Which expressions are equivalent to 3(6+b)-(2b + 1)?

Mathematics

1 answer:

Anna [14]2 years ago

7 0

Answer:

18+3b-2b-1

b+17

Step-by-step explanation:

$\mathrm{Using\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b$

$-\left(2b+1\right)=-2b-1$

$=3\left(6+b\right)-2b-1$

$=18+3b-2b-1$

$\mathrm{Group\:like\:terms}$

$=3b-2b+18-1$

$\mathrm{Subtract\:the\:numbers:}\:18-1=17$

$=3b-2b+17$

$\mathrm{Add\:similar\:terms:}\:3b-2b=b$

$=b+17$

[RevyBreeze]

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<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>