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3 years ago

-4x+2y=5 is this in a standard form

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

8 0

Right. Your answer is still no because your x-value needs to be positive.

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Which expression is equal to 13 more than the quotient of n and 8

Juli2301 [7.4K]

Answer:

(n/8)+13

Step-by-step explanation:

6 0

3 years ago

The length of a paper clip chain is directly proportional to the number of paper clips. If a chain with 65 paper clips has a len

Ghella [55]

<u>Answer:</u>

The length of a paper clip chain is directly proportional to the number of paper clips. If a chain with 65 paper clips has a length of 97.5 inches then the length of chain with 14 paper clips is 21 inches.

<u>Solution:</u>

Given that the length of a paper clip chain is directly proportional to the number of paper clips. Directly propotional means when the length of paper clip increases, then the number of paper clips also increases in same ratio.

Hence, by above definition, we get

$\frac{l_{1}}{l_{2}} = \frac{n_{1}}{n_{2}}$ ------- eqn 1

From question, for a chain with 65 paper clips has a length of 97.5 inches, we get

$l_{1} = 97.5 \text { and } n_{1} = 65$

Similarly, for a chain with 14 paper clips with length to be found, we get

$n_{2}=14 \text { and } l_{2} = ?$

Now by using eqn 1, we can calculate the length of 14 paper clips is,

$\frac{97.5}{65}=\frac{l_{2}}{14}$

Rearranging the terms we get,

$l_{2 }= \frac{97.5 \times 14}{65}$

$l_{2}=21 \text { inches }$

Hence the length of chain with 14 paper clips is 21 inches.

3 0

3 years ago

A bag contains the following marbles: 6 black marbles, 18 blue marbles, 16 brown marbles, and 12 green marbles. What is the rati

netineya [11]

Answer:

1 : 3

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

A serving of filet mignon is generally considered to be about 1/4

dybincka [34]

If 1 serving = 1/4 pound, then 4 servings = 1 pound. 6 pounds *4=24 servings. That leaves 1/3 of a pound. 1/4 pound is less than 1/3 pound, so you get one more serving.

That makes 25 servings, and 1/12 of a pound left over.

How do you know it is 1/12? Well, LCD (lowest common denominator) shows that 1/3-1/4= 4/12-3/12=1/12.

3 0

3 years ago