For each question, calculate the slope of a line that passes through the points

Kylie has 14 polished stones. Her friend gives her 6 more stones. Write an expression to match the words

Elis [28]

An expression is like an equation, but without an equal sign.

Therefore, you could say...

14 stones + 6 stones

or just...

14 + 6

3 0

2 years ago

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Find all solutions of each equation on the interval 0 ≤ x < 2π.

Korvikt [17]

Answer:

$x = 0$ or $x = \pi$ .

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

$\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}$ .

$\displaystyle \sec{x} = \frac{1}{\cos{x}}$ .

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, $\sin^{2}{x} = 1 - \cos^{2}{x}$ . Therefore, for the square of tangents,

$\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}$ .

This equation will thus become:

$\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2$ .

To simplify the calculations, replace all $\cos^{2}{x}$ with another variable. For example, let $u = \cos^{2}{x}$ . Keep in mind that $0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1$ .

$\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2$ .

$\displaystyle \frac{(1 - u) + u - u \cdot (1- u)}{u^{2}} = 2$ .

Solve this equation for $u$ :

$\displaystyle \frac{u^{2} + 1}{u^{2}} = 2$ .

$u^{2} + 1 = 2 u^{2}$ .

$u^{2} = 1$ .

Given that $0 \le u \le 1$ , $u = 1$ is the only possible solution.

$\cos^{2}{x} = 1$ ,

$x = k \pi$ , where $k\in \mathbb{Z}$ (i.e., $k$ is an integer.)

Given that $0 \le x < 2\pi$ ,

$0 \le k$ .

$k = 0$ or $k = 1$ . Accordingly,

$x = 0$ or $x = \pi$ .

8 0

2 years ago

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X+8=17 what is the value of x makes the sentece true

melisa1 [442]

Answer:

x = 9

Step-by-step explanation:

Step 1: Write equation

x + 8 = 17

Step 2: Solve for <em>x</em>

Subtract 8 on both sides: x = 9

Step 3: Check

<em>Plug in x to verify it's a solution.</em>

9 + 8 = 17

17 = 17

7 0

3 years ago

What is the equation of the horizontal line that passes through the point (-2, -1)

diamong [38]

Answer:

y= -1

Step-by-step explanation:

A horizontal line would mean that it has no slope, since the line is not decreasing or increasing. The horizontal line drawn through (0, -1) would pass through (-2, -1), since they share the same y coordinate.

5 0

3 years ago

The open house sells an average of 1,700 tickets per night when the price of each ticket is $25 an employee of the opera house n

kompoz [17]

the correct anwser is 42

4 0

3 years ago