MATHEMATICS HIGH SCHOOL

Solving Trig. Equations:

csc^2x-2cot^2x=0

Answers

Answer 1
Answer: csc^2x-2cot^2x=0;\ D:x\neq k\pi\ (k\in\mathbb{Z})\n\n(1)/(sin^2x)-2\cdot(cos^2x)/(sin^2x)=0\n\n(1-2cos^2x)/(sin^2x)=0\iff 1-2cos^2x=0\n\n-2cos^2x=-1\ \ \ /:(-2)\n\ncos^2x=(1)/(2)\n\ncosx=\sqrt(1)/(2)\ \vee\ cosx=-\sqrt(1)/(2)\n\ncosx=(\sqrt2)/(2)\ \vee\ cosx=-(\sqrt2)/(2)


x=(\pi)/(4)+2k\pi\ \vee\ x=-(\pi)/(4)+2k\pi\ \vee\ x=(3\pi)/(4)+2k\pi\ \vee\ x=-(3\pi)/(4)+2k\pi\n\n\nAnswer:x=(\pi)/(4)+(k\pi)/(2)\ (k\in\mathbb{Z})

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Evaluate f(x) = X(With an exponent of 2) -3x +2, given f(x + 1).

Answers

Answer:

f(x + 1) = x² - x

Step-by-step explanation:

f(x) = x² - 3x + 2 when f(x + 1)

f(x + 1) = (x + 1)² - 3(x + 1) + 2

f(x + 1) = (x² + 2x + 1) + (-3x - 3) + 2

f(x + 1) = x² - x + 0

f(x + 1) = x² - x

Best of Luck!

The variables x and y are directly proportional, and y = 2when x = 3. What is the value of y when x = 9 ?

Answers

Direct proportionality:
y=kx
k - the constant of proportionality

y=2 \hbox{ when } x=3 \n \Downarrow \ny=kx \n 2=3k \nk=(2)/(3) \n \ny=? \hbox{ when } x=9 \n\Downarrow \ny=kx \n y=(2)/(3) * 9 \ny=2 * 3\ny=6 \n \n\boxed{y=6 \hbox{ when } x=9}

Given a = {1, 3, 5}, b = {2, 4, 6} and c={1, 2, 3, 4, 5, 6}, then a ∪ (b ∩
c. =

Answers

Match the following. Given A = {1, 2, 3, 4, 5} B = {2, 4, 6} C = {1, 3, 5}?1. A ∪ B __ {1, 2, 3, 4, 5} 
2. A ∪ C __ null, or empty set 
3. A ∩ B __ {1, 3, 5} 
4. A ∩ C __ {1, 2, 3, 4, 5, 6} 
5. B ∩ C __ {2, 4}

Final answer:

The result of a ∪ (b ∩ c) equals the union of set a with set b, since set b is completely contained within set c. The final answer is {1, 2, 3, 4, 5, 6}.

Explanation:

The question involves concepts of set theory and specifically deals with the union and intersection of sets. The sets given are a = {1, 3, 5}, b = {2, 4, 6}, and c = {1, 2, 3, 4, 5, 6}. We're asked to find the result of a ∪ (b ∩ c), which means we want to determine the union of set a with the intersection of sets b and c. First, we need to find b ∩ c, which are the elements common to both b and c. Since c contains all the elements of b, the intersection b ∩ c is simply b, which is {2, 4, 6}. Now, we take the union of set a with this result, so a ∪ (b ∩ c) = a ∪ b = {1, 2, 3, 4, 5, 6}. Hence, a ∪ (b ∩ c) contains all elements from both set a and set b, as there were no common elements in set a and set b originally.

Learn more about Union and Intersection of Sets here:

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Which of the following statements shows the distributive property?5 + (4 – 2) = 20 – 10

5(4 – 2) = 20 – 10

5 + (4 – 2) = 9 + 3

5(4 – 2) = 9 – 7

Answers

Answer:

\displaystyle 5(4 - 2) = 20 - 10

This is a genuine statement of you look real closely at it.

I am joyous to assist you anytime.

Someone plz help me :(

Answers

Answer:

i can JUST GET ON YOUR CROME BOOK

Step-by-step explanation:

Ashley is shopping for a fruit basket to send to her grandmother. A fruit basket fromMabel's Gift Shop costs $13 for the basket plus $1.50 for each piece of fruit. Jenny's Gifts
and More charges $15 for a similar basket with an additional cost of $1.25 per plece of
fruit.
Which Inequality can be used to find the amount of fruit, x, at which it would be less
expensive for her to order from Mabel's Gift Shop?

Answers

Answer:

13 + 1.5x < 15 + 1.25x

Step-by-step explanation:

Mabel: 13 + 1.5x

Jenny: 15 + 1.25x

Less expensive to shop at Mabel's. Less than sign <.

13 + 1.5x < 15 + 1.25x
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