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Solve the following problems in essay form (1 to 2 paragraphs for each problem is fine). Please show all work and show how you came up with the answer. Please make sure that you address the following questions: (1) How did you get your answer? (2) What steps did you take? (3) Where did you begin? (4) Why did you do what you did? (5) Explain in detail what your answers to the problems are?
Problem 1 -
Mr. Smith invited 17 guests to his "Disco-reunion" party. He assigned each guest a number from 2 to 18, keeping 1 for himself. When everyone was dancing, he noticed that the sum of each couple's numbers was a perfects square. What was he number of Mr. Smith's partner?
Problem 2 -
Define "prime date" to be a date during the year where both the months (as a number, i.e. January is 1, February is 2, etc) and the day are both prime numbers. What is the average number of prime dates per week in one year?
write the equation in slope-intercept form of the line that has a slope of -5 and a y-intercept of
Determine if the function is even, odd, or neither. Compare the graph of the given quadratic function f with the graph of y = x2.
Show specifically how row operations can be used to solve the matrix.
How for does the projectile travel (horizontally) before it hits the ground? What is the maximum height above the ground that the projectile attains?
Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Please show your answer using both words and mathematical notation.
Let S be the set of ordered pairs of positive integers, let z = (5,8), and define R so that (x1, x2) R (y1, y2) means that x1 + y2 = y1 + x2.
A launched rocket has an altitude, in meters, given by the polynomial , where is the height, in meters, from which the launch occurs, at velocity in meters per second, and is the number of seconds for which the rocket is airborne.
In a town election, the winning candidate had 220 more votes than the loser. If 810 votes were cast in all, how many votes did each candidate receive?
Calculate the marginal cost of the bags.
Using mathematical induction, prove or disprove that all checkerboards of these shapes can be completely covered using right triominoes whenever n is a positive integer.
the 6th grade class has 12 boys and 20 girls. the teacher wants to divide them into groups that have the same number of
What are the similarities and differences between the procedures needed to solve each of the following problems? Show your work and include a verbal breakdown of each step.
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