[(14,7 + 5,9) x 5,8] / 2 = 59,74 cm^2
There's an app called photo math that can really help you with your problem
You did it right (almost, I got 21 instead of 19) but didn't finish. You need to show your discriminant is never negative.
x² + (p+1)x = 5-2p
x² + (p+1)x +(2p-5) =0
Real roots mean a positive (or at least non-negative) discriminant:
D = b² - 4ac = (p+1)² - 4(1)(2p - 5) = p² + 2p + 1 - 8p + 20
D = p² - 6p + 21
It's not totally obvious that D>0; we prove that by completing the square by noting
(p-3)² = p² - 6p + 9
so
p² - 6p = (p-3)² - 9.
D = p² - 6p + 21
D = (p-3)² - 9 + 21
D = (p-3)² + 12
Now we clearly see D>0 always because the squared term can't be negative, so D is always at least 12. We always get two distinct real roots.
Assuming that the cost of the fine is proportionate per each 20mph increase, then a 40mph speeding ticket should be $4, and if they received a fine of $150 would be a crazy amount of speed, is there something you did not attach?
So, to solve the questions on your paper, you need to first have all of the bottom numbers on the fractions similar numbers. So if you have the numbers 1/4 and 4/8, you need to get them to both be the same number. Therefore, 1/4 should become 2/8, because you doubled the bottom number (you also then need to do the same to the top number). You don't need to change 4/8, because it's bottom number is already 8. Then, you can take 4/8 and 1/8 and add them. To add them, you just add the top numbers. The top numbers make 5, so then you add the denominator, and make the number 5/8. Since you can't simplify 5/8, just keep it. But if it was 4/8, you could simplify it to 1/2. You can do all of this same to all of the numbers on your paper. :D If you are subtracting, subtract only the top numbers, but if you need to multiply or divide, multiply/divide both numerator AND denominator. :D I hope I helped! If I didn't, please tell me, or just delete my answer. :D
