Quadratic function graph does not cross x-axis, but crosses y-axis once. Which statement is correct according to the fundamental theorem of algebra? A, B, C, or D?
What separates the terms of a polynomial? A) Multiplication or division B) Addition or subtraction C) Parentheses or grouping symbols D) Commas or dashes
Solve the quadratic equation v2+10v−33=0 for v. Express the solutions as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
Find the total number of votes when the ratio of yes to no votes is 2:3 and there are 1338 yes votes. Solution: Let the total number of votes be x. Then the number of yes votes is 1338 and the number of no votes is 53x−1338. The ratio of yes to no votes is 2:3, so 32x=1338. Solving for x, we get x=2007.
Find the number of tires to produce at each of Timo's two factories, Λ and B, to minimize the total pollutant f(x,y)=x(x+4)+y(y+2) while producing 3025 tires.
A local hamburger shop sold a combined total of 592 hamburgers and cheeseburgers. The number of cheeseburgers sold was 3x where x is the number of hamburgers sold. Find x.
Find the range and intervals where the quadratic function f(x)=x2−2x−3 is increasing and decreasing. Range: [−4,∞)
Increasing: (−∞,21+13)
Decreasing: (21+13,∞)
Rewrite the first problem statement:
Find the intervals where C=305x+840 and R=25x break even, i.e., C=R. Rewrite the second problem statement:
Find the intervals where C=20x+550 and R=45x break even, i.e., C=R. Rewrite the third problem statement:
Solve the quadratic inequality x2−2x≤2 and express the solution set in interval notation.
Determine the number of solutions for the given equations and inequalities. For equations with one or two solutions, state the solutions.
1) 5+2(x−4)=2x+3
2) 5+2(x−4)<2x+3
3) (5x−3)/4=(2−4x)/3