I am submitting this for the second time, because the person that answered the first time definitely did not read my last two paragraphs. I need to DISCUSS, why the theorem works when adding a point D. I cannot draw a triangle and throw point D on it. I understand up to a certain point, but I have no idea what my professor is looking for in my answer. I have included her comments to hopefully help you help me. Thank you.

My question is based on the following:

Consider the axiomatic system and theorem below:

Axiom 1: If there is a pair of points, then they are on a line together.

Axiom 2: If there is a line, then there must be at least two points on it.

Axiom 3: There exist at least three distinct points.

Axiom 4: If there is a line, then not all of the points can be on it,

Theorem 1: Each point is on at least two distinct lines.

I have proven and understand up to 3 points, but I am struggling with explaining what happens with the 4th point.

If I use Axiom 3 to create 4th point D (the first 3 being A, B, and C), this will give me distinct lines AD, BD, CD, ADB, ADC, and BDC.

ADB, ADC, and BDC were all previously existing lines, and AD, BD, and CD are new lines, correct?

These are two separate cases because I cannot have point D on a previously existing line, and a new line, at the same time. I feel I understand up to this point. I need to discuss these two possibilities separately, but I am confused on how to go about that.

My professor states that I need to "discuss the different possibilities for how many distinct lines those are, we do not know if those are 3 distinct lines or not, this is where the different cases come in". I don't understand AT ALL what she is looking for.

Which of the following are linear transformations?

Choose Linear Not Linear  The function f:ℝ3→ℝ2 defined byf([x y z]^T)=[x−y 3y+z]^T.

Choose Linear Not Linear  The function a:ℝ→ℝ such that a(x)=(x−1)+(x−2)^2.

Choose Linear Not Linear  The function g:M2,2(ℝ)→M2,2(ℝ) defined by g(A)=2A+[1 2

3 4] Here, M2,2(ℝ)) is the vector space of 2×2matrices with real entries.

Choose Linear Not Linear  The function h:ℝ2→ℝ defined by h([xy])=x^2−y^2.

Express the point (10,20) as a convex combination of (0,0), (0,40), (20,20) and (30,30).

Please explain the "algorithm" on how to solve this type of problem.

(a) Calculate the five-number summary of the land areas of the states in the U.S. Midwest. (If necessary, round your answer to the nearest whole number.)

(b) Explain what the five-number summary in part (a) tells us about the land areas of the states in the midwest.

(c) Calculate the five-number summary of the land areas of the states in the U.S. Northeast. (If necessary, round your answer to the nearest whole number.)

(d) Explain what the five-number summary in part (c) tells us about the land areas of the states in the Northeast.

(d) Contrast the results from parts (b) and (d).

A company produces individual resistors and transistors as well as computer chips. Each set of resistors requires 2 units of copper, 2 units of zinc, and 1 unit of glass to manufacture. Each set of transistors requires 3 units of copper, 3 units of zinc and 2 units of glass. Each set of computer chips requires 2 units of copper, 1 unit of zinc, and 3 units of glass. If there are 150 units of copper, 110 units of zinc, and 160 units of glass available, how many sets of resistors, transistors, and computer chips should the company manufacture to use all of its available supplies or raw materials? how many resistors, transistors and computer chips?

Holly Krech is planning for her retirement, so she is setting up a payout annuity with her bank. She wishes to receive a payout of $1,700 per month for twenty years. (Round your answers to the nearest cent.)

(a) How large a monthly payment must Holly Krech make if she saves for her payout annuity with an ordinary annuity, which she sets up thirty years before her retirement? (The two annuities pay the same interest rate of 7.8% compounded monthly.) $

(b) How large a monthly payment must she make if she sets the ordinary annuity up twenty years before her retirement? $

Use a software program or a graphing utility to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x5 = t and solve for x1, x2, x3, and x4 in terms of t.) x1 − x2 + 2x3 + 2x4 + 6x5 = 16 3x1 − 2x2 + 4x3 + 4x4 + 12x5 = 33 x2 − x3 − x4 − 3x5 = −9 2x1 − 2x2 + 4x3 + 5x4 + 15x5 = 34 2x1 − 2x2 + 4x3 + 4x4 + 13x5 = 34 (x1, x2, x3, x4, x5) =

After a weekend of lucrative gigs, a singer finds herself with an extra $ 1,500. She currently has $4350 of credit card debt, on which she is charged an annual yield of 24%. Putting $1,500 toward this would cut that debt to $1,850. Calculate the annual rate of return if she does this. Round, if necessary, to the nearest 0.1%.

  Solve

a.      x + y = 3, 2x – y = 1

b.      3x + 2y = 6, x = 3

c.      2x + y = 4, y = -2x + 1

d.      x – 3y = 6, 2x – y =1

Question # 5
a. Briefly explain how the Bernoulli equation is derived. Discuss its application in oil / gas productions, including its limitation. [4 marks]
b. The water level in a tank shown in Figure Q5b is 20 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank cover is airtight, and the air pressure above the water surface is 4 atm gage. Assuming the system is at sea level, determine: [5 marks]
i. The maximum height to which the water stream could rise.
ii, If the water level in the tank was 15 m, would the maximum water rise at the nozzle increase? Justify with calculation. (4 marks]
iii. If the gauge pressure increases to 5 atm for 20 m water level, show the formula of finding water velocity at the nozzle exit. [4 marks] 4 atm 20 m Figure Q5b

Graph all vertical and horizontal asymptotes of the function.

f(x)=-4x+11/-2x+7

Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money?

First, determine what information you need to answer this question,

How much water does Janine drink in a day? She normally drinks 4 bottles a day, each 16.9 ounces.

How much does a bottle of water cost? She buys 24-packs of 16.9 ounce bottles for $3.79.

How much does a reusable water bottle cost? About $10.

How long does a reusable water bottle last? Basically forever (or until you lose it).

How much does a water filter cost? How much water will they filter?

A faucet-mounted filter costs about $28 and includes one filter cartridge. Refill filters cost about $33 for a 3-pack. The box says each filter will filter up to 100 gallons (378 liters)

A water filter pitcher costs about $22 and includes one filter cartridge. Refill filters cost about $20 for a 4-pack. The box says each filter lasts for 40 gallons or 4 months

An under-sink filter costs $130 and includes one filter cartridge. Refill filters cost about $60 each. The filter lasts for 500 gallons.

Which option is cheapest over one year (365 days)? Select an answer Water bottles faucet-mount filter filter pitcher under-sink filter  

The cheapest option saves her $ over a year?

Give your answer to the nearest cent. Pro-rate the costs of additional filters (so if you only use part of a filter, only count the corresponding fraction of the filter cost).

Write out the addition and multiplication tables for the ring Z₂[x]/(x^2 + x). Is Z₂[x]/(x^2 + x) a field?

The Sandersons are planning to refinance their home. The outstanding principal on their original loan is $120,000 and was to amortized in 240 equal monthly installments at an interest rate of 10%/year compounded monthly. The new loan they expect to secure is to be amortized over the same period at an interest rate of 7%/year compounded monthly. How much less can they expect to pay over the life of the loan in interest payments by refinancing the loan at this time? (Round your answer to the nearest cent.)
$

In the real vector space R ³, the vectors u1 =(1,0,0) and u2=(1,2,0) are known to lie in the span W of the vectors w1 =(3,4,2), w2=(0,1,1), w3=(2,1,1) and w4=(1,0,2). Find wi, wj ?{w1,w2,w3,w4} such that W = span({u1,u2,wk,wl}) where {1,2,3,4}= {i,j,k,l}.