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3 years ago

the area of a rectangle with the width x-5 and the length x-12 is 44 square feet. what are the dimensions

Mathematics

1 answer:

Black_prince [1.1K]3 years ago

7 0

Answer: 23

Step-by-step explanation:

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Kofi electronic bought a shipment of Tv's at a net price of $477.36 each,after a discount of 15%,10% and 4%. What is the list pr

mart [117]

Answer

15% discount= $561.60

10% discount= $530.40

4% discount = $490.25

step by step

_15% discount_

85% sale percent =$477.36

The list price is 100%

If more less divide

(100/85) * $477.36

=$561.60

_10% discount_

90% sale percent =$477.36

The list price is 100%

If more less divide

(100/90) * $477.36

=$530.40

_4% discount_

96% sale percent =$477.36

The list price is 100%

If more less divide

(100/96) * $477.36

=$497.25

3 0

3 years ago

I'm sorry but these are the multiple choice answers.

Sunny_sXe [5.5K]

$\bf \qquad \qquad \textit{Future Value of an ordinary annuity}
\\\\
A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]$

$\bf \qquad 
\begin{cases}
A=
\begin{array}{llll}
\textit{original amount}\\
\textit{already compounded}
\end{array}&
\begin{array}{llll}

\end{array}\\
pymnt=\textit{periodic payments}\to &200\\
r=rate\to 7\%\to \frac{7}{100}\to &0.07\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, four quarters}
\end{array}\to &4\\

t=years\to &12
\end{cases}
\\\\\\
A=200\left[ \cfrac{\left( 1+\frac{0.07}{4} \right)^{4\cdot 12}-1}{\frac{0.07}{4}} \right]$

7 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>

<u>The Problem:</u>

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

<u>Question-1:</u>

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

<u>The Process:</u>

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)

<u>Question-2:</u>

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

<u>The Process:</u>

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

Use quadratic formula to find the solutions to 3x^2 - 10x + 5 =0

Roman55 [17]

Answer:

My bad i meant to click on my notification thing.

Step-by-step explanation:

5 0

3 years ago

How do you determine what bn should be in a limit comparison test and a comparison test? When do you know that the series should

Andreyy89

Step-by-step explanation:

Pick a function that is the same "family". It needs to be a function that you know diverges or converges. So p-series and geometric series are common choices. Often we make the numerators the same so that it's easy to compare.

For example, if you have an = 1 / (n − 1), you would choose bn = 1 / n. Since n − 1 is less than n, we know an is greater than bn. And since we know bn diverges, that means the larger function an also diverges.

Or, if you have an = 1 / (n + 1), we again choose bn = 1 / n. However, comparison test is inconclusive here (an < bn, bn diverges), so we use limit comparison test instead.

lim(n→∞) an / bn

lim(n→∞) 1 / (n + 1) / (1 / n)

lim(n→∞) n / (n + 1)

The limit is greater than 0, and bn diverges, so an also diverges.

Let's try something more complicated. Let's say an = e⁻ⁿ / (n + cos²n). The numerator e⁻ⁿ is always less than 1, and the denominator is always greater than n.

If we again choose p-series bn = 1 / n, we know bn > an, and bn diverges, so comparison test is inconclusive. Limit comparison test is possible, but tricky.

But, if we choose geometric series bn = e⁻ⁿ / 1, we know bn > an, and bn converges, so by comparison test, an converges as well.

We can try one more: an = (n² + 2) / (n⁴ + 5). Let's choose bn = (n² + 2) / n⁴ = 1 / n² + 2 / n⁴.

The numerators are the same, but an has a larger denominator, so bn > an. bn is the sum of two p-series which converge, so bn converges. Therefore, an converges.

8 0

4 years ago