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Just multiply 1.67 x 132.67

OK

Let x be the rate of one car and let x + 20 be the rate of the other......

So the rate of the 1st car times the time it travels plus the rate of the second car times the time it travels equals the total distance covered by both cars (400 miles).....mathematically, we have

4x + 4(x + 20) = 400

4x + 4x = 80 = 400      simplify and subtract 80 from both sides

8x = 320       divide by 8 on both sides

x = 40mph .....   and that's the slower car's rate....and the faster car's rate  = x + 20 = 40 + 20 = 60mph

50 - 30 = 20

20 / 2 = 10

Everything is OK until after this step:

(2 + 2 - 9/2)² = (5 - 9/2)²

Note that the quantity inside the parenthesis on the left is actually -1/2 , while on the right, the quantity inside the parentheses is 1/2. And when we square both, we get the same result = 1/4.

But, in the next to the last step, we've taken the negative square root of 1/4 on the left, while on the right, we've taken the positive square root. Thus, the two sides always differ by 1. Thus, it appears that 4 = 5.

To see this more clearly, note that

(7 - 3)² = (3 - 7)²

(-4)² = (4)²    →  (16) = (16)

But, if I stealthily take the negative root of 16 on the left and the positive root on the right, then we could claim that:

-4 = 4

Which clearly isn't true.......It also proves that we need to be careful when squaring things in an equation.....the square of one side might equal the other, but the original quantities might not.....

-

they are both lines

Find the gradient of each

If they are not parallel then there is one real solutions.

Iam not quite sure about the terminology but

gradient of (1) = -4/8=-1/2

gradient of (2) = 3/6=1/2

they are both lines and they are not parallel so there is one real solution.

$${\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{45}}^\circ\right)}}^{\,{\mathtt{2}}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\mathtt{0.500\: \!000\: \!000\: \!000\: \!639\: \!9}}$$

you type it in as cos(x)^2

Yes @ Pyramid

@@ End of Day Wrap         Wed 15/10/14         Sydney, Australia        Time 8:50pm     ♬

Hi everyone,

Today was really busy,  if it were not for Geno3141 and CPhill  hardly any would get answered.  Thanks so much.  

Our other wonderful answerers today were Heureka, alan, TakahiroMaeda, Kitty and Pyramid.  A big thank you to each of you.     

Here are some interest posts:

1) a bit of light fun.  

Thursday  15/10/14

1) Let's start with some really cool photography.

I can't find problem 32 on that test.

It's all a mystery to me.    

$$\\(3x-2)^2-(2x+6)(3x-1)\\\\
=9x^2-12x+4-(6x^2-2x+18x-6)\\\\
=9x^2-12x+4-(6x^2+16x-6)\\\\
=9x^2-12x+4-6x^2-16x+6\\\\
=3x^2-28x+10$$

if you mean sin(-145)/200 you can do it on the site calc on the home page.  :)

Here's the cattledog called zero.  She's got her eye on you!

Unfortunately the calculator will only be as good as its operator.  Sad, I am sure you agree. 

Yes it is a mystery to me too and I am too tired and too busy to work it out right now.

Still the answer was right.

Thanks Pyramid   and   Alan.  

That's the strangest math I've ever seen, Pyramid!!!......I don't know how you arrived at the correct answer......the ancient Egyptians used to solve problems by the use of something called "the method of false positioning."  Egyptians.....Pyramid.........Mmmmm......

I think Anonymous is saying that planet x's moon has a diameter of 5235.98. Anonymous, you better go to formulary>sphere. Don't forget to multiply by 3.

no it is a mixed numeral

the decimal equivalent is found by putting  -(1+1/3) into the calc on the home page.

It is a recurring decimal

Thanks, Alan, for that info........

Use the calc on the home page.

Beats me.  

Just enter it straight into the calc on the home page 

That's fine, though it might be worth explaining what you are doing at each step.  Your fourth line threw me!

.

$$\\\dfrac{5pq^3}{4p^3q^2}\\\\\\
=\dfrac{5\not{p}\;q\not{q}\not{q}}{4\not{p}\;p\;p\not{q}\not{q}}\\\\\\
=\dfrac{5q}{4p^2}\\\\$$