Solve for x in the equation x^2-14 x + 31 = 63.

Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. the punch has 2 liters of ginger ale. part a: write an equation using one variable that can be used to find the total number of liters of cranberry juice and ginger ale in the punch. define the variable used in the equation and solve the equation. hint: 0.8x represents the number of liters of cranberry juice in the punch. (5 points) part b: how many liters of cranberry juice are present in the punch? show your work.

Identify the number 127 as a rational or irrational. explain

The weight of a radioactive isotope was 96 grams at the start of an experiment. after one hour, the weight of the isotope was half of its initial weight. after two hours, the weight of the isotope was half of its weight the previous hour. if this pattern continues, which of the following graphs represents the weight of the radioactive isotope over time? a. graph w b. graph x c. graph y d. graph z