With all those parantheses, your equation can get a little confusing. It can be rewritten like this: [4(2)(-5)-4^2]/(4*2). If you know PEMDAS, Parantheses, Exponenets, Multiplication, Division, Addition, Subtraction, you do the parantheses first, but within the parantheses you do exponents first, so [4(2)(-5)-16]/(4*2), then multiplication... [-40-16]/(8) so -56/8 which is -7.
Case 1: You pick no red marbles... to get that you would have to pick either green or blue marbles only. So there would be 6x5x4=120 ways.
Case 2: You pick only 1 red marble. There are 3 ways to pick a red marble and then 6x5 more ways to choose a green or blue marble, so 6x5x3=90 ways.
So you add up both cases and get 120+90=210 ways.
If the difference in the areas is 33, then when A is the smaller square's area and B is the larger square's area, then: a+a+33=65, and if you subtract 33 from both sides, you get 2a=32, so the smaller square's area is 16, so therefore the larger square's area is 65-16=49. If you find the square root of the smaller and larger areas, 4 and 7 respectively, you can add 4+4+4+4+7+7+7+7=44.
If you know The Pythagorean Thereom, you know that a^2+b^2=c^2 where A and B are the two shorter sides, and C is the longest side. So if you draw out the right triangle, the side lengths of A and B will be 10 and 10, and you just have to plug in the values, 10^2+10^2=100+100=200, but you have to find the square root of 200, and \(\sqrt200\) simplifies to \(10\sqrt2\)
1. So basically all of the 4 people are 6 years older, so a total of 24 years older in total... so 20+24=44 years in total.
2. Each of them would be 4 years younger, which is 12 years younger in total... so 38-12=26 years in total.
3. Each year, each person gains one year and a total of 2 years gained a year... so 10/2=5 years until their combined ages are 40.
4. Basically the key is to find the total sum of their ages now... so you add 12 to 18 because that is their past age plus their 2 ages increasred by 6... thus the sum of their ages is 30. If Jeremy is twice as old as Randy, he has 2/3 of the total age and Randy 1/3, therefore, 2/3 of 30 is 20, and Jeremy is 20 years old.
5. Like the previous problem, the key is to find the total sum... so you subtract 14 and the total sum of their ages if 40, Tom is 4 times older than Kaden so therefore Tom is 32 years old.
Hopefully this helps you to understand the next... hundred problems