Determine the student's Level of Van Hiele Model of Geometric Thought based on the response given. For example: Is the student at Level 1 (Basic Level): Visualization, Level 2: Analysis, Level 3: Informal Deduction, Level 4: Formal Deduction, or Level 5: Rigor? Explain your decision.

Miss Gonmez gave her students a paper polygon and asked them to identify the given shape and explain how they decided which polygon it was.

James responded that the shape was a rectangle. He decided this because he folded the polygon in half length-wise and found that it had opposite sides the same length.

He compared the corners of the polygon by placing them on top of each other and found they were all the same. He concluded they must all be right angles.

A land surveyor places two stakes 500 ft apart. He locates the midpoint between the two stakes and creates a perpendicular to the line that connects these two stakes. He needs to place a third stake 100 ft away along this perpendicular line. To apply the Perpendicular Bisector Theorem, the land surveyor would need to identify

  the location of the third stake as equidistant from the original two stakes

the location of the third stake as closer to one of the original two stakes

a line parallel to the line connecting the two stakes

a line congruent to the line connecting the two stakes

Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $3.00. Also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day. Because of a backlog of orders for model A grates, Kane's manager had decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit?

How many 5-card hands have at least one pair?

Chloe is buying souvenirs on vacation. She wants to spend 70 dollars at most, but only has 60 cubic inches of space available in her luggage. If bracelets cost 7 dollars and take up 3 inches of space and t-shirts are 5 dollars but take 15 inches of space, write and graph a system of four inequalities that model Chloe's possible purchases.Let x=the number of bracelets and y=the number of t-shirts. Use a scale of 2 on both axes.

So my inequalities are as follows: x >= 0
y >= 0
7x+5y<=70
3x+15y<=60

Can you please check if my inequalities are correct and show me how to graph them? Thanks!

a) For the following polynomial; a. Use the Rational Zero Test to list all possible rational roots b. Use Descartes Rule of Signs to provide the possible numbers of positive and negative real roots c. Factor the polynomial completely. ? 3 + 4? 2 + 9? + 36

b) For the following polynomial; d. Use the Rational Zero Test to list all possible rational roots e. Use Descartes Rule of Signs to provide the possible numbers of positive and negative real roots f. Factor the polynomial completely. ? 4 + 3? 3 − 7? 2 − 27? − 18

75 million people died in World War 2 spread over 6 years. Right now in the World 13 000 people have died due to the pandemic. If the doubling time is 5 days (many people think it will decrease to 3 days) how long before the death toll will be greater than World War 2?

For the following exercises, assume α is opposite side a,β is opposite side b, and γ is opposite side c. Determine whether there is no triangle, one triangle, or two triangles. Then solve each triangle, if possible. Round each answer to the nearest tenth.

1) α=119°,a=14,b=26

2) a=7, c=9,  α= 43°

Use the given conditions to write an equation for the line in​ point-slope form and in​ slope-intercept form.

Passing through (-2,-5) and parallel to the line whose equation is y=-4x+2

There are 2 different catalogs sent to customers. One of the catalogs costs 50 cents to make and is 50 pages long. The conversion rate for the catalog is 5% and each customer brings in 315 dollars. The second catalog costs 95 cents to make, is 100 pages long and each customer brings in 300 dollars from it. The profit margin is 30%. What should the conversion rate for the second catalog be to make at least the same amount of profit as the first one.

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?