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Juli2301 [7.4K]
3 years ago
12

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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The answer is an average rate of change of 110 more dollars in her account per week. You find this by first subtracting the starting amount of 250 from the end amount of 800 that equals 550. then you divide that number by five, the number of weeks, to get the average rate of change.
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What’s an equation that passes through the ordered pair (3,7)and has a slope of -4
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For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

y = mx + b

Where:

m: It is the slope of the line

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According to the statement data we have:

m = -4\\(x, y) :( 3,7)

Then, the equation is of the form:

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We substitute the given point and find "b":

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Finally, the equation is of the form:

y = -4x + 19

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Step-by-step explanation:

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Read 2 more answers
Charlie does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at lea
german

Answer:

(x_1,y_1) = (0,9)

(x_2,y_2) = (6,3)

(x_3,y_3) = (6,12)

Step-by-step explanation:

Given

x = hours spent on cardiovascular work

y = hours spent on weight training

From the first statement,

Each week: he spends at least 9 hours

This is represented as:

Total \ge 9

x + y \ge 9

From the second statement,

Each week: he spends a max of 12 hours on weights

This is represented as:

Weight \le 12

y \le 12

From the third statement,

Each week: he spends a max of 6 hours on cardio works

This is represented as:

Cardio \le 6

x \le 6

So, the inequalities are:

x + y \ge 9

y \le 12

x \le 6

See attachment for the graph where the solution are also highlighted

From the attachment, the solutions are:

(x_1,y_1) = (0,9)

(x_2,y_2) = (6,3)

(x_3,y_3) = (6,12)

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