Questions in mathematics

Questions in mathematics

📝 Answered - To each element of the set S = {1, 2, ..., 1000} a colour is assigned. Suppose that for any two elements a, b of S, if 15 divides (a + b) then they are both assigned the same colour. What is the maximum possible number of distinct colours used?

📝 Answered - Part of a proof that co-interior angles on parallel lines add up to 180° is shown below. Fill in the gaps by choosing from the options provided in the boxes. You may use each option more than once. [tex]x + y = 180[/tex] because 1 2. [tex]y = z[/tex] because 1 2. Therefore [tex]x + z = 180[/tex] so co-interior angles add up to 180°. Options for 1: - angles on a straight line - angles around a point - angles in a triangle - vertically opposite angles - corresponding angles - alternate angles Options for 2: - are equal - add up to 180° - add up to 360°

📝 Answered - 1. What is the domain of the function [tex]$f(x)=\sqrt{x}$[/tex]? 2. What is the range of [tex]$f(x)=e^x$[/tex]?

📝 Answered - How many 5-digit odd numbers can be formed using the digits 3, 4, 5, 6, 7, 8 if: i) Repetition of digits is not allowed? ii) Repetition of digits is allowed?

📝 Answered - Polynomials with 4 Terms 9) [tex]f(x)=x^3+2 x^2+5 x+10[/tex] A) [tex]f(x)=(x+2)(x^2+5)[/tex] B) [tex]f(x)=(x+2)(x^2+7)[/tex] C) [tex]f(x)=(x+1)(x^2+5)[/tex] D) [tex]f(x)=(x+2)(2 x^2+5)[/tex] E) [tex]f(x)=x(x^2+5)[/tex] 10) [tex]f(x)=x^3-3 x^2+5 x-15[/tex] A) [tex]f(x)=(x-3)(x^2+4)[/tex] B) [tex]f(x)=(x+4)(x^2+5)[/tex] C) [tex]f(x)=(x-3)(x^2+3)[/tex] D) [tex]f(x)=(x-3)(x^2+6)[/tex] E) [tex]f(x)=(x-3)(x^2+5)[/tex]

📝 Answered - Design your own equations (two for each) on associative, commutative, and distributive properties and give solutions to each. Explain each step of your solution clearly to an Intermediate Phase learner so they can understand.

📝 Answered - Using all the given digits and without repeating any of the digits, make the smallest and greatest number. a) $3,5,1,3,0$ b) $2,6,9,1,7$

📝 Answered - Find the equilibrium point of the demand and supply equations. [tex]\begin{array}{cl}\text { Demand } & \text { Supply } \\p=110-0.05 x & p=65+0.1 x \\(x, p)=(\square) &\end{array}[/tex]

📝 Answered - The function [tex]$D(t)$[/tex] defines a traveler's distance from home, in miles, as a function of time, in hours. [tex]$D(t)=\left\{\begin{array}{cl} 300 t+125, & 0 \leq t<2.5 \\ 875, & 2.5 \leq t \leq 3.5 \\ 75 t+612.5, & 3.5\end{array}\right.$[/tex] Which times and distances are represented by the function? Select three options. A. The starting distance, at 0 hours, is 300 miles. B. At 2 hours, the traveler is 725 miles from home. C. At 2.5 hours, the traveler is still moving farther from home. D. At 3 hours, the distance is constant, at 875 miles. E. The total distance from home after 6 hours is [tex]$1,062.5$[/tex] miles.

📝 Answered - What is the slope of a line that is perpendicular to the line [tex]$2 y-3 x=8$[/tex]?