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Papessa [141]
2 years ago
7

Can anyone help me with my homework

Mathematics
1 answer:
aleksley [76]2 years ago
7 0

Answer:

x = the number

Step-by-step explanation:

15.) 2x + 9 = 25

16.) 3x - 6 = 21

17.) 7x = 12 + 3x

18.) 4x = 18 + x

19.) 2x + 24 = 8x

20.) 30 - x = 4x

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Express the function graphed on the axes below as a piecewise function.
adoni [48]

Answer:

  f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

__

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

  f(x) = x-3 for x ≤ -1

__

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

  y -(-1) = -3(x -5)

  y = -3x +15 -1 = -3x +14

The second piece can be written ...

  f(x) = -3x +14 for x > 5

__

<h3>Whole function</h3>

Putting these pieces together, we have ...

  \boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}

_____

<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

3 0
2 years ago
The distance d in miles that can be covered by a rabbit in X hours is given in the equation y = 30 x The distance covered by a b
AveGali [126]

Answer:

Rabbit is faster than bear.

Step-by-step explanation:

Speed of rabbit or bear is determined by their rate of change of their distances with time.

The distance covered by rabbit in x hours is given as:

y=30x

The above equation is of the form y=mx, where, m is the rate of change of y with x.

Therefore, the rate of change of rabbit's distance with time is 30 mi/h.

Now, from the graph, the slope is given as the rise over run.

Rise is 50 miles and run is 2 miles.

So, rate of change of bear's distance with time is, m_b=\frac{50}{2}=25\ mi/h

Now, 30 is greater than 25. So, rabbit is faster than bear.

6 0
3 years ago
A submarine started at 750 meters below sea level. It rose 50 meters per hour over a 4-hour period. Which expression represents
Cerrena [4.2K]

Answer:

y(t) = 750 -50t

Step-by-step explanation:

We want to model the position of the submarine as a function of time.

Notice that we have a constant amount. The initial depth: 750 meters

 Then we have a factor that varies over time. Every hour the submarine ascends 50 meters. therefore as t increases the depth y(t) of the submarine decreases. Then the factor is:

-50t.

Where t represents the time in hours.

Then the equation that represents the new position of the submarine in relation to the level of the sea:

y(t) = 750 -50t

4 0
3 years ago
Read 2 more answers
What is 23.5% as a Fraction? Will make brainliest btw :&gt;
Anastasy [175]

Answer:

23 1/2 or 47/2

Step-by-step explanation:

it just is

7 0
3 years ago
Read 2 more answers
_2. You have a part-time job 4 days per week, 5 hours per day. How many hours will you work in two weeks?
marta [7]

Answer:

C) 40

Step-by-step explanation:

For every one day your work is 5 hours.

1 day = 5 hours

Set up a proportion so it would be:

\frac{1 day}{5 hours} = \frac{4 days}{x hours}

4 days x 5 hours = 20 hours/week

So now you know you know you work 20 hours/week, then multiply by 2 since they're asking how many hours will you work in two weeks:

20 hours x 2 weeks = 40 hours in two weeks

6 0
2 years ago
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