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stiks02 [169]
3 years ago
6

How do you simplify this expression step by step using trigonometric identities?

Mathematics
1 answer:
olga55 [171]3 years ago
5 0

\bf \textit{Pythagorean Identities}\\\\ 1+tan^2(\theta)=sec^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sec^2(\theta )cos^2(\theta )+tan^2(\theta )\implies \cfrac{1}{\begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} +tan^2(\theta ) \\\\\\ 1+tan^2(\theta )\implies sec^2(\theta )

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I need help!!!
Nataly_w [17]

Answer:

y = 3

Step-by-step explanation:

8(y + 2) = 40 \\ y + 2 =  \frac{40}{8}  \\ y + 2 = 5 \\ y = 5 - 2 \\ y = 3

6 0
3 years ago
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From a standard deck of 52 cards, what is the probability of picking a King at random from the deck?
MaRussiya [10]

Answer:

1/13

Step-by-step explanation:

there are 4 kinds and 52 cards so its 4/52 which simplifies to 1/13

7 0
3 years ago
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How can an expression using the distributive property can be simplified to 12a + 18b - 6c
elena-s [515]
Look for a common number in all the terms

6(2a+3b-c)
3 0
3 years ago
You believe that eating an apple a day is healthy and want to design an experiment to find out. You have available 40 volunteers
Gwar [14]

The best design for this experiment would be a repeated measures design. This is ideal to determine if eating an apple makes you healthy.

<h3>What is an experimental design?</h3>

An experimental design refers to the general structure of an experiment including how people are distributed into the control and experimental group to test a specific phenomenon.

<h3>What is a repeated measures design?</h3>

In a repeated measures design all participants are both parts of the control group, in this case, people who do not eat apples, and the experimental group, or people who eat apples.

<h3>What does this design imply?</h3>

In the case of determining if eating an apple every day, this design implies:

  • All participants will be asked to not eat apples every day for a specific period such as one or two months, and health levels will be measured during this time.
  • After the first step, all participants will be asked to eat an apple every day during the period, and their health will be measured.
  • The researcher can compare the results of each participant, which is more accurate than comparing one participant to another.

Learn more about experiments in: brainly.com/question/1452319

7 0
3 years ago
Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1. (2 points)
umka2103 [35]

Focus of the parabola is (-5,5) and directrix is y = -1.

Let's assume a point (x,y) on parabola.

According to definition of parabola, the distance between point (x,y) and focus (-5,5) would be same as the distance between the point (x,y) and directrix y = -1.

\sqrt{(x+5)^2+(y-5)^2} = \sqrt{(y+1)^2} \\\\(x+5)^2+(y-5)^2=(y+1)^2 \\\\(x+5)^2 + y^2 - 10y +25 = y^2 +2y +1 \\\\(x+5)^2 =  -y^2 +10y -25 + y^2 +2y +1 \\\\(x+5)^2 = 12y -24 \\\\12y =  (x+5)^2  +24 \\\\ y = \frac{1}{12} (x+5)^2  +2

Hence, option D is correct, i.e. f(x) = one twelfth (x + 5)2 + 2.

7 0
3 years ago
Read 2 more answers
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