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DiKsa [7]
3 years ago
9

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
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