Solve the system of equations by the substitution method.

Mathematics

1 answer:

victus00 [196]3 years ago

3 0

Answer:

Step-by-step explanation:

Are you certain you wrote the question accurately?—because none of the choices is correct.

rearrange 3x+y =-5 to solve for y:

y = -3x-5

substitute -3x-5 for y into the second equation:

12x + 3y = 13

12x + 3(-3x-5) = 13

12x - 9x - 15 = 13

3x = 28

x = 28/3

y = -3x-5 = -33

solution: (28/3, -33)

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Which graph best represents the relationship between time and the number of teams registered?

alexdok [17]

<h2>Explanation:</h2><h2></h2>

The complete question is in the attached file. So we have to choose between two graphs. On of them is a linear model while the other is an exponential model. From the statements, we have a relationship between time and the number of teams registered. So we can establishes variables in the following form:

$x:\text{Time} \\ \\ y:\text{Number of teams registered}$

We also know that each week 6 teams register to participate, so:

$\bullet \ \text{For week 0:} \rightarrow \text{0 teams registered} \\ \\ \bullet \ \text{For week 1:} \rightarrow \text{6 teams registered} \\ \\ \bullet \ \text{For week 2:} \rightarrow \text{12 teams registered (Because 6+12)} \\ \\ \bullet \ \text{For week 3:} \rightarrow \text{18 teams registered (Because 12+6)}$

As you can see, as x increases one week, y increases at a constant ratio of 6. Therefore, this can be modeled by a linear function given by the form:

$y=6x$

In conclusion, <em>the linear model (first graph below) is the one that bests represents the relationship between time and the number of teams registered.</em>