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Why is the answer to number 5 on the Lesson 1: Coordinate Plane 5? Please give me an explanation and how you got to that answer. Thanks so much.

Excellent question and it seems the answer explanations were not provided. They are available now.

Basically, the line between the points forms a hypotenuse of a right triangle with sides parallel to the x and y axes. Apply the Pythagorean theorem to solve for hypotenuse distance given an x and y distance of 3 and 4 for the triangle sides. I could relay the distance formula provided in the answer as well, but it is the same thing and easier to think of it as a right triangle. This is a typical Pythagorean triplet (integer side length results) known as a 3-4-5 right triangle.

On Lesson 1 in the section Powers of 10 question 5, I am a little confused as to how to get to 10 as the final product, and what the binary system is supposed to represent or how it’s used. Thank you and I hope to hear back soon.

Great question. We count in 10s. We only have 10 digits to represent any number…0,1,2,3,4,5,6,7,8,9. When you exhaust all of them in the single digit place you must add a new digit place to represent a higher number and that is the 10s place as we know it and then when you pass 99 you will need to add another digit again the hundreds column and so on.You are so used to that you probably never even considered that there could be any other way to count. A computer for example can only have a circuit on or off represented with a 1 or 0. Those binary codes must represent the numbers (and everything else you see… letters etc. on your screen). However, they must be counted using only two digits so when you exceed 2 another digit place must be added and then after 4 another digit place and so on. e.g.

259 to us represents 2 x 10^2 + 5 x 10^1 + 9 x 10^0 = 200 + 50 + 9

In order to represent the same value in binary (base 2 numeral system) it would have to be…

100000011 = 1 x 2^8 + 0 x 2^7 + 0 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 1 x 2^1 + 1 x 2^0 = 256 + 2 + 1

Do you see the pattern? …of the digits in the number? …of the powers of the base numeral of the system?

Let’s look at it in reverse for a base 8 numeral system. If another culture counted with only 8 symbols(digits) 430 for them would represent…

4 x 8^2 + 3 x 8^1 + 0 x 8^0 = 4 x 64 + 3 x 8 + 0 x 1 = 280 to us

Good catch Alissa. The correct answer is not -3. That is a mistake in the answer explanation. It seems the problem was changed, but not the explanation. The correct answer is 1 and the explanation has been updated. I apologize for the mistake.

For Prime And Composites Number 4 it is incorrect because the sum of all the prime numbers from 10-30 is actually 112 and not 99, and 112 is not marked as the correct answer.

I am guessing your confusion is the way it is written? How can the solution be an “and” condition or intersection of both at once? Wouldn’t that be the null set? Yes, it would. The correct statement should be -6 ≥ x or x > 2. The correct graph includes an open middle and a solid circle or point at -6 with everything to the left shaded and an open circle at 2 with everything to the right shaded.

Why is the answer to number 5 on the Lesson 1: Coordinate Plane 5? Please give me an explanation and how you got to that answer. Thanks so much.

Excellent question and it seems the answer explanations were not provided. They are available now.

Basically, the line between the points forms a hypotenuse of a right triangle with sides parallel to the x and y axes. Apply the Pythagorean theorem to solve for hypotenuse distance given an x and y distance of 3 and 4 for the triangle sides. I could relay the distance formula provided in the answer as well, but it is the same thing and easier to think of it as a right triangle. This is a typical Pythagorean triplet (integer side length results) known as a 3-4-5 right triangle.

On Lesson 1 in the section Powers of 10 question 5, I am a little confused as to how to get to 10 as the final product, and what the binary system is supposed to represent or how it’s used. Thank you and I hope to hear back soon.

Hi Alissa,

Great question. We count in 10s. We only have 10 digits to represent any number…0,1,2,3,4,5,6,7,8,9. When you exhaust all of them in the single digit place you must add a new digit place to represent a higher number and that is the 10s place as we know it and then when you pass 99 you will need to add another digit again the hundreds column and so on.You are so used to that you probably never even considered that there could be any other way to count. A computer for example can only have a circuit on or off represented with a 1 or 0. Those binary codes must represent the numbers (and everything else you see… letters etc. on your screen). However, they must be counted using only two digits so when you exceed 2 another digit place must be added and then after 4 another digit place and so on. e.g.

259 to us represents 2 x 10^2 + 5 x 10^1 + 9 x 10^0 = 200 + 50 + 9

In order to represent the same value in binary (base 2 numeral system) it would have to be…

100000011 = 1 x 2^8 + 0 x 2^7 + 0 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 1 x 2^1 + 1 x 2^0 = 256 + 2 + 1

Do you see the pattern? …of the digits in the number? …of the powers of the base numeral of the system?

Let’s look at it in reverse for a base 8 numeral system. If another culture counted with only 8 symbols(digits) 430 for them would represent…

4 x 8^2 + 3 x 8^1 + 0 x 8^0 = 4 x 64 + 3 x 8 + 0 x 1 = 280 to us

On question five for Law of Exponents drills, it says that n = -3, but when I type -3, it says that I am wrong. Please help

Good catch Alissa. The correct answer is not -3. That is a mistake in the answer explanation. It seems the problem was changed, but not the explanation. The correct answer is 1 and the explanation has been updated. I apologize for the mistake.

I was curious, for Probability (More Difficult Word Problems) what is the answer explanation for number 3?

For Prime And Composites Number 4 it is incorrect because the sum of all the prime numbers from 10-30 is actually 112 and not 99, and 112 is not marked as the correct answer.

Good catch. The answer explanation is correct, but the multiple choice answer is not. It has been updated.

Also for Lesson 6: Binomial Factors for Number 3, there is only one acceptable answer, even two of the choices are the same.

(x + 9)(x – 4) and (x – 4)(x + 9) are the same thing, so why is (x+9)(x-4) the answer?

I see (x+9)(x-4) and (x-4)(x-9). ????

for lesson 1 (number line), how do u solve it (question: Which number line below represents the solution set for -6 ≥ x > 2?

huh??

I am guessing your confusion is the way it is written? How can the solution be an “and” condition or intersection of both at once? Wouldn’t that be the null set? Yes, it would. The correct statement should be -6 ≥ x or x > 2. The correct graph includes an open middle and a solid circle or point at -6 with everything to the left shaded and an open circle at 2 with everything to the right shaded.