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


Answer 1
\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)  }

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Which is the better buy?17-ounce jar of pickles for $8.842-pound jar of pickles for $25,28

To make lemonade you can mix 4 teaspoons of lemonade powder with 16 ounces of water. What is the ratio of powder towater?




Step-by-step explanation:

divide all of it by 2, you get 16:64. Again, 8:32. Again, 4:16



Answer: The first choice should be correct

Step-by-step explanation:

Well I hope this is correct

Option C or they are alternate interior angles is correct.

When two lines are crossed by another line (called the Transversal): Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal

Megan’s room is expanded so the width is 150% of 3 meters. What is the new width?


Since Megan’s room is expanded so the width is 150% of 3 meters, the new width is 4.5 meters.

How to calculate the perimeter of a rectangle?

In Mathematics and Euclidean Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(h + w)


  • P represent the perimeter of a rectangle.
  • w represent the width of a rectangle.
  • h represent the height of a rectangle.

Note: 150% = 150/100 = 1.5

In this context, the new width can be calculated as follows;

New width = 150% of 3

New width = 1.5 × 3

New width = 4.5 meters.

Read more on perimeter of a rectangle here:


Answer: 4.5 meters

Work Shown:

The keyword "of" means "multiply".

150% = 150/100 = 1.5

150% of 3 = 1.5*3 = 4.5

In the figure, side AB is given by the expression (5x + 5)/(x + 3), and side BC is (3x + 9)/(2x - 4).The simplified expression for the area of rectangle ABCD is _______, and the restriction on x is ____.



The simplified expression for the area of rectangle ABCD is ( 15(x + 1))/(2(x - 2)), and the restriction on x is x≠2 .

Step-by-step explanation:

Side AB = Width of rectangle = (5x + 5)/(x + 3)

Side BC = Length of rectangle =  (3x + 9)/(2x - 4)

Area of Rectangle = Length * Width

Putting values:

Area\,\,of\,\,rectangle =( (3x + 9))/((2x - 4)) * ((5x + 5))/((x + 3))


Area\,\,of\,\,rectangle =( 3(x + 3))/((2x - 4)) * (5x + 5)/((x + 3)) \nArea\,\,of\,\,rectangle =( 3)/(2(x - 2)) * 5x + 5\nArea\,\,of\,\,rectangle =( 3(5x + 5))/(2x - 4)\nArea\,\,of\,\,rectangle =( 15x + 15)/(2x - 4)\nArea\,\,of\,\,rectangle =( 15(x + 1))/(2(x - 2))

The restriction on x is that x ≠ 2, because if x =2 then denominator will be zero.

So, the answer is:

The simplified expression for the area of rectangle ABCD is ( 15(x + 1))/(2(x - 2)), and the restriction on x is x≠2 .

Please answer this, I am confused (5^2)(7^2)(3^2)



The expression is:


To find:

The value of the given expression.


We have,


On simplification, we get



Therefore, the value of the given expression is 11025.

Why are people with savings hurt by inflation? A. The money is worth more now than it was in the past, leading to a higher tax bill.
B. Inflation discourages people from saving.
C. The money they saved in the past is worth less in the future.
D. Inflation reduces the interest savings accounts pay.


i took personal finance, sorry if i,m wrong but i think its C