idyllic

first, we can rewrite x^6 as (x^2)^3, and we can also rewrite 343 as 7^3.

now, we can apply the Sum of Cubes formula.

here is the sum of cubes formula, for future reference (if needed): \(x^3+y^3 = (x+y)(x^2-xy+y^2)\)

now to apply it to the current problem.

our x in this case is x^2, and our y would be 7.

so the factored form:

\(x^6+343 = (x^2+7)(x^4-7x^2+7^2)\)

= \((x^2+7)(x^4-7x^2+49)\), which is option D.

hope this helped! please let me know if you are confused about anything i did :)

20% = 1/5.

so if 20% of the students in the class are left handed, then 20/5 = 4 students are left handed.

so the amount of students that are right handed are 20 - 4 = 16.

hope this helped! please let me know if i am incorrect, or if you are confused about anything i did :)

oh, oops, i forgot that the circumference is just the diameter * pi. 

good work, Guest !!

the perimeter of the figure is:

10 + 4 + 4 + (10/2 * pi) / 2 = 18 + 5/2 pi 

to the nearest hundredth (assuming pi is 3.14), that would be 18 + 7.85 = 25.85.

now for the area:

10 * 4 + (10/2)^2 * pi = 40 + 25pi

to the nearest hundredth, that would be 40 + 78.5 = 118.5.

hope this helped! sorry if my explanations weren't too clear. please let me know if you are confused about anything i did 

i believe that the copy shape is just the original, except each side is scaled down by a factor of 3.

so x and y would be the corresponding dimensions divided by 3.

x would be 8/3, and y would be 5/3.

hope this helped! please let me know if i am incorrect, or if you are confused about anything i did 

let's draw a bigger rectangle surrounding the shape.

the area of the shape would be the area of the bigger rectangle minus the area of the smaller rectangle (outside of the shape).

the area of the larger rectange is just 7 * 7 = 49.

the area of the other small rectangle is 6 * 2 = 12.

so the area of the composite shape would be 49 - 12 = 37.

hope this helped! please let me know if you have any follow-up questions :)

check out CPhill's answer here: https://web2.0calc.com/questions/help-due-2moro_2

i feel like i've seen this problem on AoPS Alcumus before, it was a tough one for me!

i went back to my problem logs (scrolled a while), and saw that the answer was 6 + sqrt6.

though i hope you are not just asking this question for the answer alone to get points. i'd recommend you to read the solution by AoPS thoroughly and understand it, as it can help you learn a lot.

hope this helped! 

by vertical angles, angle e is 49 degrees.

angle f shares a straight angle with the 49 degree angle, so angle f is 180 - 49 = 131 degrees.

similarily, angle d shares a straight angle with the right angle, so angle d is simply 180 - 90 = 90 degrees.

hope this helped! please let me know if you are confused about anything i did :)

hi Melody (i'm not Jenny), but i think the link is here:

https://web2.0calc.com/questions/probability_72128