In need of some help! Thank you in advance. 100 points <3 1: Explain why the equation (x-4)^2-17=8 has two solutions. Then solve the equation to find the solutions. Show your work.

2: This is Josh’s solution for the equation x^2+4x+3=0:

x^2+4x+3=0
x^2+4x=-3
x^2+4x+4=-3+4
(x+2)^2=1
x+2=1
x=-1

Is Josh’s solution correct? Explain.

3:Use the quadratic formula to solve x^2-6x+7. Show your work. Then describe the solution. No work, no credit.

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

As part of an annual fundraiser to raise money for diabetes research, diane joined a bikeathon. the track she biked on was 1,920 yards long. diane biked 38.5 laps. her sponsors agreed to donate an amount of money for each mile she biked. how many miles did she bike? first fill in the blanks on the left side using the ratios shown. then write your answer. given ratios: 5280ft / 1 mi , 1 mi /5280 ft , 1,920 yards / 1 lap , 1 lap / 1,920 yards , 3 ft / 1 yard , 1 yard / 3 ft. blanks: 38.5 laps / 1 yard x (blank) x (blank) x (blank) = (blank) miles i'm really confused on how to do this, and the explanations aren't exactly . if you could walk me through how to do this, it would be greatly appreciated.

The volume of gas a balloon can hold varies directly as the cube of its radius. imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. how many cubic inches of gas must be released to reduce the radius down to 2 inches?