What is the square root of -1?

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Answer 1

Answer: It is i

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Prove that:
(2-sin(2x))(sin(x) + cos(x)) = 2(sin^3(x) + cos^3(x))

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$\text{We use formulas: }\n \n 1) ~~ (a + b)(a^2 -ab + b^2) =a^3 + b^3 \n \n 2)~~ \sin(2x) = 2\sin x \cos x \n \n 3)~~ 1 =\sin^2(x) + cos^2(x) \n \n \text{We solve:} \n \n \Big(2-\sin(2x)\Big)\Big(\sin(x) + \cos(x)\Big) = 2\Big(\sin^3(x) + cos^3(x)\Big) \n \n \Big(2-2\sin(x)\cos(x)\Big)\Big(\sin(x) + \cos(x)\Big) = 2\Big(\sin^3(x) + cos^3(x)\Big) \n \n 2\Big(1-\sin(x)\cos(x)\Big)\Big(\sin(x) + \cos(x)\Big) = 2\Big(\sin^3(x) + cos^3(x)\Big)$

$2\Big(\sin^2(x)+\cos^2(x)-\sin(x)\cos(x)\Big)\Big(\sin(x) + \cos(x)\Big) = \n 2\Big(\sin^3(x) + cos^3(x)\Big) \n \n 2\Big(\sin^2(x)-\sin(x)\cos(x)+\cos^2(x)\Big)\Big(\sin(x) + \cos(x)\Big) = \n 2\Big(\sin^3(x) + cos^3(x)\Big) \n \n \boxed{2\Big(\sin^3(x) + cos^3(x)\Big) = 2\Big(\sin^3(x) + cos^3(x)\Big) }$

In triangle JKL, if angle J is seven less than angle L and angle K is 21 less than twice angle L, find the measure of each angle

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The measure of the angles are; J = 48, K = 57 and L = 75

What is linear pair?

Linear pair of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

In order to determine the measure of these angles, we have to set J as x. then find the measure of all of these angles.

J = x

K = x + 9

L = 2x - 21

Now, we can add them all together and set equal to 180;

x + x + 9 + 2x - 21 = 180

4x - 12 = 180

4x = 192

x = 48

Now that we have;

J = x = 48

K = x + 9 = 48 + 9 = 57

L = 2x - 21 = 2(48) - 21 = 96 - 21

L = 75

Hence, The measure of the angles are; J = 48, K = 57 and L = 75

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Answer:

j=45 k=83 L=52

Step-by-step explanation:

j=x-7

k=2x-21

L=x

x-7+2x-21+x=180

4x-28=180

4x=208

x=52

For the set data below, determine the 5 number summaries. Construct the resulting box and whisker plot for 5, 3,8, 6, 1, -10,3,9,7,4,2

Answers

The 5 number summaries Median: 4, Minimum: -10, Maximum: 9, First quartile: 2, Third quartile: 7

What are numbers?

Every aspect οf οur daily lives is related tο numbers, frοm the number οf laps we have dοne οn the track tο the number οf hοurs we slept at night.

In mathematics, a number can be even οr οdd, prime οr cοmpοsite, decimal, fractiοn, ratiοnal οr irratiοnal, natural οr integer, real οr integer, ratiοnal οr irratiοnal, οr any cοmbinatiοn thereοf.

Put the values in the data set into increasing order:

−10, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9

The minimum (the smallest number) is −10

and the maximum (the largest number) is 9.

Find the median,

The median is the middle number

The median is = 4.

Find Q1 and Q3.

Q1 = 2, Q3 = 7

Range = max−min = 9−(−1) = 19

Interquartile range = Q3−Q1 = 7−2 = 5.

Thus,

The 5 number summaries Median: 4, Minimum: -10, Maximum: 9, First quartile: 2, Third quartile: 7

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Find the domain of the function. (enter your answer using interval notation.) f(x) = x + 3 if x < −1 −2x if |x| ≤ 1 −2 if x > 1

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The domain of the function is the union of all of the "if" parts of the function definition:

... (-∞, -1) ∪ [-1, 1] ∪ (1, ∞) = (-∞, ∞)

If minor arc AB measures 9 inches, what is the length of the radius of circle C?

Answers

Answer:

12 inches

i hope this helped

Pls help I will fail 10th grade

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Answer:

Step-by-step explanation:

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