Given a segment, construct its perpendicular bisector.

Given a line an a point, construct the perpendicular to the line through the point.

Given a line an a point not on the line, construct the parallel to the line through the point.

A company sells washing machines for $340 each. To produce a batch of n washing machines, there is a cost of $249 per washing machine and a fixed or setup cost of $14,600 for the entire batch. Determine a function that gives the profit in terms of the number of washing machines produced. What is the least number of washing machines the company can sell in order to have a profit of $14,000?

Prove that two quadrilaterals are congruent if a side, angle, side, angle, side of one are equal to the corresponding parts of the other, the five parts in each case being consecutive on the quadrilateral. (can you find a counter example if the quadrilaterals are not convex?)

A pizza pan is removed at 4:00 pm from an oven whose temperature is fixed at 450 F into a room that is constant 73 F. after 5 minutes, the pizza is at 300 F.
a)at what time is the temperature of the pan 125 F?
b) determine the time that needs to elapse before the pans is 180 degree .
c)what do you notice about the temperature as time passes?

Prove that (1,0, 0), (1,1,1), (1,2,3)) is linearly independent, and its span is R3.

1. For a map f : V ?? W between vector spaces V and W to be a linear map it must preserve the structure of V . What must one verify to verify whether or not a map is linear?

2. For a map f : V ?? W between vector spaces to be an isomorphism it must be a linear map and also have two further properties. What are those two properties? As well as giving the names of the properties, explain what the names mean.

3.Every linear transformation is an isomorphism, but the isomorphism f : x y ?? x y is not a linear transformation. Why

Below you are given the description of two quadrilaterals. On a piece of paper (labelled and in order), use the appropriate tools (straightedge, compass, etc.) to construct the described quadrilaterals and the perpendicular bisectors of each of their sides. After each construction, state why there is no circle that will circumscribe the quadrilateral. 1. a parallelogram that is not a rectangle 2. a non-isoceles trapezoid. There is no diagram.

let triangle ABC be a triangle in which all three interior angles are acute and let A'B'C' be the orthic triangle.

a.) Prove that the altitudes of triangle ABC are the angle bisectors of triangle A'B'C'.

b.) Prove the orthocenter of triangle ABC is the incenter of traingle A'B'C'.

c.) Prove that A is the A' -excenter of triangle A'B'C'.

Given A*B*C and A*C*D, prove the corollary to Axion B-4.

Prove the following problems using the complex plane model of Euclidean geometry, in the spirit of Erlangen Program: 1. Prove that the diagonals of a parallelogram bisect each other. 2. Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of all the sides of the parallelogram. 3. Prove the Cosine Law for triangles: In a triangle with the sides a, b, and c, the square of the side opposite C = is expressed as c2 = a2 + b2 - 2 b a cos . 4. Prove the theorem: The bisector of an angle of a triangle divides the opposite side into two segments which are proportional to the sides that include the angle.

Prove the following using the triangle inequality:

Given a convex quadrilateral, prove that the point determined by the intersection of the diagonals is the minimum distance point for the quadrilateral - that is, the point from which the sum of the distances of the vertices is minimal.

Plot the following parabolic functions in Excel and then answer the discussion question below . Use at least 8 points for each plot: Each graph is worth 15 points and must include 8 points. 1) y=x2-6x+8 2) y=x2+4 3) y=(-1/2)(x2) 4) What is the maximum number and the minimum number of x-intercepts for a parabola? Why? (15 points) In order to obtain full credit, you will need to plot the functions in Excel or using the Open Office feature and attach the results to your response.

Four people are using a voting weight system to make decisions. They have the weights of 7,5,4,and 2. They use a quota of 13. Compute the Banzhaf power index for the voter of weight 5.

1) Determine the two angles

sin(2θ)=0.9179.

2)Determine the solution sets

12cos^2θ=3

I have no idea of what is happening when the professor explains how they got the angles or soln sets, they automatically know what quadrant it is in and what angle it should be, and what the next angle(s), sets are. I cant imagine it. I don't know how they see that on the unit circle.

Suppose you have a piece of cardboard with length 32 inches and width 20 inches and you want to use it to create a box. You would need to cut a square out of each corner of the cardboard so that you can fold the edges up. But what size square should you cut? Cutting a small square will make a shorter box. Cutting a large square will make a taller box.

Since we haven’t determined the size of the square to cut from each corner, let the side length of the square be represented by the variable x. Write a simplified polynomial expression in x and note the degree of the polynomial for each of the following geometric concepts:

The length of the base of the box once the corners are cut out, the width of the base of the box once the corners are cut out, the height of the box, the perimeter of the base of the box, the area of the base of the box, the volume of the box.