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You'll have to explain what the & symbol represents. In logic and computer science there is a binary operator denoted & but I highly doubt it would be used with 3x and -3x.

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Since c < d, it follows c-d < 0, regardless of whether c and d are positive or negative. To rewrite with a positive exponent, we reciprocate it, yielding

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The rational expression is undefined when the denominator is zero and the numerator is non-zero (if we get 0/0 we say the expression is indeterminate). Here, we set r^2 - 64 equal to 0, which implies r^2 = 64, r = 8 or -8. In either case, the numerator is non-zero.

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5/7 = .7142857...

9/11 = .81818181...

We could just think of a random string of numbers and claim it is irrational. For example, we could say that .76395882019... is irrational because it is assumed to be non-repeating, and cannot be expressed as a ratio of integers.

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40 grams (after five seconds, one half-life has elapsed).

Fortunately, the half-life of unobtanium is longer than 5 seconds. Otherwise, Avatar's Hallelujah Mountains would become lose its magnetic fields (as unobtanium is theoretically a superconductor) and crash to the ground.

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If you buy the coupon book, you pay $26 but you save $1 for each ride. Hence, after 26 rides you will pay $26 and save $26, in which the total is the same.

You can also set it up as an algebraic equation, with "r" being the number of rides:

1.75r = 26 + .75r

r = 26

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Just use a unit multiplier. There are roughly 2.2 lb in one kilogram, so

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See my lesson on complementary and supplementary angles here:

http://www.algebra.com/algebra/homework/Angles/change-this-name27510.lesson

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90 - 20 = 70 degrees, the complement.

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What is "the graph to the right?"

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If you are talking about 340 = 2x + 2y, the problem won't be any different. Other than the fact that the variables are changed.

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You are correct in setting up the equation, and your final answer is correct; you probably typoed when you wrote "180 = 219" when it should be "180 = 219 - x." And the complement of 39 degrees is 90 - 39 = 51 degrees. You do not have to state the supplement or the complement for this problem.

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Because the height as a function of time is a quadratic, there can be two answers. The graph of the quadratic and the height h = 15 m intersect at two places, as shown:



Note that the height vs. time graph is quadratic because acceleration due to gravity is constant (ignoring air resistance) and from this we can show that the position vs. time graph is quadratic using introductory physics and calculus.

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The function is undefined or indeterminate when the denominator is equal to zero; i.e. x-7 = 0, x = 7. Hence the domain is

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"Selection" not "sedlection."

There are 9! ways to arrange nine distinct letters. However we divide by 2! because of the E's. If we were to treat the E's as distinct there would be 9! ways but here, we can arrange the E's themselves in 2! ways, leaving 9!/2! = 181440.

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s is supplementary to r, meaning that r+s = 180, s = 130. This is equal to 2x+30 so we set up an equation

2x+30 = 130

2x = 100

x = 50

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44 has two fours. There are 19 numbers, but 20 4's.

An easier way to count them is to list the numbers by unit digit and by tens digit, and always use the ellipsis (...) if necessary. You can organize them into sets like {4, 14, ...,94} and {40, 41, ..., 49}. Without writing every term you can easily count the number of elements by doing certain transformations like

{4, 14, ..., 94} --> {0, 1, ..., 9} (removed 4's) --> {1, 2, ..., 10} (added 1), 10 elements.

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Complementary angles, by definition, add up to 90 degrees, so the complement of 89 degrees is 90 - 89 = 1 degree.

Similarly, you'll see the other definition, supplementary angles. They are similar, except that the two angles sum up to 180, not 90.

The concept of complementary and supplementary angles is extremely useful in geometry. However I rarely see these words in advanced geometry problems, mainly because the question will be worded something like "Prove that ABC + CBD = 90" instead of "Prove that ABC and CBD are complementary" (possibly because foreign students might not know the terminology). But on certain problems involving parallel lines or right angles, this concept is crucial.

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4% of a 1 L NaCl solution is .04 L = 40 mL = 40 cm^3. However we want to find the mass of the salt by doing a unit conversion (had to look up the density online):

(40 cm^3)(2.165 g/cm^3) = 86.6 g

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Note that the y-intercept is 6, so the graph will go through the point (0,6). It has a slope 7/5, which is slightly higher than 1, so if you draw it by hand draw it a little steeper than a line with a slope of 1.

It should look something like this:



The fact that fractions are involved shouldn't make it any harder than if it was with integers.

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Given the fact that the number is an integer, we can guess and check by inputting small integer values. Here we will get 2 as our answer. To show that it is the only answer, we can write a quadratic:





where C is the other root.

Here, we expect the constant term, 3(-2)(-C) to equal -22 --> 6C = -22. This implies C = -11/3, not an integer, so 2 is the only integer root.

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I think I've already solved this problem; there is no such positive integer. This is because the digit sum remains the same, so the remainder upon dividing by 9 will be the same.

To see this, take some random numbers like 583, 79, and 1056. Reversing their digits we get 385, 97, and 6501. If we take their differences we get

583 - 385 = 198 = 22*9
79 - 97 = -18 = -2*9
1056 - 6501 = -5445 = -605*9

In all these cases we are essentially adding or subtracting multiples of 9, and since 12 is not a multiple of 9 we cannot make a number increase by 12.

However this is entirely possible in other bases. If we have (12 in base 13 = 15) and we reverse the digits we get , and



See if you can find the smallest base-10 number that, when written in a different base, the property holds (here the base-10 number was 15).

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Usually, but not always true. Sometimes a proof might begin by introducing an entirely new concept and showing how it relates to and supports the original proof.

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5y = 2x + 3x

5y = 5x

y = x?

Also that doesn't look like linear algebra to me...linear algebra is a completely different subject.

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(the symbol is the Greek letter theta)


It might look something like this (copy and paste link):

http://www.wolframalpha.com/input/?i=y+%3D+3+sin+x%2C+0+%3C+x+%3C+2pi

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Use the point-slope form:





This is also equivalent to its slope-intercept form, y = 4x - 10.

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You have two expressions that are equal, so you can manipulate them the same way and still get an equality. Here if we divide both sides by 6 we will get

b/6 = 6c/6

c = b/6

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You will have to determine graphically whether that point lies within the shaded boundaries of each inequality.

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What is "the following?"

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3.5 inches, because 3.5 + 4 = 7.5, and the triangle inequality says that the sum of any two sides must be strictly greater than the third side.

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A quarter pound is roughly 113.4 grams. 15% of this is fat, so (113.4 g)(.15) = 17.01 grams of fat in this burger. There are 9 calories per gram of fat, so in 17.01 calories there are (17.01 g)(9 Cal/g) = 153.09 Calories. 153 Calories is a good approximate answer.