All categories

3 years ago

The function c=180n+250 represents the total lodging cost c (in dollars) for a stay at a vacation destination of n nights.

Mathematics

1 answer:

Svetlanka [38]3 years ago

8 0

Given:

The function for the total lodging cost c (in dollars) for a stay at a vacation destination of n nights is

$c=180n+250$

Budget = $900

To find:

The number of nights you can stay at you vacation destination.

Solution:

Since, budget is $900, therefore, the cost must be less than or equal to $900.

$c\leq 900$

$180n+250\leq 900$

$180n\leq 900-250$

$180n\leq 650$

Divide both sides by 180.

$n\leq \dfrac{650}{180}$

$n\leq 3.611$

Number of nights must be a whole number. So, greatest whole value of n is 3.

Therefore, you can stay 3 nights, i.e., n=3.

You might be interested in

Please help...it says to use distributive property...but I dont get it....please help.

Ann [662]

In this situation, using distributive property means multiplying the number outside of the parentheses, in this case 8, by each of the numbers inside the parentheses. Once you have those two numbers, add them together. Does that make sense?

3 0

4 years ago

Read 2 more answers

Determine the vertical asymptotes and holes for the graph of the equation below.

Lapatulllka [165]

Since x ² + 8x + 7 = (x + 7) (x + 1), we have for x ≠ -7,

y = (x + 7) / (x ² + 8x + 7) = 1/(x + 1)

so y is undefined at x = -1, indicating a vertical asymptote, and there is a hole/removable discontinuity at x = -7. Then the answer is D.

5 0

3 years ago

Which is the graph of y= 2(x-3)^2 +2

WINSTONCH [101]

The graph of y = 2(x - 3)² + 2 can be seen in the attached picture. This problem can be solved through the concept of parabola and transformation.

<h3>Further explanation</h3>

The Problem:

Which is the graph of y = 2(x - 3)² + 2?

Question-1:

How to make a graph y = 2 (x - 3) ² + 2 through the concept of a parabola.

The Process:

The equation of a parabola is given by $\boxed{ \ y = a(x - h)^2 + k \ }$ .

Keep in mind the following points:

vertex point at (h, k)
axis of symmetry at x = h
a > 0 the parabola opens upward
a < 0 the parabola opens downward
the y-intercept is $\boxed{ \ y = ah^2 + k \ }$ at x = 0.

From our case it can be concluded as follows:

the graph of y = 2(x - 3)² + 2 opens upward
vertex point at (3, 2)
axis of symmetry at x = 3
the y-intercept is 2(3²) + 2 = 20 or in coordinates of (0, 20)

Question-2:

How to make the graph of y = 2(x - 3)² + 2 through the transformation.

The Process:

To plot the graph of y = 2(x - 3) ² + 2 we apply for the following transformation order:

Step-1: clearly, to obtain the graph of y = (x - 3)² we shift the graph of y = x² to the right 3 units.

Step-2: to obtain the graph of y = 2(x - 3)², we stretch the graph of y = (x - 3)² by a factor of 2 (in other words, multiply each y-coordinate by 2).

Step-3: finally, to obtain the graph of y = 2(x - 3)² + 2 we shift the graph of y = 2(x - 3)² upward 3 units.

Thus the construction of the graph y = 2 (x - 3) ² + 2 is completed.

The graph of y = 2(x - 3) ² + 2 is drawn by the combination of shifting the graph of y = x² to the right 3 units and upward 2 units, and also stretch by a factor of 2. Between vertical shift and stretch steps, it is the same whatever steps are taken first.

- - - - - - - - - -

Notes

The transformation of graphs is changing the shape and location of a graph.
There are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching/shrinking).
In this case, the transformation is shifting horizontally and vertically and also stretching vertically.

In general, given the graph of y = f(x) and v > 0, we obtain the graph of:

$\boxed{ \ y = f(x) + v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ upward v units.
$\boxed{ \ y = f(x) - v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ downward v units.

That's the vertical shift, now the horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:

$\boxed{ \ y = f(x + h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the left h units.
$\boxed{ \ y = f(x - h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the right h units.

Hence, the combination of vertical and horizontal shifts is as follows:

$\boxed{ \ y = f(x \pm h) \pm v \ }$

The plus or minus sign follows the direction of the shift, i.e., up-down or left-right .

Notice the following definitions for stretch and shrink.

In general, given the graph of $\boxed{y = f(x)}$ , we obtain the graph of $\boxed{y = cf(x)}$ by stretching $\boxed{ \ c > 1 \ }$ or shrinking $\boxed{ \ 0 < c < 1 \ }$ the graph of $\boxed{y = f(x)}$ vertically by a factor of c.
In general, given the graph of $\boxed{y = f(x)}$ , we obtain the graph of $\boxed{y = f(cx)}$ by stretching $\boxed{ \ 0 < c < 1 \ }$ or shrinking $\boxed{ \ c > 1 \ }$ the graph of $\boxed{y = f(x)}$ horizontally by a factor of c.

<h3>Learn more </h3>

What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? brainly.com/question/1332667
Transformations that change the graph of (f)x to the graph of g(x) brainly.com/question/2415963
Which statement correctly describes the graph brainly.com/question/10929552

8 0

3 years ago

Read 2 more answers

Which value is included in the solution set for the inequality graphed on the number line

marissa [1.9K]

Answer:

-5

Step-by-step explanation:

On the number line, the arrow is from -2 (opens) to the left; that means solutions will be any values less than -2

-5 < -2 : YES ( solutions will be any values less than -2)

-2 = -2 : NO (solutions will be any values less than -2)

0 > -2 : NO (solutions will be any values less than -2)

3 > -2 : NO (solutions will be any values less than -2)

Answer

- 5

3 0

3 years ago

Read 2 more answers

A box contains four blue and eight red balls. Jim and Jack start drawing balls from the box, respectively, one at a time, at ran

aleksandrvk [35]

Answer:

the probability that Jack draws the blue ball is 0.38539

Step-by-step explanation:

Given the data in the question;

box contains

blue balls = 5

red balls = 8

Jim and Jack start drawing balls from the box, respectively, one at a time, at random, and without replacement

Now,

on the first attempted;

⇒ ( 8/13) × ( 5/12) = 10/39

on the second attempt;

⇒ ( 8/13 ) ( 7/12) ( 6/11 ) ( 5/10 ) = 14/143

on the third attempt;

⇒ ( 8/13 ) ( 7/12) ( 6/11 ) ( 5/10 ) ( 4/9 ) ( 5/8 ) = 35/1287

on the fourth attempt;

⇒ ( 8/13 ) ( 7/12) ( 6/11 ) ( 5/10 ) ( 4/9 ) ( 3/8 ) ( 2/7 ) ( 5/6 ) = 5/1287

so we add everything;

⇒ 10/39 + 14/143 + 35/1287 + 5/1287

= 0.38539

Therefore, the probability that Jack draws the blue ball is 0.38539

5 0

3 years ago