just pick two of the purple dots on the graph and fill in the equation.

I'll pick the dot that's (-4, 1) and (4, -7).

Now I just do $\frac{7 - 1}{4 - -4}$ , which is just $\frac{3}{4}$ when simplified.

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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 graph of a quadratic function has a vertex at (5,3) and goes through the point (-1,-9). What is the equation of the function

kotegsom [21]

Answer:

$y=-\frac{1}{3} (x-5)^2+3$

Step-by-step explanation:

We are given the following;

Vertex of a quadratic function = (5,3)
A point where the function passes through (-1, -9)

Required to determine the equation of the function;

We need to know the vertex form of a quadratic function is;

$y=a(x-h)^2+k$ , where h and k correspond to the vertex (h,k)

Therefore, we can replace the variables h and k of the vertex in the equation;

That is;

$y=a(x-5)^2+3$

Then we use the equation and the point given to solve for a

x = -1 and y = -9

We get;

$-9=a(-1-5)^2+3\\-9 = a(36) + 3\\-9 - 3 = 36a\\-12 =36a \\a=-\frac{1}{3}$

Substituting the values of a, h and k in the equation, we get;

$y=-\frac{1}{3} (x-5)^2+3$

Thus, the equation of the function in the vertex form is $y=-\frac{1}{3} (x-5)^2+3$

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3 years ago

(2x + 3) and (2x - 3) are special factors because the only thing that distinguishes between the

diamong [38]

Answer: Conjugates

Step-by-step explanation:

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3 years ago