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Quadratic congruences

8. Find all solutions to the quadratic congruences, if they exist. (a) x2 + x + 1 ≡ 0 (mod 7). (b) x2 ≡ 55 (mod 179)

Quadratic residue

Classify every integer a, 1<=a<11 as to whether it is a quadratic residue or nonresidue modulo 11.

Problem Set

(See attached file for full problem description with proper symbols) --- 1. Given that s = 1.59t(1-3v), obtain the value of v when s = 3.52 and t = 21.56. 2. If y = x , calculate the value of p given that y = 2.65 and x = 0.745. 3. If x = (1 + 1nr), evaluate r when x =0.34, P = 1.08 and

Writing and solving word problems.

For example: 1. What amount is left after ____ time? Equation to solve Solution 2. How much time will you take it for there to be _____ (amount)? Equation to solve Steps to solve (requires the use of logs) Solution

Scatter Plot

Question 6: House cat owners invest a lot of time and expense to find just the right cat food for their finicky, spoiled and pampered pets. Some house cat owners believe that the reaction of the house cat, in terms of how much time passes between the serving of the food and the point at which the finicky, spoiled and pampered

Fundamental Theorem of Arithmetic

Please show complete solution so that I may understand the reasoning behind each step. I will need a thorough understanding to complete future assignments. See attached file for full problem description.


The current cost of a cruise you wish to take in 6 years is $4,250.00. You expect it will increase by 4% annually. I can earn 5% on my savings. How much do I need to save at the end of each month so I can afford to take the cruise in six years? Note: I understand that I need to consider the future amount. Future amount=

Exponential Growth Rates

Consider the following disaggregation of carbon emissions: Carbon emissions(kg C/yr)= Population x (Energy(kJ/yr)/Person) x (Carbon (kgC)/Energy(kJ)) Using the following estimates for the United States and assuming that growth rates remain constant, Population (kJ/yr)/Per

Parallel and perpendicular lines

Are the following lines parallel, perpendicular, or neither? L1 with equation x - 7y = 35 L2 with equation 7x + y = 7 A) Parallel B) Perpendicular C) Neither

Word problem

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? (Please show steps) I'm trying to figure out what the steps would be to come to this conclusion. The problem says "220 more votes". I understand that (I think) to be +200, but

Given information in attachment, please sketch the graph

(See attached file for full problem description with proper equations) --- Given information in attachment, please sketch the graph. For the rational function f(x) = (x2 - 1) / (x2 - 9), give the intercepts and asymptotes and sketch the graph. Let f(x)=0, we get x=1 or x=-1. So, the x-intercepts: x=1 or x=-1. Let x=

Rational function

For the rational function (see attached file) a.) determine the equation of the oblique asymptote b.) determine the x-intercepts c.) determine the y-intercepts d.) determine the equation of the vertical asymptote e.) sketch the graph

A computer is infected with the Sasser virus.

A computer is infected with the Sasser virus. Assume that it infects 20 other computers within 5 minutes; and that these PCs and servers each infect 20 more machines within another five minutes, etc. How long until 100 million computers are infected?

Synthetic Division, Intermediate Value Theorem and Asymptotes

21) Use synthetic division to find: f(?2) f(x)=2x3?3x2+7x?12 21) 22) For the function f(x) = ?x3 + 8x2 ? 40 Show how to use synthetic division to find out if -1 is a zero. 22) 23) One of the zeros of the function f(x) = ? 7x2 + 17x ?15 is 2-i. Find all the other zeros. 23) ____________________ 24) Use the intermediate val

Please explain in detail these two word problems.

12. The second of three negative numbers is 6 less than the first negative number. The third negative number is 3 times the second number. Find the set of all possible third numbers given that twice the sum of the first two numbers is greater than the third number. 13. A woman can row 11 miles downstream in the same

Axis of symmetry

Given the quadratic function y = 9 x 2 - 6 x + 3, What is the equation of the axis of symmetry ? 1) x = 2/3 2) x = - 1/3 3) x = - 2/3 4) x = 1/3


Determine the domain of the function: f (x) = sqrt( -2 - x)

Word Problem

How many quarts of 60% alcohol solution must be added to 20 gallons of 20% alcohol solution to obtain a mixture that is 30% alcohol?

Solve for x

(See attached file for full problem description)

The answer to Geometric sequence

Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8, find the following: a. What is r, the ratio between 2 consecutive terms? b. Using the formula for the sum of the first n terms of a geometric series. What is the sum of the first 10 terms? Please round your answer to 4 decimals. c. Using the formula f

Arithmetic Sequence Differences

Use the arithmetic sequence of numbers 1, 3, 5, 7, 9, ..... to find the following: a. What is d, the difference between any 2 terms b. Using the formula for the nth term of an arithmetic sequence, what is 101st term? c. Using the formula for the sum of an arithmetic series, what is the sum of the first 20 term? d.

Geometric sequence

The classic problem - put a penny on first square of a checkerboard, and then double the amount on each succeeding square. How much money would be put on the 32nd square? How much money would you recieve if there only 32 squares? How much money is needed to fill all 64 squares of the checkboard? Thank you!