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3 years ago

Tracy has a cell phone plan that provides 250 free minutes each month for a

Mathematics

1 answer:

Rufina [12.5K]3 years ago

4 0

Answer:

$f(x)=\left \{ {{29\,\,for \,\,x\,\leq 250 } \atop {29+0.35(x-250)\,\,for \,x>250}} \right.$

Step-by-step explanation:

If we call "x" the number of call minutes used with this plan, the piecewise function used to describe it must represent;

a) a constant value of 29 for any x value smaller than or equal to 250

b) a line with positive slope of 0.35 for the region with x larger than 250. The mathematical representation of such increasing straight line, should be given by a line of slope m = 0.35, and containing the point (250, 29) which is the starting point for this right hand side portion of the domain:

$f(x)=0.35(x-250)+29\\f(x)=0.35 x-87.5+29\\f(x)=0.35 x-58.5$

So the function should look like:

$f(x)=\left \{ {{29\,\,for \,\,x\,\leq 250 } \atop {29+0.35(x-250)\,\,for \,x>250}} \right.$

or as shown above, in a more simplified form:

$f(x)=\left \{ {{29\,\,for \,\,x\,\leq 250 } \atop {0.35x-58.5\,\,\,for \,\,x>250}} \right.$

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3 years ago

Simplify 81p6q2÷3p2q5 HELPPP

goldfiish [28.3K]

Answer:

$\displaystyle \frac{81\, p^{6}\, q^{2}}{3\, p^{2} \, q^{5}} = \frac{27\, p^{4}}{q^{3}}$ .

Step-by-step explanation:

Make use of the fact that for any $x \ne 0$ and integer $n$ :

$\displaystyle \frac{1}{x^{n}} = x^{-n}$ .

For example, in this question:

$\displaystyle \frac{1}{p^{2}} = p^{-2}$ .

$\displaystyle \frac{1}{q^{5}} = q^{-5}$ .

Thus, the original expression would be equivalent to:

$\begin{aligned}& \frac{81\, p^{6}\, q^{2}}{3\, p^{2} \, q^{5}} \\ =\; & \frac{81}{3}\, (p^{6}\, p^{-2})\, (q^{2}\, q^{-5}) \\ =\; & 27\, (p^{6}\, p^{-2})\, (q^{2}\, q^{-5})\end{aligned}$ .

Also make use of the fact that for any $x \ne 0$ , integer $m$ , and integer $n$ :

$x^{m}\, x^{n} = x^{m + n}$ .

Thus:

$\begin{aligned}& 27\, (p^{6}\, p^{-2})\, (q^{2}\, q^{-5}) \\=\; & 27\, p^{6 + (-2)}\, q^{2 + (-5)} \\ =\; & 27\, p^{4}\, q^{-3} \\ =\; & \frac{27\, p^{4}}{q^{3}}\end{aligned}$ .

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2 years ago

Find two ratios equivalent to the ratio in exercise 1 8:5 4:19 6:23

Ne4ueva [31]

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Check:
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8/5=24/15
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6:23 12:46 18:69

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3 years ago