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If I understand your question correctly, this is just the associative property.
If a=b and b=c then a=c.

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Well, if you look at 3:00, that is a right angle. Also, the face of a clock is a circle. That is 360 degrees. There are twelve numbers on the clock face so that says that every number of the clock face is 30 degrees. So, you estimate and answer for 5:00 should both easily be 150 degrees since 5 * 30 = 150. It is obtuse because it is larger than 90 degrees. Acute would be less than 90.

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You have to use the distributive property for every term on the whole trinomial. It's messy, but you have to do it.
For example:

In reality, this is what you are doing when you square a binomial. This works for any polynomial.

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When your x terms are equal, the slope is simply zero. That line segment is just a straight line on x=-2 between 4 and -5.

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given the following two complex numbers, a=3+7i and b=-2-2i,calculate the following
a+b
a-b
a*b
a/b
Ok, for the most part, treat i like a variable.


a*b is just simply:
Remember that i^2 = -1. So we simplify into:
a/b is
To simplify, you multiply the numerator and denominator by the denominator's complex conjugate which is -2+2i.

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This is where learning Pythagorean Triples is helpful. The smallest one is the 3,4,5 right triangle. So, the measure of the other leg is 4. Fortunately, you are in luck. Since Tangent is sine/cosine(or opposite/adjacent), you only have to find two tangents. The tangent for the right angle is undefined. It would be 1/0 and we know that you can't do that. If you picture it on the unit circle, sine is the y axis and cosine is the x axis. As you move up the circle towards 90 degrees, your sine(y) approaches 1. However, your cosine(x) approaches zero. The other tangents however are easy. Just remember SOH CAH TOA. Sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent. So your other two tangents are 3/4 and 4/3.

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Make x one of those numbers and the x+1 would be the next consecutive number.



then
so and are solutions. Since a negative squared is positive, you can just use 6 and 7.

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I would personally expand the first.
That gives us:

Then multiply by the 2:

Then subtract the 3:

You aren't going to like this, but you have to use the quadratic formula for this one.

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Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=24 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6.22474487139159, 3.77525512860841. Here's your graph:

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To solve this, multiply by in the first fraction and in the second. That makes:

Now multiply both sides by 35 to get rid of the fractions.

That gives us and

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is irrational. For a number to be rational, it must be able to be expressed as a fraction of two integers in lowest terms(prime numbers).
One major thing to know, and you should investigate this for yourself, is that there is no prime number that will have a rational square root. 77 is a product of 11 and 7, both are primes and that means that it will not have a rational square root.
__________
Is rational or irrational? Well, that all depends on the x. It will definitely have a complex root(imaginary), but that doesn't mean that it will be irrational. It all depends on the x for the same reason in the first question.
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Is that a right triangle? And what do you mean by altitude in regards to the triangle?
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The rule is so your answer is . This also applies to your next question.
The cube root of 1/64. Same thing as above except for cube roots. The cube root of 1 = 1; the cube root of 64 = 4. So the cube root of 1/64 = 1/4.

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You need to find the greatest common divisor. In this case it is 3xy. So it would be

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Ahh. This is a simple application of the Pythagorean Theorem! Think of the rope that Anne is pulling on as the hypotenuse since she is standing away from the tree and the rope is attached to the top of the tree and the problem said that the rope is longer than the tree's height. Then, think of the height of the tree as a side of a right triangle.
__|\
__|_\
48|__\_60
__|___\
__|____\
____x
Let's call x the distance that Anne is from the tree. The theorem is
so in our case and .
So & .
Then
so
Then so Anne is standing 36ft from the tree.
Also, if you notice, 48 and 60 are multiples of 12. If you divide them by 12 you get 4 and 5. That follows special triangles with sides called Pythagorean Triples. One of them is 3,4,5. So if you can notice a right triangle as having two of those sides, you can immediately know what the third side is. But, remember always show your work to get full credit in class ;-)

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Divide and conquer! Split this up and you will get it.
is the first part. This is a simple expansion of

The second part: is a simple expansion of
if you first factor out a -1, which is already in the problem.
This is done when you put your parentheses around the second polynomial
So, the factored version is

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Let x be the number of nickels. So .05x is the amount of money in nickels and 0.10(x+2) is the amount of money in dimes since there are two more dimes than nickels. Think "number of nickels + 2 = number of dimes. So, .10(x+2) + 0.05x = $1.70.
To make this a lot easier, let's multiply it all by 100 to get rid of the decimal, which we will replace later.
10(x+2) + 5x = 170 That's much better isn't it?
10x + 20 + 5x = 170 Use the distributive property.
15x + 20 = 170 Add your x's
15x = 150 Subtract the 20 from both sides, now divide
x = 10 So there are 10 nickels.
Now, back to the original form:
0.10(10 + 2) + 0.05(10) = 1.70
0.10(12) + 0.05(10) = 1.70
1.20 + .50 = 1.70.

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You are starting with 1 and adding 2 to it each line. The x in x(y) is the number of times you add y to 1.

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If x does not equal 0, then (2^4x)(8^2x) =
(2^4x)(2^3)^2x =
(2^4x)(2^6x) =
2^(4x+6x) =
2^(10x) =
(2^10)^x = 1024^x

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Your answer is correct.
22/21 = 127/x
22x = 21*127

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bottles.
oz of juice.
There are 128 ounces to a gallon, so divide 15360 by 128 and you have the number of gallons.
gallons.

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You need to know if 4 and 25 are perfect squares or not. If they are not, then you have to do some algebra. Otherwise, you can just take their square roots.

Then check

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Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=144 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5, -7. Here's your graph:

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is the correct setup.
When you do the algebra on this, I wouldn't worry about the canceling out.
Here is how I would work this.

Then clean this up a bit. Cancel the and subtract the 16 on both sides.
Then divide both sides by 8 and you're done.

So, the sides for the triangle are 6, 8, and 10. If you cut each in half, this is a special type of right triangle called a 3,4,5 triangle.

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If you rearrange this, you can work this easily.
.
The fractions add up to zero so they go away. You are left with 5x-x, which would be
.