The freezing point of water is 32 degrees f. tim added potassium and found out that the freezing point went down by 8 degrees f. what is the freezing point of the water with the added potassium?

What is the value of the discriminant of the quadratic equation -2x = -8x + 8 and what does its value mean about thenumber of real number solutions the equation has?

Amovie theater owner determined that about 2 out of every 5 customers purchases popcorn. which simulation could be used to answer questions about customers purchasing popcorn?

Question 1: runners in the half marathon entered in three waves. there were 341 runners in the first wave, 295 runners in the second wave, and 316 runners in the third wave. if seven out of eight runners finished the race, how many did not finish? question 2: a flagpole casts a 20foot shadow at the same time lexi casts 5 foot shadow. if lexi is 5'9'', find the height of the flagpole. question 3: the barnes family has a coupon for 10% off their dinner. if their bill comes to $82.50 and they wish to tip 15% what will they pay in total? question 4. gas prices are typically marked up for holiday travel. if the price are marked up 17.5% and the regular price per gallon is $2.40, how much will mitch pay for 16 gallons of gas? question 5. a $1,349 television is on sale for 20% off. if sales tax is 8%, find the price of the television including tax? question 6. a sign above a basket of dvds reads 3 for $17. kellen decides to buy 6 dvds and use a coupon for 25% off. if sales tax is 6% what will he pay in total.