What is the range of the function below in set builder notation? y=|x-3|

Answers

Answer 1

Answer:

Answer: $\{y | \ y \in \mathbb{R}, \ y \ge 0\}$

This translates to "y is any real number such that it is 0 or larger".

The reasoning is that the result of any absolute value function is either 0 or positive. In other words, we'll never get a negative result of an absolute value function. This is due to how absolute value represents distance. Negative distance does not make sense.

So if y = |x-3| then y = 0 is the smallest output possible. We could have any positive output we want.

In terms of a graph (see below), the V shape is at the lowest point (3,0). The y coordinate is all we care about in terms of finding the range. So we see the lowest y value is y = 0.

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Alicia cashed her paycheck and used half her earnings to take three friends to dinner. She spent $42.15 on dinner and she brought home more than $20.00. Write an inequality to represent the situation, using x to represent the amount of Alicia's paycheck

Answers

If you would like to write an inequality to represent the situation, you can do this using the following steps:

x ... the amount of Alicia's paycheck

x/2 - $42.15 >= $20
x/2 >= $20 + $42.15
x/2 >= $62.15 /*2
x >= $62.15 * 2
x >= $124.3

The correct result would be x >= $124.3.

Solve the system:
2x-5y=7
3x-2y=-17

Answers

$\begin{cases}2x-5y=7 \ \ /*3 \n 3x-2y=-17\ \ / *(-2) \end{cases}\n \n\begin{cases}6x-15y=21 \n -6x+4y= 34 \end{cases}\n+ \ ------- \n-11y=55 \ \ / :(-11)\n \ny=-(55)/(11)$

$y=-5 \n \n 2x-5y=7\n \n2x-5*(-5)=7\n \n2x+25=7\n \n2x=7-25$

$2x=-18\ \ /:2 \n \n x=-(18)/(2) \n \nx=-9 \n \n\begin{cases} x=-9 \n y=-5 \end{cases}$

Given the functions f(x) = 7x + 13 and g(x) = x + 2, which of the following functions represents f[g(x)] correctly?f[g(x)] = 7x + 15
f[g(x)] = 7x + 27
f[g(x)] = 7x2 + 15
f[g(x)] = 7x2 + 27

Answers

f[g(x)] = f[x + 2] = 7(x + 2) + 13 = 7x + 7(2) + 13 = 7x + 14 + 13 = 7x + 27

f[g(x)] = 7x + 27

The correct answer is B.

Two cell phone companies have different rate plans. Runfast has monthly charges $25 plus $10 per gig of data. B A &D’s monthly charge is $18 plus 15 per gig of data. Your task is to determine under what circumstances each company has the better pricing. You will derive and solve a set of equations, graph those equations, and evaluate the meanings for these events. Don’t worry; I have a series of questions to guide you through the process. Good luck!Determine the equation for the monthly charges for Runfast and BA&D.

Runfast= $35 per month

BA&D= $33 per month

Answers

Given:
Runfast = 25 + 10g
BA&D = 18 + 15g

Runfast = 35 per month
35 = 25 + 10g
35 - 25 = 10g
10 = 10g
10/10 = g
1 = g

BA&D = 33 per month
33 = 18 + 15g
33 - 18 = 15g
15 = 15g
15/15 = g
1 = g

If g = 2;
Runfast = 25 + 10(2) = 25 + 20 = 45
BA&D = 18 + 15(2) = 18 + 30 = 48

Based on my computation, if the gig of data is only equivalent to 1g then BA&D is cheaper. However, if 2gig or above is used, then Runfast is cheaper.

A women set an Olympic record in the 100m freestyle with a time of 54.64 secs. What was her average speed in mis

Answers

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Find the slope between the two points: (9,9) and (12,15)

Answers

The slope formula is $(Y2-Y1)/(X2-X1)$ . For the two points, $(x,y)$ . You can pick any of the Y and X from these two points, but only once. $(9-15)/(9-12)$ = $(-6)/(-3)$ = 2 or $(15-9)/(12-9)$ = $(6)/(3)$ = 2 and both will equal to. The answer for the slope is 2.

Slope = Change in y / Change in x

Between (9, 9) and (12, 15).

We would use the coordinates from the second point minus that from the first point.

1st point = (9, 9), 2nd point = (12, 15)

Slope = (15 - 9) / (12 - 9)

= 6 / 3

= 2

Slope = 2

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The product of 16 and 4 less than a number is 208. Find the number.

A mad scientist develops a new memory pill and wishes to test it on a group of 11th grade students. He has a large number of sugar pills manufactured that look and taste exactly like the memory pills. He asks the manufacturer to prepare 50 envelopes, each containing a month's worth of doses of the memory pills, and 50 more envelopes with the same doses of sugar pills.The manufacturer then randomly labels the 100 envelopes with numbers from 00 to 99 and delivers them to the scientist. It has recorded which numbers go with the real pills, but it doesn't tell him. Which of the following adjectives describes this experiment? A. Double-blind B. Explanatory C. Hawthorne D. Blocked E. Multi-factor

To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm. Which inequality can be used to represent the lengths of the glass that will fit in the frame?.