6) The product of two numbers is equal to 192. Find values for these numbers such that the sum is minimal.

Q: Solve the following inequality graphically in two-dimensional plane:y < – 2

A: We first draw y=-2 line

Q: A pool is 50 meters long and 15 meters wide. if it is to be filled with water to a uniform depth of…

A: Volume of a pool

Q: I have 250 unique pairs of socks. If I want to have a pair of socks, what is the minimum number of…

A: Matching Pair: A matching pair is an experimental design where objects having the same…

Q: Q2: The plane is divided into a finite number of regions by drawing infinite straight lines in an…

A: Let n denote number of lines drawn on plane. We will prove the result with the help of mathematical…

Q: The numbers 1, 2, ... 10 are written in a row. Is it possible to put signs - and + between them so…

A: We know that the sum of all the numbers from 1 to 10 is 55

Q: Find proj, u and scalyu by inspection without using formulas. 10- projyu = 6- 4- 2- -10-8-6-4 2 -2-…

A:

Q: find Len th of avectors 2く3,-S,\> D=くW5> ビ,37 andd And Draw the coordinates for each point

A:

Q: Provide solution from the given problem on Pigeonhole Principle. Problem: In a room of 499 people,…

A: The given problem is: In a room of 499 people, there exist two who share a birthday.

Q: When 5 is added to natural number n it gives a perfect square and when 11 is subtracted from n it…

A: When 5 is added to natural number n it gives a perfect square and 11 is subtracted from n it also…

Q: 5. Assume that each scoop can only hold a maximum of 8 pieces and a minimum of 2. How many ways are…

A:

Q: A 6x 6 square is tiled by 2x 1 dominoes. Prove that it has at least one fault-line, that is, a…

A: Consider a 6×6 square which is tiled by 2×1 dominoes. Suppose the 6×6 square has no fault lines.…

Q: Suppose you must use 1x“-tile and 10 x-tiles. You only have up to 15 1-til use. How many of the…

A: Introduction: A rectangle is a quadrilateral with equal angles and opposite sides that are equal and…

Q: Find the equation of the line through P = (4, 12) such that the triangle bounded by this line and…

A:

Q: A cube has four diagonals. Show that no two of them are perpendicular.

A: Given: A cube has four diagonals.

Q: Suppose that two nondimensional quantities are exactly A chapter, express the four quantities (A+B),…

A: Given,          A=8.73       3 siginficant figuresB=1.389     4 siginficant figures

Q: In a city each person earns at most $5000 per month and every house is occupied by at most five…

A: HERE Given  Maximum earnings of of person = $5000 Maximum person in one one house= 5

Q: When I arrange the members of a marching band in rows of 2, 3, or 4, there is always 1 person left…

A: To solve the given problem

Q: Suppose the schedule at Pierce University has x mathematics courses and y computer science courses.…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: The lengths of the sides of a triangle are 5, 6. and x. Then x must begreater than ____ and less…

A: Using the triangle side inequality, the sum of two sides of the triangle should be greater than the…

Q: Hew.b prove that CAXB)-Ais atways-Zero

A: Topic:- vector  algebra

Q: What is the sum of all critical numbers of 8 (x) =x*– 14x2+ 24x +27

A:

Q: Prove analytically that the sum of the squares of the four sides of a parallelogram is equal to the…

A: Apollonius's theorem   for triangle ABC with M being the midpoint of BC, the following equation…

Q: Suppose than an open box is to be made from a square sheet of cardboard by cutting out 3-inch…

A:

Q: Assume that a circular pizza is being cut into pieces. If there are C cuts and I points of…

A: It is a counting problem .

Q: Find the intersection of the lines 2 x space plus space 3 y space equals space minus 7 and 3 x space…

A: From the given statement the lines are 2x +3y = -7 and 3x - 2y = 9.Solving the equations as follows.

Q: When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the…

A:

Q: y is a positive integer. If x-(-y)=z, will z be greater than or less than x?

A: Here we have the relation z=x+y. and y is always a positive integer.  So z is always greater than x.

Q: 19. The sum of 3 real numbers is known to be zero. If the sum of their cubes is e™, what is their…

A: Solve #19

Q: 4. The sum of two consecutive even integers is less than 55 but greater than 21. Find at least 3…

A: Given that the sum of two consecutive even integers is less than 55 but greater than 21. We have to…

Q: I have a rectangular carton filled with Each of my 6 friends can be assigned an equal number of…

A:

Q: A fence is composed of x posts, each of which is 4 cm wide. If there is 6 cm of space between each…

A: The solution is given below.

Q: Find all points where fex)= |21x-131 fails be be differenbiadle

A: Given:- f(x) = |21x-13| To find:- All points where function non differentiable

Q: Find the condition for the two lines to be coplanar. a1 + bjx + C7x + d, =0 = az + b2x + C2x + d2 az…

A: The given lines are    a1 +b1x+c1x+d1=0a2+b2x+c2x+d2=0a3+b3x+c3x+d3=0a4+b4x+c4x+d4=0  To examine…

Q: Let us assume that we have a small internet only consisting of four web pages: 2 4 An arrow from…

A: Solution

Q: 2) Prove by using the pigeonhole principle that among any 17 points in a square of side one there is…

A: Given: A square of side one contains 17 points. To show: There is at least a pair whose distance is…

Q: help!! the assignment is on quadrilaterals, similar triangles, and circles! I really need this…

A:

Q: Between the two sections of a math class, there are 24 students. Sometimes students like to study…

A: Pigeonhole principle: If there are n pigeons and m holes where m<n. Then at least two pigeons…

Q: 4. Assume that each scoop can only hold a maximum of 8 pieces. How many ways are there to sprinkle…

A:

Q: Show that if ƒ′′> 0 throughout an interval [a, b], then ƒ′ has at most one zero in [a, b] . What…

A: Given:

Q: Since a line segment is defined by two distinct points, therefore the total number of line segments…

A:

Q: Suppose you have 1000 blocks, each of which is 1.0 cm on a side. If all 1000 of these blocks are…

A: First consider the case of 1000 blocks stacked to give a cube 10 cm on a side. The block which have…

Q: To complement the other paintings, you can make a painting with different geometric shapes: Choose…

A: simply make drawing by assuming values corresponding to limits

Q: If the red triangle with a radius of 0.3 and the blue one with a radius of 0.15 find all angles and…

A:

Q: Prove that a quadrilateral with vertices J(2,-1), K(-1,-4), L(-4,-1) and M(-1, 2) is a square. 10 4…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: If x and y are positive numbers with x > y, show that a triangle with sides of length 2xy, x2-y2,…

A:

Q: Four consecutive positive integers are such that the smallest is a multiple of 5, the second is a…

A:

Q: Let S = {2x, 1 – x, x² + x – 1,x + 1,x – 2}. Then %3D P3 P2

A:

Q: The technique of boxing in a triangle and determing its area by using rectangle and right triangle…

A: Let ABC is triangle with vertices, Ax1,y1,Bx2,y2,Cx3,y3. WhereDx1,0, Ex2,0, Fx3,0 are points on…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.