What is the value of x?

A mattress store is having a sale all mattresses are 30% of. Nate wants to know the sale price of a mattress that is regularly $

koban [17]

Answer: $700

Step-by-step explanation:

The store is selling at 30% off.

If a mattress is $1,000, first find out what 30% of $1,000 is:

= 1,000 * 30%

= $300

The store is selling 30% off, this means that they are reducing the price by 30%:

= 1,000 - 300

= $700

5 0

3 years ago

If the area of a rectangle with length (4x) is 4x2 + 12x, find the width.

8090 [49]

Answer:

The width of a rectangle is: w = x+3

Step-by-step explanation:

Given

The length of rectangle = l = 4x

The area of rectangle = A = 4x² + 12x

To determine

The width of rectangle = w = ?

We know that the formula of the area of the rectangle is

$A = wl$

substitute A = 4x² + 12x and l = 4x in the equation to determine the width w of the rectangle

4x² + 12x = w×4x

w = [4x² + 12x] / [4x]

Factor 4x² + 12x: 4x(x+3)

w = [ 4x(x+3) ] / [4x]

w = x+3

Therefore, the width of a rectangle is: w = x+3

3 0

3 years ago

Graph the function and analyze it for domain, range, continuity, increasing or decreaseing behavior, symmetry, boundedness, extr

Sunny_sXe [5.5K]

Answer:

$f(x) = 3 \cdot 0.2^x$

Step-by-step explanation:

$f(x) = 3 \cdot 0.2^x$

Domain of f: "What values of x can we plug into this equation?" This makes sense for all real numbers so the domain is $\mathbb{R}$

Range of f: "What values of f(x) can we get out of the function?" From the graph we see we can get any real number greater than 0 out of the function by choosing a suitable x-value in the domain. The range is therefore $(0, \infty)$ .

Continuity: Since the graph is one, unbroken curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We see that "roughly speaking" the function is continuous.

Increasing or decreasing behaviour: For all x in the domain, as x increases, f(x) decreases. This means the function exhibits decreasing behaviour.

Symmetry: It is clear to see the graph of f(x) has no symmetry.

Boundedness: Looking at the graph we see it is unbounded above as when we choose negative values, the graph of f(x) explodes upwards exponentially. Choose a value of x, plug it in, next choose (x-1), plug this in and we observe $f(x-1) > f(x)$ for all x in the domain.

The function is however bounded below by 0: no value of x in the domain exists which satisfies $f(x) < 0$ .

Extrema: As far as I can tell, there are no turning points on the curve. (Is this what you mean by extrema?)

Asymptotes: Contrary to the curve's appearance, there are no vertical asymtotes for this curve. The negative-x portion of the curve is just growing so quickly it appears to look like an asymptote. There is a value of f(x) for all x<0. There is however a horizontal asymtote: $y=0$ .

End behaviour: As $x \rightarrow \infty, f(x) \rightarrow 0$ . As $x \rightarrow -\infty, f(x) \rightarrow +\infty$

5 0

3 years ago

The circle passes through the point (4.5,0). What is its radius?

Andreyy89

Answer:

4.5 units

Step-by-step explanation:

In this case, if we draw the point on the xy cartesian plane, we know that the value of "x" is 4.5 and the value of "y" is 0.

Which means that when I draw this in any way, the maximum value it will take is 4.5 units, therefore the radius should not exceed this value, nor should it be less than 4.5 units since the circle would be distorted.

Which means that the radius is 4.5 units

4 0

3 years ago

Read 2 more answers

Circles are described below by the coordinates of their centers, C, and one point on their circumference, A. Determine an equati

Art [367]

Using the given center and point at the circumference, the equation of the circles are: