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When AND  is in a word problem it means that you add not multiply. 

no you have to combine like terms if the numbers are not like terms then that is the anwser 10+6d

Distance / Time  =   Rate

Convert  2 hrs +  43 minutes  to a fractional equivalent =  2  + 43/60    = 163/60

So

26.2 miles  / [163/60] hrs  = 

26.2 * 60 / 163  ≈  9.64 mph

9s+4 = -32s      subtract 9s  from  both sides

4  = -41s          divide both sides by -41

-4/41   = s

There is an algebraic way of summing it up, but I will use a simple summation formula on my computer to sum them all up!!. Too lazy!!.

∑[ (10^n - 1), n=1 to 999] =1111111111 1111111111 1111111111.........1111110111 =1.11111 x 10^999 !!!.

The sum is given by

 9n  + 90 (n - 1)   +  900 (n - 2) + 9000 (n - 3)   ....  etc.   ......  where n is the largest number of 9s in the sum

most likely means adding

E  =  3/20  =  15/ 100  =  15%

D  = 6/20  =  30 / 100   = 30%

C  = 7/20  = 35 / 100 + 35%

B =  4/20  = 20 / 100  = 20%

The 72° angle and angle a form a straight line.

72° + angle a  =  180º     →     angle a  =  180° - 72°  =  108°

The 72° angle and angle b are vertical angles, so they have the same measure.

angle b  =  72°

Angle a and angle c are vertical angles, so they have the same measure.

angle c  =  angle a  =  108°

The measures of the other three angles are  108°, 72°, and 108° .

If x = 1.33, then:

2x =1.33 x 2 =2.66

Diagonal^2 =1.33^2 + 2.66^2     [Pythogoras's Theorem]

Diagonal^2 =1.7689 + 7.0756

Diagonal^2 =8.8445                         Take the Square Root of both sides.

Diagonal =2.974

In logic:

AND is the equivalent of multiplying.

OR is adding.

The same situation is starting to happen to me as well, however, I've noticed this usually happens when I'm in a 'private' browser.

What is 10+6d?

To begin, you have to realize that d is a variable. This means d can be any number.

In this equation, d is multiplied by 6. So you must think about order of operations.

If you have 2 numbers multiplied by each other, you have to find their product before you can add any other numbers.

Ex- d=4

If d equals 4, you plug in anywhere there is a d.

10+6(4)

Notice my use of parenthesis. If the number were negative, you would want to make sure the negative is inside the parenthesis.

Simplify.

6*4=24

10+24=?

10+24=34

A good way to remember order of operations is PEMDAS.

Some people use PEMDAS as the acronym Please Excuse My Dear Aunt Sally (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction) in that order. For example, you would have to do parenthesis before exponents, or multiplication before addition.

Hope this explanation helps!

Sum =F x [1 - R^N] / [1 - R], where F=First term, R=Common ratio, N=Number of terms

Sum =-1 x [1 - (-2^10] / [1 - (-2)]

Sum =-1 x [1 - 1,024] / [3]

Sum =-1 x[ -1023] / 3

Sum = 1,023/3

Sum = 341

10 mi/h= ft/h

1 mile =5,280 feet

10 miles/h =5,280 x 10 =52,800 Feet/h

Let the bill before VAT =B

B x 1.23 =295.20 Euros.     divide both sides by 1.23

B =295.20 / 1.23

B =240 Euros - the bill before VAT was added.

Consider the infinite Geometric series $\displaystyle \frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}+\dots$  .

Its sum to infinity (I think that there is a mistake in the question, there should be a plus sign and a series of dots after that last term), is $\displaystyle \frac{1}{x-1}$.

Equate the two, differentiate both sides, and then substitute x = 3.

Tiggsy

$\sqrt2\approx 1.414213562$

I suppose you could just use closer and closer estimations of sqrt2 and see if the answers keep getting closer...

$\sqrt2 \approx 1.4\\ {4\over 3-2\sqrt{2}}\approx {4\over 3-2*1.4}\approx \frac{4}{0.2}\approx 20\\ 12+8\sqrt2\approx 12+8*1.4=12+8+3.2=23.2$

$\sqrt2 \approx 1.41\\ {4\over 3-2\sqrt{2}}\approx {4\over 3-2*1.41}\approx \frac{4}{0.18}\approx 22.2\\ 12+8\sqrt2\approx 12+8*1.41=12+11.28=23.28$

The answers are getting close, answer certainly passes reasonable checks :)

121^1/2

$121^{1/2}=\sqrt{121}=11$

I guess you could do this sort of quesion by raising the numbers to a power until they are whole numbers and then working it out.

Raising the first one by squaring it gives

$6*9,100,49*2=54,100,98$

therefore the result would be

$3\sqrt{6},7\sqrt{2},10$

for the second one squaring it would be

$-4*3,-16,-9*2,-4*\frac{7}{2}=-12,-16,-18,-14$

so it is

$-3\sqrt{2},-4,-2\sqrt{\frac{7}{2}},-2\sqrt{3}$

(note that I changed to negative because of that)

for the third one you need to cube it

$21,27*2,21.952,8*5=21,54,21.952,40$

Then it becomes

$\sqrt[3]{21},2.8,2\sqrt[3]{5},3\sqrt[3]{2}$

(Sorry for errors, I kind of rushed it)

They are trying to be tricky, here  !!!

Remember that    a√b  is just  √ [a^2 * b ]

And    a  =  √a^2

And    a∛ b     is just  ∛  [ a^3 * b ]

So

3√ 6 ,  10  ,  7√2    can be written as

√54 , √100 ,  √ 98          see  ???.......you can arrange these for yourself

Similarly

-2√3 ,  -4 , -3√2,  -2√ [7/2]       becomes

- √12, -√16, -√18  and  -√ [ (4 * 7) / 2 ]  =  - √14

Again you can arrange these....just remember that, for instance,  -√13 > -√25   !!!!

Lastly

∛21 , 3∛2 , 2.8 , 2∛5    become

∛21, ∛54, ∛21.952  and  ∛40

And you can handle this one, too !!!

Simplify the following:
4/(3 - 2 sqrt(2))

Multiply numerator and denominator of 4/(3 - 2 sqrt(2)) by 2 sqrt(2) + 3:
(4 (2 sqrt(2) + 3))/((3 - 2 sqrt(2)) (2 sqrt(2) + 3))

(3 - 2 sqrt(2)) (2 sqrt(2) + 3) = 3×3 + 3×2 sqrt(2) - 2 sqrt(2)×3 - 2 sqrt(2)×2 sqrt(2) = 9 + 6 sqrt(2) - 6 sqrt(2) - 8 = 1:
(4 (2 sqrt(2) + 3))/(1)

(4 (2 sqrt(2) + 3))/(1) = 4 (2 sqrt(2) + 3):
4 (2 sqrt(2) + 3) =8sqrt(2) + 12

We can split this into  two series

2 + 8 + 32 +  128  + 512      and     -1 + -4 + - 16 + - 64 + -256  = - [ 1 + 4 + 16 + 64+ 256 ]

Note that the first series can be written as

2 [ 1 + 4 + 16 + 64+ 256 ] 

So the sum of the two series  is

2 [A]  - [A]       =   A   

Where A  is just  1 + 4 + 16 + 64+ 256   =  341 !!!