### Linear Congruences ( Part I) Incongruent Solutions

Find the solutions of (a) 4x is congruent to 3(mod 7) (b) 9x is congruent to 11(mod 26) (c) 3x + 1 is congruent to 4(mod 5) (d) 8x is congruent to 6(mod 14).

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Find the solutions of (a) 4x is congruent to 3(mod 7) (b) 9x is congruent to 11(mod 26) (c) 3x + 1 is congruent to 4(mod 5) (d) 8x is congruent to 6(mod 14).

Please see the attached file for full problem description Find ten real numbers in the closed interval [0,1] such that for each value m from 2 to 10, the numbers lie so that there is one of them in each of the open intervals [Note that these conditions for m = 1,2......,10 all have to hold simultaneously for your

I have two sets of 64 numbers (1.1 to 7.4). Both number sets are created using the same equation for values of i from 0 to 63. m = 1.1 + ( i * 0.1 ) n = 1.1 + ( i * 0.1 ) I am trying to understand if the following equality is false in all cases except when the terms in each expression are equal (e.g. m^-12 = n^-12 and

The graph of the quadratic equation x^T Ax = [0,0,1]x, where A = [ 1/(alpha^2) 0 0 ] [ 0 -1/(beta^2) 0 ] [ 0 0 0 ] is a(n): A. ellipse B. hyperbola C. elliptic paraboloid D. parabolic cone E. hyperbolic paraboloid

Let f1, f2, f3 be unit vectors in R3 such that < f1, f2 >= 1/2. Give a necessary and sufficient relationship between x =< f1, f3 > and y =< f2, f3 >. Please be sure to be rigorous and as detailed as possible.

E^x*e^x+1=e^x-1

10^x=200

Ln (under radical)=1 (x+2)

Lnx+ln(x+2)=ln3

Solve for x in the following logarithmic equation. Please show a detailed step by step solution. logx - log2 = 5

Given that S=(R+D)^(1/3) and T=(R-D)^(1/3) where D= square root(R^2+Q^3), show that ST=-Q

Hi, can someone please explain to me how sqrt (square root of)128 becomes 8sqrt2 ; or sqrt68 becomes 2sqrt17? ; or sqrt45 becomes 3sqrt5? Thank you

Simplify the following expressions: a. 3x-2/2x2+x-3 Divide by 9x-6/2x-2 b.(108)1/2- (48)1/2+ (192)1/2 (should be exponent 1/2) c. (20x3+3x2-4x+5)/(4x2+3x-7) (should be exponent 3 and 2,2).

Factor the following: a. 81a4- 16b4 (should be exponent 4) b. 12x2+ x- 35 (should be exponent 2)

3 years ago, Liz's age was 1/3 of her mother's age. Now, 7 years later, her age will be 1/2 of her mother's age. How old are Liz and her mother?

Please see the attached file for full problem description. I would like to get some assistance in setting up this problem. A=1.645 and they give the answer of x as .56506 Thank You

Logarithms and exponents. See attached file for full problem description.

For the given functions f and g, find: (a) the composition of (f o g) (4) (b) (g o f) (2) (c)( f o f) (1) (d) (g o g) (0) f(x) = 2x; g(x) = 3xsquared + 1

For the given functions f and g, find the following functions and state the domain of each. (a) f + g (b)f - g (c)f x g (d) f / g f(x)= square root of x + 1; g(x) = 2 / x

Sketch the graph of each function. Be sure to label three points on the graph. If f(x) = integral (2x), find: (a) f(1.2) (b) f(1.6) (c) f(-1.8)

Please help me with #4, #10, and #16. I am having trouble woth these. Please show your work so that I may better understand the process.

Solve: x3 - 2x2+x=-5(x-1)2.

Let m be the smallest positive integer such that @^m=E for all @eS_n. Show that m=lcm(2,3,4,5,...,n). note: e denotes element of

Assume that the sum and product of two roots of a quadratic equation are 5 and 6, respectively. Find two roots.

I am asked to verify Fubini's Theorem for an integral evaluated over an equilateral triangle. I am asked to fully discuss the reasons for the limits of integration in my solution. See attached file for full problem description.

9q^2-72q+750

Test the following for divisibility by 2,3,4,5,6,8,9,and 10. (No calculator, explain your thinking). i. 6 543 210 b. What is the smallest whole number that is divisible by 2,3,4,5,6,8,9 and 10.

Simplify each of the following expressions further and identify the number property(ies) used in each. 1. 2 x (15+8)= (2 x 15)+ (2 x 8)= 2. 5/2 x (3/4 x 2/5)= (5/2 x 2/5)x 3/4=

Please see the attached file for the fully formatted problems. Find the following: a) The coefficient of x in the expansion of b) The coeffiecient of in the expansion of c) The coefficient of in the expansion of d) The coefficient of in the expansion of is equal to the coefficient of in the

Three numbers are in arithmetic progression. The sum of the three numbers is 30 and the sum of their squares is 398. What are the three numbers? b) An arithmetic series is such that its first term is a and its third term is b. The sum of the first n terms is Sn . Find S4 in terms of a and b. Given that S4, S5 , S7 are con