Logarhythm

y - b = m(x - a)

(y - b)/m = x - a

a = x - ^(y-b)/_m 

like that?

1) If you start writing out the next terms of the pattern, you'll see that, well, there is a pattern.

13, 28, 520, 133, 55, 250, 133...

The 100th term would be 133. 

s + d = 260

35s + 60d = 14000

35s = 14000 - 60d

s = 400 - 12d/7

s + d = 260

(400 - 12d/7) + d = 260

-12d/7 + d = -140

-12d + 7d = -980

-5d = -980

d = 196

s + d = 260

s + (196) = 260

s = 64

The hotel has 196 double rooms :)

v + b = 12 

8v + 30b = 228

8v = 228 - 30b

v = 28.5 - 3.75b

v + b = 12

(28.5 - 3.75b) + b = 12

2.75b = 16.5

b = 6

v + b = 12

v + (6) = 12

v = 6

There were 6 buses and 6 vans

Proof:

6 * 8 + 6 * 30 = 48 + 180 = 228

fox:coyote = 3:8 

coyote = 32

32 ÷ 8 = 4

3 * 4 = 12 pounds (fox)

wolf = 120 - 32 - 12 

       = 88 - 12

       = 76, which is your answer :)

You want to find all the terms that have x as the variable.

This means: tx * 7 + 10 * -6x = 7tx - 60x, or (7t - 60)x.

Now we look at the coefficient in the question. The coefficient of x is -39. 

7t - 60 = -39 

7t = 21

t = 3 and bam that's your answer :)

 

30% of 1000 = 300 students. 

0.2x + 0.7(1000 - x) = 0.3 * 1000 

0.2x + 700 - 0.7x = 300

0.5x = 400

     x = 800
1000 - x = 200

There were 800 students in the north campus and 200 students in the south campus :)

A + B + C + D = 36

A + 2 = B - 2 = C x 2 = D ÷ 2

A = B - 4
B = 2C + 2

C = D ÷ 4

D = 2A + 4

Let's find A first.

D = 2A + 4

C = (2A + 4) ÷ 4

    = 0.5A + 1
B = A + 4 

A + B + C + D = 36

A + A + 4 + 0.5A + 1 + 2A + 4 = 36

4.5A + 9 = 36

4.5 A = 27

A = 6

Since A = 6, 
B = A + 4 

   = (6) + 4

   = 10

C = 0.5A + 1

    = 0.5(6) + 1

    = 3 + 1

    = 4

D = 2A + 4 

    = 2(6) + 4

    = 12 + 4

    = 16

Which means the product of the four, ABCD = 6 * 10 * 4 * 16 = 3840, which is your answer :)

The answer isn't 17 because you're discounting something that is already discounted.. 

First discount --> x * 0.88 

Second discount --> x * 0.88 * 0.95 = 0.836

(1 - 0.836) * 100 = 0.164 * 100 = 16.4%

Proof:

Let's say x = 100 for ease.

You discount 12%, which means you take off 12 dollars. 

100 - 12 = 88 dollars left.

Now from that 88 dollars, you discount another 5%. This means:
88 - (88 * 0.05) 

= 88 - 4.4

= 83.6

100 - (100 * 0.164) = 83.6 

Hope that helps :)

First we know that x ≠ odd. This is because for it to be divisible by 42, it needs to be even. 

This means we can try 2, 4, 6 and 8 as x

235792 ÷ 42 ≈ 5614.0952

435794 ÷ 42 ≈ 10,376.0476

635796 ÷ 42 = 15,138

835798 ÷ 42 ≈ 19,899.9524

This means x = 6, which is your answer :)