Multiplication always sometimes or never true

What is the value of the underlined digit? 35,028 (3 is underlined)

LenKa [72]

Step-by-step explanation:

30,000

Hope this helps. Good luck!!

6 0

2 years ago

Use the diagram to find the measure of the given angle.

Lyrx [107]

Answer:

50

Step-by-step explanation:

4 0

3 years ago

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

3 years ago

Read 2 more answers

What is the median of 1.6 , 2.3 , 1.4 , 2.5 , 1.7

lisov135 [29]

First, reorder the numbers from least to greatest

1.4, 1.6, 1.7, 2.5, 2.5

The median is the middle number

1.7 is your answer

hope this helps

6 0

3 years ago

Please help me with these two questions

melisa1 [442]

Hi! It will be a pleasure to help you finding the solution to this problem, so let's solve each part:

<h2>PART 1.</h2><h3>Finding the correct expression.</h3><h3>Correct answer:</h3>

$\boxed{A. \ 1.50h+4}$

From the problem, we know the following data of the problem:

Laval parked at the beach.
Laval paid a fixed price of $4 for a pass.
Laval paid $1.50 for each hour.

Our goal is to find the the expression for the total cost for parking at the beach for h hours. So:

Step 1: Since we have a fixed price, this value will appear in our expression:

$4$

Step 2: Since Laval paid $1.50 for each hour, this can be represented as the following expression:

$1.50h$

Finally, we can write total cost (C) as the sum of these two expressions:

$C=1.50h+4$

Finally, our correct option is A:

$\boxed{1.50h+4}$

<h2>PART 2.</h2><h3>Finding h.</h3><h3>Correct answer:</h3>

5 hours

Here we have to find how many hours Laval spent at the beach knowing that he paid a total amount of $11.50. From the previous part, we know that our expression is:

$C=1.50h+4 \\ \\ For \ C=11.50 \\ \\ 11.50=1.50h+4 \\ \\ Subtracting \ 4 \ from \ both \ sides: \\ \\ 11.50-4=1.50h+4-4 \\ \\ 7.5=1.50h \\ \\ Dividing \ both \ sides \ by \ 1.50 \\ \\ h=\frac{7.5}{1.50}=5$

Finally, he spent 5 hours at the beach

6 0

3 years ago