Given the polynomial f(x)=2x2−2x−3, what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a?

Aiden buys two bags of chips at $1.09 each and a 20 ounce soda for $1.20 at the gas station.he knows that the state tax is 5.5. how much change will he receive from a $5 bill?

Imogene invested $8,000 in a bank account that pays 8 percent simple interest at the end of each year. her friend invested the same amount in stocks where the growth of the investment is represented as 2,000 times the square root of 2 less than the time lapsed in years. if y1 and y2 represent the amount earned in dollars and t is the time lapsed in years, which system of equations correctly represents the situation?

Ineed with angles and the measure of them i have abc a is 65 and b is (3x-10) and c is (2x) find the value of x