Solve each problem. Dimensions of a Square. If the length of each side of a square is decreased by 4 in., the perimeter of the new square is 10 in. more than half the perimeter of the original square. What are the dimensions of the original square?

Solve each problem. Alcohol Mixture Barak wishes to strengthen a mixture that is 10% alcohol to one that is 30% alcohol. How much pure alcohol should he add to 12 L of the 10% mixture?

Solve each problem. Speed of a Plane Mary Lynn left by plane to visit her mother in Louisiana, 420 km away. Fifteen minutes later, her mother left to meet her at the airport. She drove the 20 km to the airport at 40 km per hr, arriving just as the plane taxied in. What was the speed of the plane?

Solve each problem. (Modeling) Lead Intake As directed by the 'Safe Drinking Water Act' of December 1974, the EPA proposed a maximum lead level in public drinking water of 0.05 mg per liter. This standard assumed an individual consumption of two liters of water per day. If EPA guidelines are followed, write an equation that models the maximum amount of lead A ingested in x years. Assume that there are 365.25 days in a year.

Solve each problem. (Modeling) Online Retail Sales Projected retail e-commerce sales (in billions of dollars) for the years 2016–2022 can be modeled by the equation y=52.304x+396.80, where x=0 corresponds to 2016, x=1 corresponds to 2017, and so on. Based on this model, find projected retail e-commerce sales in 2022 to the nearest tenth of a billion. (Data from www.statista.com)

Perform each operation. Write answers in standard form. (6-i) + (7-2i)

Perform each operation. Write answers in standard form. 15i- (3+2i) -11

Perform each operation. Write answers in standard form. (-8+2i)(-1+i)

Perform each operation. Write answers in standard form. (5-11i)(5+11i)

Perform each operation. Write answers in standard form. -5i(3-i)²

Perform each operation. Write answers in standard form. (-12 -i) / (-2 -5i)

Simplify each power of i. i¹¹

Simplify each power of i. i¹⁰⁰¹

Simplify each power of i. i^-27

Simplify each power of i. 1/i¹⁷

Solve each equation. 2x²+x-15 = 0

Solve each equation. -2x² +11x = -21

Solve each equation. (2x+1)(x-4) = x

Solve each equation. x²- √(5x) -1 = 0

Solve each equation. (x+4)(x+2) = 2x

Which equation has two real, distinct solutions? Do not actually solve.

A. (3x-4)² = -9 B. (4-7x)² = 0 C. (5x-9)(5x-9) = 0 D. (7x+4)² = 11

Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. 8x² = -2x -6

Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. -8x² + 10x = 7

Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. 16x² +3 = -26x

Dimensions of a Right Triangle The shortest side of a right triangle is 7 in. shorter than the middle side, while the longest side (the hypotenuse) is 1 in. longer than the middle side. Find the lengths of the sides.

Solve each equation. 4x⁴+3x²-1 = 0

Solve each equation. 2 - 5/x = 3/x²

Solve each equation. 10/(4x-4) = 1 /(1-x)

Solve each equation. (x-4)^2/5 = 9

Solve each equation. (x-2)^2/3 = x^1/3