August 2016 Common Core Algebra 1 Regents, Part 1

What follows is a portion of the Common Core Integrate Algebra exam. Other parts will be posted on other days. Illustrations will be added at a later time when they become available.

Part II is available here.
Parts III & IV are available here.

August 2016 Algebra Regents, Part I

1. The graph below shows the distance in miles, m, hiked from a camp in h hours.
Which hourly interval had the greatest rate of change?

(1) hour 0 to hour 1. The line is the steepest between 0 and 1 hour, which means is has the greatest slope, or the greatest rate of change. In the first hour, 2 miles were hiked, then only 1.5 miles, then 1 mile, then 0.5 miles. In the last hour, the hikers did not move away from camp at all.

2. The solution of an equation with two variables, x and y, is

(3) the set of all ordered pairs, (x, y), that make the equation true. That's the definition of a solution to an equation. It is not about solving for the zeroes, as in choices (1) and (2).

3. Which statistic can not be determined from a box plot representing the scores on a math test in Mrs. DeRidder's algebra class?

(4) the score that occurs most frequently. You cannot tell the mode from a box plot (also known as a box and whisker plot). You can only see the quartiles, including the minimum, median and maximum.

4. Which chart could represent f(x) = -2x + 6?

(4). You don't need to calculate anything. You can figure this one out logically. When x = 0, f(x) must equal 6. Only choices (1) and (4) have (0, 6) for (x, f(x)). The rate of change is -2, but choice (1) has a positive rate of change, so it is incorrect. Choice (4) is the only one left.

If you put y = -2x + 6 into your graphing calculator and check the table, you will see that (4) has the correct ordered pairs.

5. If f(n) = (n - 1)² + 3n, which statement is true?

(2) f(-2) = 3. You can skip (1) because in this function a positive number can't give a negative result. (-2 - 1)² + 3(-2) = (-3)² - 6 = 9 - 6 = 3.

6. The table below shows 6 students' overall averages and their averages in their math class.
If a linear model is applied to these data, which statement best describes the correlation coefficient?

(2) It is close to 1. You don't need to put this in your calculator. (You could if you truly weren't sure. When the top row is higher, the bottom is higher. When it is lower, the bottom is lower. There is a positive correlation, so choices (1) and (3) are out. Furthermore, the pairs are very close together, suggesting a strong correlation, which means that it would be closer to 1 than it would be to 0.5.

7. What is the solution to 2h + 8 > 3h - 6?

(1) h < 14.
Subtract 2h from both sides, you get 8 > h - 6
Add 6 to each side, you get 14 > h
Turn it around, h < 14

8. Which expression is equivalent to 36x² - 100?

(2) 4(3x + 5)(3x - 5). You can tell by looking at it that it will be a Difference of Squares problem because it has no middle term. That means that the two factors will be conjugates; that is, the binomials will be the same except that one will have addition and one will have subtraction. That difference is what causes the middle terms to cancel out. So (1) and (3) are immediately eliminated.

3x times 3x is 9x², which when multiplied by 4 has a product of 36x², as given in the question. However, 9x times 9x is 81x², which is already too big. Choice (4) is eliminated.

9. Patricia is trying to compare the average rainfall of New York to that of Arizona. A comparison between these two states for the months of July through September would best be measured in

(3) inches per month. This is a strange question. It assumes you know something about rainfall in Arizona. (Because it is a New York state exam, it's fair to assume that you know something about the rainfall in New York -- you live here.)

There isn't a lot of rainfall in Arizona, even when there may be in New York. Measuring the rainfall by the hour is just silly -- it doesn't rain for that many hours in an entire summer, so the ratio would be a tiny, tiny decimal. Rain, like snow, is usually measured in inches, not feet. It is not uncommon to hear forecasts of 10-14 inches of snow, as opposed to 1-2 feet of snow. Even when talking about the entire accumulation for the season, you are more likely to hear, say, 24 inches, rather than 2 feet.

So for a bunch of reasons, a few actually having to do with math, the best answer is inches per month.

10. Which function defines the sequence -6, -10, -14, -18, ..., where f(6) = -26?

(1) f(x) = -4x - 2. The sequence is going down by four. Only one choice, (1), has -4x in it.
Check: -4(6) - 2 = -24 - 2 = -26. Yes.

11. Which function has the greatest y-intercept?

(4) (the graph). The y-intercept of the graph is 5. In choice (1), 3(0) = 0, which is less than 5. In choice (2), if 2(0) + 3y = 12, then y = 4, which is less than 5. In choice (3), if there is a point on a line at (1, -4) and the slope is 2, then subtract 2 from the y value and you find that the line crosses the y-axis at (0, -6), which is less than 5.

12. What is the product of 2x + 3 and 4x² - 5x + 6?

(3) 8x³ + 2x² - 3x + 18. Notice that the first and last terms are the same for all four choices, so we don't have to worry about those.

(2x)(-5x) = -10x² and (3)(4x²) = 12x², -10 + 12 = -2. so we can eliminate choices (1) and (2).

(2x)(6) = 12x and (3)(-5x) = -15x, 12 - 15 = -3. So the choice is (3).

13. The height of a rocket, at selected times, is shown in the table below.

Based on these data, which statement is not a valid conclusion?

(3) The rocket was in the air approximately 6 seconds before hitting the ground. It was still above the ground after 7 seconds. The other choices give information that can be found in the table. It was at 180 feet at 0 seconds (launch); it hit is maximum at 3 seconds; it was above the 300 feet for 2 seconds from about t = 2 to t = 4.

14. A parking garage charges a base rate of $3.50 for up to 2 hours, and an hourly rate for each additional hour. The sign below gives the prices for up to 5 hours of parking.
Which linear equation can be used to find x, the additional hourly parking rate?

(3) 2x + 3.50 = 14.50. Four hours cost $14.50, which is the first 2 hours plus 2 additional hours. The first 2 hours = $3.50 and the additional 2 hours are 2x.

Note that this is just one possible equation. A simpler equation would've been x + $3.50 = 9.00, but that was not an option.

15. Which function has a constant rate of change equal to -3?

(4) 2y = -6x + 10. Put the equation into slope-intercept form by dividing both sides by 2, and you get y = -3x + 5, which has a slope (rate of change) of -3.

In choice (1), the rate of change is increasing. In choice (2), the slope is -2. Choice three is not a linear function, so it does not have a constant rate of change, even though the change from x = 1 to x = 2 is, in fact, -3, but this does not continue.

16. Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought?

(3) 12x - 24 = 60. If x is the number of boxes, then 12x is the number of cookies altogether. If she kept 2 boxes, then she took away 24 cookies leaving 60.

17. The table below shows the temperature, T(m), of a cup of hot chocolate that is allowed to chill over several minutes, m.
Which expression best fits the data for T(m)?

(1) 150(0.85)^m. The hot chocolate is getting cooler, and the temperature is getting lower. Therefore, the base must be less than one (exponential decay), so choices (2) and (4) are out. If m = 0, then 150(0.85)₀ = 150(1) = 150, which fits the table. The correct choice is (1). In choice (3), m - 1 would give an exponent of -1, which would actually increase the temperature at m = 0.

18. As x increases beyond 25, which function will have the largest value?

(1) f(x) = 1.5^x. Exponential functions with bases greater than 1 will climb higher at a faster rate than quadratic or cubic functions. You can put all four of these functions in your calculator and see the results for 25 and greater.

19. What are the solutions to the equation 3x² + 10x = 8?

(1) 2/3 and -4. You can enter y = 3x² + 10x - 8 into your calculator and search for the zeroes of the function. Or you can check the numbers 2, -2, 4, and -4, in whatever order you like, to see which one makes the equation true. Because no number repeats, you don't need to worry about substituting the fractions into the equation.

20. An online company lets you download songs for $0.99 each after you have paid a $5 membership fee. Which domain would be most appropriate to calculate the cost to download songs?

(2) whole numbers greater than or equal to one. Rational numbers include fractions, and you can't download half a song (realistically, and financially, speaking). Integers less than zero are negative, which is also impossible. Whole numbers less than or equal to one means 1 and 0, only, which means you could only download at most 1 song ever.

21. The function f(x) = 3x² + 12x + 11 can be written in vertex form as

(3) f(x) = 3(x + 2)² - 1. Once again, you can put all the functions in your calculator and see which two are the same. You can save a little work if you realize that you need to divide 12 by 3 before you halve it -- so the parentheses have to say "(x + 2)" not "(x + 6)", and you can eliminate choices (1) and (2).

There is a quicker way for this particular problem if you see the relationship in the numbers -- but that is something you develop from doing a bunch of these kinds of problems, so I'll do the longer way first.

f(x) = 3x² + 12x + 11, subtract 11 from both sides
f(x) - 11 = 3x² + 12x, factor the 3 on the right side
f(x) - 11 = 3(x² + 4x), half of 4 is 2, (2)² = 4, (3)(4) = 12
.... so add 12 to both sides of the function
f(x) + 1 = 3(x² + 4x) + 12, divide the 12 by 3 to get +4 inside the parentheses to complete the square
f(x) + 1 = 3(x² + 4x + 4), factor the polynomial into a binomial squared
f(x) + 1 = 3(x + 2)², subtract 1 from both sides to isolate f(x)
f(x) = 3(x + 2)² - 1.

My "shorter" method comes from recognizes that 3 goes into 12 and if you add 1 more to 11 you get 12. If you factor 3 from 3x² + 12x + 12, you get 3(x² + 4x + 4), which you should recognize as the perfect square of (x + 2). And because 1 was added, 1 has to be subtracted from the final expression.

22. A system of equations is given below.

x + 2y = 5
2x + y = 4 Which system of equations does not have the same solution?

(4) x + 2y = 5, 4x + 2y = 12. If you double the second equation, you should have 4x + 2y = 8, not 12. In the other three choices, one of the equations is multiplied correctly.

23. based on the graph below, which expression is a possible factorization of p(x)?

(1) (x + 3)(x - 2)(x - 4). There are three zeroes, so there are three factors, eliminating choices (3) and (4). The zeroes are -3, 2, and 4, so the factors are the opposites (x - (-3)), (x - 2), (x - 4).

24. Milton has his money invested in a stock portfolio. The value, v(x) of his portfolio can be modeled with the function v(x) = 30,000((0.78)^x, where x is the number of years since he made his investment. Which statement describes the rate of change of the value of his portfolio?

(2) It decreases 22% per year. The base is less than 1, so it is decay, decreasing. The rate it is decreasing is 1.00 - .78 = .22. Each year, he loses 22% of his money, and still has 78% of it remaining.

To be edited so I can add all of the images as time permits.

END OF PART I

How did you do? Any questions?

The Interview

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(C)Copyright 2016, C. Burke.

There was a shortage of teachers. There was an excess of teachers. There were positions to fill. There were no openings.

Basically, there are lousy schools no one wants to be at, and great schools no one would want to leave. There are schools that do things by the book. There are schools that play games with the books.

I thought about doing another Big Back-To-School Production Number, but there are a couple of problems

1. I need to think of a good one that's recognizable, or easily referenced
2. I need time to write the words for the lyrics
3. I need time to create (or find) artwork to support it
4. I usually need to edit them down to a manageable size
5. And I have to start thinking about all of that long before I actually do start thinking about all of that.

Good luck to all the teachers going back, or who have already gone back. Have a great year!




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August 2016 Common Core Algebra 1 Regents, Parts 3 and 4

What follows is a portion of the Common Core Integrate Algebra exam. Other parts will be posted on other days. Illustrations will be added at a later time when they become available.

Part II is available here.

August 2016 Algebra Regents, Part III

33. The data table below shows the diameter of grains of sand and the slop of the beach for 9 naturally occurring ocean beaches.
Write the linear regression equation for this set of data, rounding all values to the nearest thousandth.

Using this equation, predict the slope of a beach, to the nearest tenth of a degree, on a beach with grains of sand having a median diameter of 0.65 mm.

First, a naturally occurring ocean beach is one that isn't artificial or man-made. The sand comes onto the shore because of nature. This is not important for solving the problem, but don't let it throw you if you don't know what it is.

Second, I cannot stress this enough, if you do not round everything correctly, you will lose 1 of the 3 points for a -- yes, I will go there -- STUPID reason. "Nearest thousandth" means three decimal places.

Put the data into LISTs on the graphing calculator. Put the x values in L1 and the y values in L2. Double check your values, making sure you have all of them entered correctly, and that the x and y values match those on the table. (If you switch two x values without also switching the y values, you will get the wrong answer. It's like you mixed up coordinates!)

Press STAT. Right arrow to CALC. Press 4 for LinReg(ax + b)4. Hit Enter. (Depending upon your calculator's operating system, you may have to hit Enter again.)

You should get the following:
y=ax+b
a=17.15936928
b=-2.475925196

33. Shawn incorrectly graphed the inequality -x - 2y > 8 as shown below.

Explain Shawn's mistake.
Graph the inequality correctly on the set of axes below.

Shawn shaded the graph incorrectly. If you pick (0, 0) as a test point,
-(0) - 2(0) is not greater than or equal to 8, 0 < 8. He should have shaded below the line.

One possible error, but we cannot be sure of this because we don't have his work, is that Shawn forgot to flip the sign when rewriting the equation in slope-intercept form when he divided by -2.

You can graph the equation either by finding the x-intercept and the y-intercept or by rewriting the equation in slope-intercept form, which can then be put in your calculator.

If -x - 2(0) = 8
the -x = 8
and x = -8, so there is a point at (-8, 0)

If -(0) - 2y = 8
the -2y = 8
and y = -4, so there is a point at (0, -4)

Draw a solid line. That includes these points. The slope is down 4, right 8, which is -4/8 or -1/2.

Checking a test point, (0, 0), which is not on the line, we can see (as mentioned above) that (0, 0) is NOT a solution to this inequality, so it cannot be in the shaded region. That means that the other side of the graph, below the line, needs to be shaded. You can check this by picking another point, say (0, -10).

-(0) - 2(-10) > 8?
0 + 20 > 8?
20 > 8. Check.

Your graph should like as follows:

35. A drama club is selling tickets to the spring musical. The auditorium holds 200 people. Tickets cost $12 at the door and $8.50 if purchased in advance. The drama club has a goal of selling at least $1000 worth of tickets to Saturday's show.

Write a system of inequalities that can be used to model this scenario.

If 50 tickets are sold in advance, what is the minimum number of tickets that must be sold at the door so that the club meets its goal? Justify your answer.

Let x be the number of advance-sale tickets, and let y be the number of at-the-door tickets. The total number of tickets must be less than or equal to 200 people.

So x + y < 200.

The amount of money raised by selling x advance tickets is $8.50x. The amount of money raised at the door is $12y. The total of these two amounts needs to be more than $1000.

So 8.50x + 12.00y > 1000

That is your system of inequalities.

If 50 tickets are sold in advance, then the second inequality becomes

8.50(50) + 12.00y > 1000
425 + 12.00y > 1000
12.00y > 575
y > 47.9166666...

So y has to be 48 or higher. Therefore, the minimum number of tickets sold at the door is 48.

Pointswise: if you had the correct system of inequalities, you scored 2 points, 48 was worth another point, and the work to justify 48 is the final point.

36. Janice is asked to solve 0 = 64² + 16x - 3. She begins the problem by writing the following steps:

Line 1 0 = 64² + 16x - 3
0 = B² + 2B - 3
0 = (B + 3)(B - 1)
Use Janice's procedure to solve the equation for x.

Explain the method Janice used to solve the quadratic equation.

Janice simplified the problem by substituting the letter B in place of 8x, which is a factor of both 64x² and 16x.
(8x)² = 64x² and 2(8x) = 16x. These substitutions will give you the original equation back.

Following Janice's logic:
B + 3 = 0 or B - 1 = 0
So B = -3 or B = 1
However, B = 8x
So 8x = -3 or 8x = 1
Therefore x = -3/8 or x = 1/8.

If you didn't do this kind of substitution, you likely would have been forced to use the Quadratic Formula to solve this equation, and there would have been BIG numbers to worry about.

If you solved it using another method, you lost a point.

August 2016 Algebra Regents, Part IV

37. For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15. 76.

Write a system of equations to represent the costs of a juice box,j, and a bottle of water, w.

Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have cost 33 cents each. Use your system of equations to justify that Kara's prices are not possible.

Solve your system of equations to determine the actual cost, in dollars, of each juice box and each bottle of water.

The first part is a straightforward system of equations, similar to the inequalities we did in the earlier problem.

The equations are

18j + 32w = 19.92
14j + 26w = 15.76

To show that Kara is incorrect, substitute 52 for j and 33 for w in BOTH equations.

18(.52) + 32(.33) = 19.92?
9.36 + 10.56 = 19.92 (check)

14(.52) + 26(.33) = 15.76?
7.28 + 8.58 = 15.76?
15.86 =/= 15.76 (does not check)

For the correct solution, you need to find the least common multiple of 14 and 18. (Yes! I hate the numbers in this problem!) The LCM is 126.

You need to multiply the first equation by 7, and the second equation by -9.

126j + 224w = 139.44
-126j - 234w = -141.84
add the equations
-10w = 2.40
w = .24.
A bottle of water = $.24.

14j + 26(.24) = 15.76
14j + 6.24 = 15.76
14j = 9.52
j = .68
A bottle of juice = $.68.

Partial credit would be given. A computational error would cost one point. Two or more computational errors would cost 2 points.

END OF PARTS III and IV

How did you do? Any questions?

August 2016 Common Core Algebra 1 Regents, Part 2

What follows is a portion of the Common Core Integrate Algebra exam. Other parts will be posted on other days. Illustrations will be added at a later time when they become available.

August 2016 Algebra Regents, Part II

25. Graph the function y = -SQRT(x + 3) on the set of axes below.

Put the equation into a graphing calculator, or make a table of values. The negative sign tells you that the graph will be inverted (upside down). The +3 under the radical sign tells you that the graph will shift three spaces to the left. Any value of x that results in a negative number under the radical can be ignored -- those values are NOT in the domain of this function. The smallest possible values is -3 because -3 + 3 = 0, and the square root of 0 is 0.

Your graph should look like the one below. Be sure to graph the following points: (-3, 0), (-2, -1), (1, -2) and (6, -3).

26. Richard is asked to transform the graph of b(x) below.

The graph of b(x) is transformed using the equation h(x) = b(x - 2) - 3. Describe how the graph of b(x) changed to form the graph of h(x).

The -2 inside the parentheses will shift the graph two places to the right. The -3 outside the parentheses will shift the graph three places down.

So the point (0, -2) will shift to (2, -5).

27. Consider the pattern of squares below

Which type of model, linear or exponential, should be used to determine how many squares are in the nth pattern? Explain your answer.

The first pattern has 2 squares, the next has 4, the one after has 8. The rate of change is not constant, so it is not linear. However, there is a constant ratio, each pattern is twice as big as the one before it, so the pattern is exponential.

You didn't need to give the function but it would be something like f(n) = 2ⁿ.

28. When multiplying polynomials for a math assignment, Pat found the product to be -4x + 8x² - 2x³ + 5. He then had to state the leading coefficient of this polynomial. Pat wrote down -4. Do you agree with Pat's answer? Explain your reasoning.

First, a reminder: You will NOT score a point for answering just "Yes" or "No" to any question like this. HOWEVER, you WILL LOSE a point if you don't include "Yes" or "No" in the answer. In this case, the answer is "No".

The leading coefficient is the coefficient of the term with the highest exponent because in standard form the term with the highest exponent comes first, and then the term with the second highest, etc.

In standard form, this expression is -2x³ + 8x² - 4x + 5. Note that the sign goes with the term the follows it. Also, for clarity when reading, the negative in front of the 4x became a minus sign. It could have been written as + (-4x). Likewise, the minus in front of 2x³ became a negative sign for the same reason.

The leading coefficient for this expression is -2.

For full credit, answer "No, I don't agree" and explain that in standard form the term with the highest coefficient is the leading term, so the leading coefficient is "-2" because -2x³ is the term with the highest coefficient.

29. Is the sum of 3*SQRT(2) and 4*SQRT(2) rational or irrational? Explain your answer.

Sorry for the lack of radical signs on my keyboard.

Each of the two expressions is irrational because they cannot be written as fractions. The sum of two positive irrational numbers is always irrational.

I added positive because there is one exception to the rule that the sum of two irrational numbers is always irrational: if the numbers are opposites, then the sum is zero, which is rational. But it is obvious that they are not opposites.

Another way to state it is that the sum of the two numbers is 7*SQRT(2), which is irrational because the product of a rational number and an irrational number is irrational.

Sue wrote her answer in point-slope form and Kathy wrote her answer in slope-intercept form. However, you still have to prove that they both have the correct answer. You can calculate that the slope is (4 - 1) / (-3 - 6) = 3 / (-9) = -1/3, which is in both equations.

Sue used the slope -3 and the point (-3, 4) to write her equation.
If you distribute the (-1/3) on the right side, and then add 4 to both sides to isolate the y, you will get Kathy's equation.

If this didn't occur to you, but you checked both points in both equations and found out that they all worked, you should get full credit.

30. The graph below shows two functions, f(x) and g(x). State all the values of x for which f(x) = g(x).

-3 and 1.

Do not give the points of intersection. They are only asking for the x values.

I'll be honest with you: I don't like this question. It feels like they should be asking for more, but they aren't. They only want the two x-values, and each one is worth 1 point.

If you give the coordinates you lose a point. So if your entire answer is (1, 3), you scored zero.

31. Find the zeros of f(x) = (x - 3)² - 49, algebraically.

You can put this in your graphing calculator to find the answers in advance, if you like. And those answers will be worth 1 of the 2 points.

Algebraically, set the function equal to 0:

(x - 3)² - 49 = 0
(x - 3)² = 49
take the square root of both sides -- don't forget to use +/-
x - 3 = +/- 7
split the equation into two parts to finish, one with +, one with -
x - 3 = 7 or x - 3 = -7
x = 10 or x = -4

32. Solve the equation below for x in terms of a.

4(ax + 3) - 3ax = 25 + 3a

Solve for x in terms of a means that you have to isolate x on the left side of the equation and have the numbers, operations and the letter a on the right side. You will not get a numeric answer.

4(ax + 3) - 3ax = 25 + 3a
4ax + 12 - 3ax = 25 + 3a
ax + 12 = 25 + 3a
ax = 13 + 3a
x = (13 + 3a)/a

Do NOT cancel out the "a" characters. You can't; it doesn't work like that.

END OF PART II

How did you do? Any questions?

I hope you did well because, overall, they weren't difficult question (in my opinion). They could have been a little trickier, even for just two points.

(x, why?) Mini: Hot and Cold

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(C)Copyright 2016, C. Burke.

Sitting next to a four-year-old on long trips really can run hot and cold.

We did visit a coal mine in West Virginia, by the way.




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(x, why?) Mini: Under the Sci...

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(C)Copyright 2016, C. Burke.

I prefer to apply Sturgeon's Law to all webcomics, not just to the 1100+ I've written.

By the way, I was just at a Sweet 16 party with an "Under the Sea" theme for the daughter of a couple of friends who go back to my Brooklyn College Science Fiction Society days, which may have played a role and bringing this back to the forefront of my brain.




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Hypersphere

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(C)Copyright 2016, C. Burke.

RIP2-D2

I was considering this months ago, but because I wanted to do it in a classroom setting and didn't have time before the end of the year, I was saving it for the fall.

However, with the passing of Kenny Baker, the man inside the droid we were looking for, I moved it up and reworked it.

For the record, the Volume inside a 4D hypersphere would be 1/2 * pi^2 * r^4.

Edit Wayne's first dialogue balloon is messed up. Two sentences were combined by accident. It will be corrected as time permits. Oopsie!




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(x, why?) Mini: Kites

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(C)Copyright 2016, C. Burke.

Actually, we went South on vacation, not North.

Throwback Thursday: I used a PC with Windows XP and Paint 5.1 to create this one. You use the tools you have not the tools you wish you have.

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(x, why?) Mini: Slugger

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(C)Copyright 2016, C. Burke.

It's all a matter of momentum and position and energy and ... stuff.

Okay, so, no, I'm really not sure how to explain it, so I'll recommend that you check out a wiki page on Liouville equations.

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Daily Regents: Similar Triangles are Proportional (August 2015)

Even though the title says "Daily", I won't be doing them daily any more, until the exams get closer. But they will be frequent.

Geometry, August 2015, Question 27

27. To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram.

Use the surveyor’s information to determine and state the distance from point B to point C, to the nearest yard

There are two right triangles. Right angles are congruent.
Both triangles contain angle A. Reflexive Property says angle A is congruent to itself.
Therefore, triangle ABC ~ ADE
If the triangles are similar, then their corresponding sides are proportional.

AE = 230, AC = 230 + 85 = 315. DE = 120. BC corresponds to DE.

Set up a proportion: AE / DE = AC / BC
230/120 = (230 + 85) / x
230 x = (120)(315)
230 x = 37800
x = 164.3478...
x = 164 yards

The distance from point B to point C is 164 yards.

Prove You're Not a Robot

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(C)Copyright 2016, C. Burke.

When we have to bow down to our Computer Overlords, someone will have to answer for this!

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(x, why?) Mini: Now Playing . . .

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(C)Copyright 2016, C. Burke.

They're here to restore Order to your Operations!

But are some operations too powerful?




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