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2 years ago

5

2. On Monday, I bought 3 dogs and 5 cats for a total cost of $8.25. On Tuesday, I bought 3 dogs and 6 cats for a total cost of $

9. Can you find the price of each item?

1 answer:

Ratling [72]2 years ago

7 0

I don’t know if you need to round, but you can do so on the answer for mondays if necessary

On Monday, the animals cost $1.03125.
On Tuesday, the animals cost exactly $1.

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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

Read 2 more answers

The Greatest Problems on Campus

PSYCHO15rus [73]

Answer: D.) This is an example of inductive reasoning because a general conclusion is reached based on a specific example,

Step-by-step explanation: Inductive reasoning simply refers to making conclusion about a specific subject or topic from patterns or insights derived from related examples. In the scenario above, the conclusion reached encompasses the overall full time 4 years college student. However, this conclusion was inferred based on a specific example comprising of only a randomized sample of 1200 full time 4 years college students in 100 campuses. random. The example failed to incorporate every student, Hence, the conclusion is induced as the choice of a sample of students may not convey the choice or decision of all.

Deductive reasoning meanwhile follows that a generally established fact is used to make conclusion about a specific example.

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3 years ago

What is 3,200,000,000,000 in scientific notation

sashaice [31]

$3 200 000 000 000= 3.2 \cdot 10^{12}$

5 0

3 years ago

What I need to prove is that a+b+c = 180

Sauron [17]

Answer:

Angles in a triangle add up to 180.

7 0

3 years ago

Help me please I really need it

Dmitrij [34]

y = - 2x + 7; slope m = -2

Parallel lines, slope is the same

So y = -2x + b

b = y + 2x

Passing thru (4 , 1)

Plug in

b = 1 + 2(4)

b = 9

Equation

y = - 2x + 9

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3 years ago