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3 years ago

What are the two questions you ask yourself before starting a synthetic division problem

Mathematics

1 answer:

ale4655 [162]3 years ago

7 0

1). Am I seated comfortably, with plenty of light on my paper ?

2). Is my pencil sharp ?

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*simplify 5|-3+(-7)|=

Lena [83]

Answer:

-2l -3

Step-by-step explanation:

5l -3+ (-7)l

5l -3 -7l

5l -7l -3

-2l -3

6 0

3 years ago

How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)

Oxana [17]

Answer:

Make use of the fact that as long as $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ :

$\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ .

$\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}$ .

$\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ .

Step-by-step explanation:

Assume that $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ .

Make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ and $\csc(\theta) = (1) / (\sin(\theta))$ to rewrite the given expression as a combination of $\sin(\theta)$ and $\cos(\theta)$ .

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}$ .

Since $\cos(\theta) \ne 0$ :

$\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

By the Pythagorean identity, $\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ . Rearrange this identity to obtain:

$\sin^{2}(\theta) = 1 - \cos^{2}(\theta)$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

Again, make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ to obtain the desired result:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}$ .

5 0

2 years ago

Express 0.1 as a percent.

Zigmanuir [339]

Answer: 10%

Explanation: 0.10=10%

6 0

3 years ago

Read 2 more answers

PLEASE HELPPPPPPPPPPP

damaskus [11]

Answer:

A. x < -4 or x >= 3

Step-by-step explanation:

A solid dot at 3, and shading to the right, means all numbers greater than or equal to 3.

An open dot at -4 and shading to the left means all numbers less than -4.

A number cannot be both 3 or greater AND less than 4, so you must use the word "or" between the the two parts of the answer.

Answer: A. x < -4 or x >= 3

3 0

3 years ago

Ashton says that the zeros of the equation y=6x^2−5x−25 are at x=52 and x=−53. Which statement correctly describes Ashton's clai

babymother [125]

Answer:

Ashton is correct. The quadratic expression has the factors (2x−5) and (3x+5), so the zeros are at x=5/2 and x=−5/3.

Step-by-step explanation:

The answer itself has the step-by-step explanation.

Step-by-step explanation:

7 0

3 years ago