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3 years ago

What is the slope of the line that is represented by the values in the table above?

Mathematics

1 answer:

denpristay [2]3 years ago

5 0

Answer:

$slope (m) = 6$

Step-by-step explanation:

To get the slope of the line of the given table of values, all we need is just 2 coordinate pairs from the table. We can pick any two.

Let's use, (-1, 0), and (0, 6).

Apply the formula, $\frac{y_2 - y_1}{x_2 - x_1}$ , where,

$(-1, 0) = (x_1, y_1)$

$(0, 6) = (x_2, y_2)$

Thus:

$m = \frac{6 - 0}{0 - (-1)}$

$m = \frac{6}{1}$

$slope (m) = 6$

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Which figure has the same area as the parallelogram shown below? A. A triangle with a base of 4 mm and a height of 20 mm B. A tr

Arisa [49]

<h2>Answer: A trapezoid with bases of 6 mm and 14 mm and a height of 8 mm </h2>

The parallelogram in the figure has an area of $80mm^{2}$ , according to the following formula, which works for all rectangles and parallelograms:

$A_{parallelogram}=(b)(h)$ (1)

Where $b$ is the base and $h$ is the height

The<u> area of a triangle</u> is given by the following formula:

$A_{triangle}=\frac{1}{2}(b)(h)$ (2)

So, for option A:

$A_{triangle}=\frac{1}{2}(4mm)(20mm)=40mm^{2} \neq 80mm^{2}$

Now, the <u>area of a trapezoid </u>is:

$A_{trapezoid}=\frac{1}{2}(b_{1}+ b_{2})(h)$ (3)

For option B:

$A_{trapezoid}=\frac{1}{2}(15mm+25mm)(2 mm)=40mm^{2} \neq 80mm^{2}$

For option C:

$A_{trapezoid}=\frac{1}{2}(6mm+14mm)(8 mm)=80mm^{2}$ >>>>This is the correct option!

For option D:

$A_{rectangle}=(30mm)(8mm)=240mm^{2} \neq 80mm^{2}$

<h2>Therefore the correct option is C</h2>

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3 years ago

A top-loading washing machine has a cylindrical basket that rotates about a vertical axis. The basket of one such machine starts

damaskus [11]

Answer:

$n_{tot}=44rev$

Step-by-step explanation:

In order to solve this problem we can make use of the following formula:

$\theta=(\frac{\omega_{f}+\omega_{0}}{2})t$

where θ is the total angle the basket has turned, ω is the angular velocity and t is the time.

Generally theta is written in radians and omega is written in radians per second. Now, since the revolutions are directly related to the radians and they want us to write our answer in revolutions, we can directly use the provided speeds in the formula, so we can rewrite it as:

$n=(\frac{f_{f}+f_{0}}{2})t$