power27

1111111*7654456346634*6436436*4363466346*346363463*6346=525026258531588673152701603124269752415298836512

Woah I didn't realize the calculator on this site can do problems this big without using scientific notation

(7y-7)(2y²-y+6) = (7y)(2y²-y+6)+(-7)(2y²-y+6)

Distrubute (2y²-y+6) acrost (7y-7)

(7y)(2y²)+(7y)(-y)+(7y)(6)+(-7)(2y²)+(-7)(-y)+(-7)(6)

Distribute (7y) and (-7)

14y³-7y²+42y-14y²+7y-42

Multiply, being careful with the negative signes and the powers of y

14y³-21y²+49y-42

Combine like terms to get the simplified answer

I think the different perimiters part is the key to solving this problem efficiently...

The maximum perimiter that any rectangle can have is 40, and you can only draw one of those.

The next biggest perimiter would be 39, but you can't draw a rectangle with integer side lengths with that perimiter.

The next one would be 38, you can draw lots of rectangles with that peremiter, but only one will count because they have to have different perimiters.

37 is out because its odd

36 is in because its even

all the way down to a peremiter of 4, which is the smallest rectangle that meets the restrictions

There are 40/2 - 1 = 19 possible rectangles.

So I'm not completely doing your homework for you, I'll just get you started.

1. To find out what type of roots a quadratic in the form ax2+bx+c, plug the coeficients into the discriminant: b2-4ac

If this is positive, there are two real solitutions. If it is negative, there are two non real solitutions. If it is 0, then there is one real solitution. You want to find the discriminants of the 5 quadratics to find the discriminant that is 0.

I'll do the first one:

a=4, b=16 and c=-9

162-4(4)(-9)=256-(-144)=400, so the first one is not the answer.

2. I'm going to interperate this one how I think you meant to write it (you didn't put parenthisies around the xy so the y should be in the numerator): \(\frac{x}{y}=\frac{225}{xy}+\frac{y}{x}\) (and this interperation works out nicely)

First I would start by multiplying by xy to remove the varaibles from the denominator:

x²=225+y²

x²-y²=225

(x+y)(x-y)=225

x and y will be integers when (x+y) and (x-y) are factor pairs of 225

The factors of 225 are:

1 and 225

3 and 75

5 and 45

ect.

For every factor pair there will be integers x and y that satisfy the equation

List the remaining factor pairs until you get to 225 and 1 and count them to get the answer.

To find the solitutions that go with the factors 1 and 225 (which you don't need to do), you would solve x+y=1 and x-y=225

https://artofproblemsolving.com/news/articles/avoid-the-calculus-trap

Thats a good article on my favorite math website

I'm pretty sure the calculus trap is breezing through school math as fast as you can, just to get to calculus and find it just as easy as all the other classes you have been taking, rather than taking classes with or being around other motovated math students and really learning how to apply and use what you learn.

Agree tbh

But I skipped 7th grade math 

You find the precent something is of a whole like this: \(\frac{\text{part}}{\text{whole}}\)

There are 10 first class seats, 10 business class seats and 30 economy seats on the plane so there are 10+10+30=50 total seats.

To find the precent of first class seats, \(\frac{\text{number of first class seats}}{\text{total seats}}=\frac{10}{50}=\frac{20}{100}=20 \text{%}\) of the seats on the plane are first class.

Only the third pie chart has the number of first class seats as 20%, so that must be the answer, but lets double check the rest.

Buesness class: There are also 10 buesness class seats, which is the same number of first class seats so it must also be 10% buesness class. This matches the third pie chart.

Economy: There are 30 economy seats, so \(\frac{30}{50}=\frac{60}{100}=60\text{%}\) economy seats, which also matches the third pie chart so the answer must be the third chart.

I'm assuming the pyramid has a square base for this

The formula for the volume of a pyramid is 1/3*base area*height

base area=220²=48400m²

^{(if the area of the base is not square, use the side length to find the area of whatever shape it is and substitute it in)}

height=105m

so the volume of the pyramid is 1/3*48400m²*105m=1,694,000m³

Except the pyramid is only 96% solid so the volume of material used is .96*1694000=1,626,240m³

can i still get some cake