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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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Vikentia [17]

Divided 300 by 30. Which is 10

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3 years ago

Read 2 more answers

Find the difference in simplest form for 3/5-1/7

morpeh [17]

Answer: 0.457

multiply 3 by 7, and get 21

multiply 1 by 5, and get 5.

5 × 7 = 35.

fraction: 21/35 and 5/35

Subtract the numerators

21 − 5 = 16 = 16/35

Now we need to simplify the fraction that we have.

17 is larger than 16. So we're done reducing numbers.

Our final answer: $16/35$

Hope this helps!

I am joyous to assist anytime.

~Jarvis

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3 years ago

How do i find the slope

Elodia [21]

Hi, I'm happy to help!

To find the slope, you need to use the slope formula, where m is the slope:

m= $\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }$

Slope means rise over run, or how much the line rises per the amount the line moves forward. This equation shows the movement from the y points to show rise, over the difference in the x points to show run.

Now, to find the slope we insert our values, starting with our second y point:

m= $\frac{2-y_{1 } }{x_{2} -x_{1} }$

Now insert our first y point:

m= $\frac{2-4 }{x_{2} -x_{1} }$

Now we insert our second x point:

m= $\frac{2-4 }{-3 -x_{1} }$

And finally our first x point:

m= $\frac{2-4 }{-3 -3 }$

Now, we solve:

m= $\frac{-2 }{-6}$

So, our slope is -2/-6, to simplify it, we remove both negatives because they cancel each other out.

m= $\frac{2 }{6}$

Now, we simplify our fraction by dividing the top and bottom by 2:

m= $\frac{1}{3}$

So, our slope is 1/3. This means that for every 1 unit the line rises, it goes to the right 3 units. The y-intercept is where the line hits the y axis.

If the question is asking for slope intercept form for the equation, you use y=mx+b

y represents any y coordinate on your line, m represents your slope (1/3), x represents any x coordinate on your line, and b represents your y-intercept (3).

If you were to insert these values, you would get:

y= $\frac{1}{3}$ x+3

You use this to find what a y coordinate would be so you can draw your line.

For the next equation we do the same thing:

m= $\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }$

Insert our values:

m= $\frac{4-1}{2-(-4)}$