geno3141

Reduce  8/12  =  2/3

Reduce  14/21  =  2/3

Since they reduce to the same value, they are proportional.

a  =  (7 - 2b)³   --->   a'  =  3(7 - 2b)² · -2   --->    a'  =  -6(7 - 2b)²

4y - 7  =  2y + 11

Subtract 2y from both sides:

2y - 7  =  11

Add 7 to both sides:

2y  =  18

Divide by 2:

y  =  9

And, from your comments, I guess that you want to show the world that, as an "American" (or is it ust a citizen of the United States -- there's a lot of America that isn't part of the United States), you have the freedom to be ignorant, insulting, and (probably) racist.

At $6.50 an hour, Fred will earn $6.50 x 26 = $169.00 in hourly pay.

To earn at least $229.00, subtract:  $229.00 - $169.00  =  $60.00.

So, Fred must earn at least $60.00 in tips.

To get an approximate answer, use logs:

x = 8²⁰¹⁵

--->   log(x)  =  log(8²⁰¹⁵)

Since exponents in logs come out as multipliers:

--->   log(x)  =  2015·log(8)  ≈  1819.726

Find the antilog:

--->   x  =  10^1819.726324

--->   x  =  10^{1819 + 0.726324}

--->   x  =  10¹⁸¹⁹ · 10^0.726324

My calculator give me the value of 5.325 for 10^0.726324

So, the answer is approximately 5.325 x 10¹⁸¹⁹

In (9r⁶)^3/2, split as (9)^3/2 · (r⁶) ^3/2

For (9)^3/2:  =  (√9)³  =  3³  =  27

In  (r⁶) ^3/2  multiply the exponents:  6 x 3/2  =  9   --->   r⁹

So the answer is  27r⁹.

For:  √(4x)  =  x   

Square both sides:   4x  =  x²

--->   0  =  x² - 4x   --->   0  =  x(x - 4)   --->   x = 0   or   x = 4

A papyrus of acient Egypt (approx 1650 BCE), listed (probably) practice problems and instructions. So, instructions in mathematics goes back many centuries.

When you have a right triangle, label the hypotenuse.

Then, look at the angle that you know (or want to know). From this angle, label the opposite side (the side across the triangle from the angle that you know) and label the adjacent side (their are two sides that touch the angle that you know, one is the hypotenuse, the other is the adjacent side).

If you know both the opposite side and the hypotenuse, use sin.

If you know both the adjacent side and the hypotenuse, use cos.

If you know both the opposite side and the adjacent side, use tan.

Did you mean that "each person could have 8/7ths of a candy bar"?

If so, divide 35 by 8/7:  35 ÷ 8/7  =  35 x 7/8  =  30.625, or 30 persons.

The chemistry teacher gave you the correct rules.

Your physical science teacher gave you someincorrect information; go to your chemistry teacher and explain what the physical science teacher told you. Your chemistry teacher can go to the physical science teacher and correct that person's misconceptions.

Rule 4 is correct.

Rule 3: Zeros to the left of the non-existing decimal point are tricky -- if any of the zeros of 90000 (without a decimal point) are significant, they need to be indicated, usually by placing a bar over the last one (to the right) that is significant. If there is a decimal point at the end, such as 90000., then all those zeros are significant.