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3 years ago

Which figure correctly demonstrates using a straight line to determine that the graphed equation is not a function of x?

Mathematics

2 answers:

Ulleksa [173]3 years ago

3 0

Answer:

Lower left.

Step-by-step explanation:

To determine if a graph is a function the "vertical line test is used. If any point on a graph has one x value go to two y values it is not a function.

Witht he four pictures, the two on the right use a horizontal line, so it doesn't tell at all, on the leftthe upper one is vertical but it doesn't show that one x value has two corresponding y values. So it must be the lower left one.

The lower left picture has a line at x=1, and it passes through the line of the graph at two different y values, 4 and -4. So this has two y values with one x value.

Semmy [17]3 years ago

3 0

Answer:

option C

Step-by-step explanation:

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Use the laplace transform to solve the given system of differential equations. dx dt + 3x + dy dt = 1 dx dt − x + dy dt − y = et

blagie [28]

Let $X(s)$ and $Y(s)$ denote the Laplace transforms of $x(t)$ and $y(t)$ .

Taking the Laplace transform of both sides of both equations, we have

$\dfrac{dx}{dt} + 3x + \dfrac{dy}{dt} = 1 \implies \left(sX(s) - x(0)\right) + 3X(s) + \left(sY(s) - y(0)\right) = \dfrac1s \\\\ \implies (s+3) X(s) + s Y(s) = \dfrac1s$

$\dfrac{dx}{dt} - x + \dfrac{dy}{dt} = e^t \implies \left(sX(s) - x(0)\right) - X(s) + \left(sY(s) - y(0)\right) = \dfrac1{s-1} \\\\ \implies (s-1) X(s) + s Y(s) = \dfrac1{s-1}$

Eliminating $Y(s)$ , we get

$\left((s+3) X(s) + s Y(s)\right) - \left((s-1) X(s) + s Y(s)\right) = \dfrac1s - \dfrac1{s-1} \\\\ \implies X(s) = \dfrac14 \left(\dfrac1s - \dfrac1{s-1}\right)$

Take the inverse transform of both sides to solve for $x(t)$ .

$\boxed{x(t) = \dfrac14 (1 - e^t)}$

Solve for $Y(s)$ .

$(s - 1) X(s) + s Y(s) = \dfrac1{s-1} \implies -\dfrac1{4s} + s Y(s) = \dfrac1{s-1} \\\\ \implies s Y(s) = \dfrac1{s-1} + \dfrac1{4s} \\\\ \implies Y(s) = \dfrac1{s(s-1)} + \dfrac1{4s^2} \\\\ \implies Y(s) = \dfrac1{s-1} - \dfrac1s + \dfrac1{4s^2}$

Taking the inverse transform of both sides, we get

$\boxed{y(t) = e^t - 1 + \dfrac14 t}$

7 0

1 year ago

Which equation shows the substitution method being used to solve the system of linear equations?

svet-max [94.6K]

The equation
(y + 5) + y = 6
shows the substitution method being used to solve the system of linear equations. So the correct option among all the options given in the question is option "D".
For a better explanation, let us first write down the two equations given in the question.
x + 5 = 6
and
x = y + 5
Now the thing that has been done is that the value of x in the first equation has been replaced by the value of x that is given in the second equation. this is actually the substitution method of solving equations.

6 0

3 years ago

Read 2 more answers

You watch a football game. The team you cheer for loses 88 yards on four plays in a row. Which expression shows the total loss i

Flauer [41]

Answer:

C. -8 * 4

Step-by-step explanation:

We are given the situation that your team loses 8 yards on four plays in a row. And you are being asked which expression shows the total loss in yards, our key word in this question is "loss" . Meaning that the result has to come out negative.

Therefore , A. is incorrect because -4 * -8 is 36 . Which is positive.

B. is incorrect because it is positive outcome

And D. is incorrect because one it is not the correct property to use and also is very inaccurate in the answer. Also, it is a positive outcome.

Leaving you with C.

8 0

3 years ago

Jennie has 177 more songs downloaded on her mp3 player than Diamond. Together, they have 895 songs downloaded. How many do each

kogti [31]

Answer:jennie has 536 songs and diamond has 359

Step-by-step explanation:

3 0

3 years ago

Hector can fit 75 compact discs into 5 boxes. How many compact discs can he fit into 14 boxes?

Karolina [17]

Answer:

Hector can fit 210 compact discs into 14 boxes.

8 0

3 years ago