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Alborosie
3 years ago
12

Prove tan(x - (π / 4)) = (sin x – cos x) / (cos x + sin x) by filling in the reasons in the table below.

Mathematics
1 answer:
Mrac [35]3 years ago
8 0

No way to know what reasons you're supposed to choose from...

By definition of tangent,

\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin\left(x-\frac\pi4\right)}{\cos\left(x-\frac\pi4\right)}

The angle sum identities give

\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x\cos\frac\pi4-\cos x\sin\frac\pi4}{\cos x\cos\frac\pi4+\sin x\sin\frac\pi4}

cos\dfrac\pi4=\sin\dfrac\pi4=\dfrac1{\sqrt2}, so we can cancel those terms to get

\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x-\cos x}{\sin x+\cos x}

as required.

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Which terms accurately classify this triangle? Choose exactly two answers that are correct. A. scalene B. obtuse C. acute D. iso
Agata [3.3K]
 the answer is D <span>isosceles triangle

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3 years ago
Calculate the percent change in estimated life expectancy for the African American female from 2001 to 2002, correct to nearest
weeeeeb [17]

Answer:

0.132%

Step-by-step explanation:

In 2001, the life expectancy for African American female is 75.5. In 2002, the life expectancy for African American female is 75.6.

Therefore, the change in the life expectancy for African American female from 2001 to 2002 is (75.6 - 75.5) = 0.1

Therefore, the percent change in estimated life expectancy for the African American female between the given period will be \frac{0.1}{75.5} \times 100\% = 0.132\% (Answer)

3 0
3 years ago
In a recent year, a letter to Europe from the United States cost $0.94 to mail. A letter mailed within the United States costs $
Ilya [14]

Answer:

She mailed 3 to Europe

Step-by-step explanation:

0.94 x 3=2.82

0.44 x 2=0.88

2.82 + 0.88=3.70

8 0
3 years ago
What is the estimated product of 1.39 x 6.76?
qwelly [4]

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7

Step-by-step explanation:

5 0
3 years ago
Each deli sandwhiches made uses 8/8 pound of roast beef.Marisa started with 5 pounds of roast beef and now has 2 3/4 pounds left
OleMash [197]

Answer:

Marisa has made 6 sandwiches.

Step-by-step explanation:

The pounds of roast beef required to make each sandwiches is \frac{3}{8}, and not \frac{8}{8} as erroneously typed in the question.

Given that each deli sandwiches made, uses \frac{3}{8} pounds of roast beef.

Marisa started with 5 pounds, and had 2\frac{3}{4} pounds left.

Thus,

pounds of roast beef used = 5 - 2\frac{3}{4}

                                             = 5 - \frac{11}{4}

                                             = \frac{20 - 11}{4}

                                             = \frac{9}{4}

                                             = 2\frac{1}{4}

Marisa had used 2\frac{1}{4} pounds of roast beef. So that;

the number of del sandwiches made = 2\frac{1}{4} ÷ \frac{3}{8}

                                                    = \frac{9}{4} ÷ \frac{3}{8}

                                                    = 6

Therefore, the number of sandwiches made by Marisa is 6.

5 0
3 years ago
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