geno3141

It isn't ... however, if  n  is a positive number that gets closer and closer to zero ...

(for instance, n = 1, then n = 0.1, then n = 0.01, then n = 0.001, etc -- never stopping)

then the fraction 1/n will get larger and larger, never stopping, so the answers approach infinity ...

but, at no time, will 1/n = infinity.

"at least" is "greater than or equal"   --->   ≥

If  n  is the number of pastries sold, they will make  2.50·n  when they sell n pastries.

Since they want at least $115.00   --->   2.50n  ≥  115.00

Now, divide both sides by 2.50:

Let                                                     log_√5125√5  =  x

Then write this into exponential notation:       √5^x  =  125√5

Now, I want to write 125 with a base of √5:

   ---  first,  125  =  5³

   ---  also,  (√5)²  =  5

   ---  so:    125  =   5³  =  [ (√5)² ]³  = (√5)⁶  

   ---  and:  125√5  =  (√5)⁶ ·√5  =  (√5)⁷

Thus:   √5^x  =  (√5)⁷     --->  x = 7

Multiply the left side by:  2√2 / 2√2:

Left side becomes:  [√x / (√3x + √2)] · [2√2 / 2√2]  =  2√(2x) / [ 2√6x + 4 ]

Now the left side and the right side have the same denominators. For the two sides to be equal, they must have equal numerators:    2√(2x)  =  1  

--->                            √(2x)  =  1/2                 divide by 2

--->                                 2x  =  1/4                  square both sides

--->                                   x  =  1/8                  divide by 2

                                                                                                -3/10x - 2  <  2/5

To get rid of fractions, multiply each term by 10:  (10)(-3/10x) - (10)(2)  <  (10)(2/5_

                                                   --->                                           -3x - 20 < 4     

Add 20 to both sides:                                                                          -3x < 24

Divide both sides by -3                                                                           x > -8  

(When you multiply both sides of an inequality by a negative number, you must change the direction of the inequality sign; you don't do this when you multiply or divide by a positive number; and you don't do this when you add or subtract either a positive or negative number.)

                                                               4 + 14b  ≥  13(b + 4)

Use the Distributive Property::                4 + 14b  ≥  13b + 52

Subtract 13b from both sides:                     4 + b  ≥  52

Subtract 4 from both sides:                                b  ≥  48

If 18 were regular, then  66 - 18  =  48  were chocolate.

Ratio of chocolate to regular:     48 : 18  =  8 : 3

There are many answers to this question. You must make certain that the sum of the two smaller sides is greater than the third side (otherwise, they won't "connect).

So, you could have: 1, 7, 7    2, 6, 7    3, 5, 7     4, 4, 7    plus many others .....

(You can't have 1, 1, 13 because the two "1" sides won't meet.)

If the number of bunnies doubles every day, then you always have to multiply the preceding day's number by 2.

If you use:  y  =  25·2^x-1

Then:  day 1:  x = 1  --->  y  = 25·2^1-1  =  25·2⁰  =  25·1  =  25

           day 2:   x = 2  --->  y  = 25·2^2-1  =  25·2¹  =  25·2  =  50

           day 3:   x = 3  --->  y  = 25·2^3-1  =  25·2²  =  25·4  =  100

           day 4:   x = 4  --->  y  = 25·2^4-1  =  25·2³  =  25·8  =  200

etc.

CPhill is correct; a  slightly different approach is:

Consecutive odd integers are like:  3, 5, 7, 9, ...   (they are 2 apart from each other)

So, three consecutive odd integers can be:  x, x + 2, and x + 4

"four times the first integer"  --->  4·x

"twice the largest integer"     --->  2(x + 4)  =  2x + 8

"difference is two" means subtract and get an answer of two; so subtact the smallest from the largest and have that answer be two:  (2x + 8) - (4x)  =  2

--->                              2x + 8 - 4x  =  2

--->   simplify   --->               8 - 2x  = 2

--->   subtract 8   --->              -2x  =  -6

--->   divide by -2   --->              x  =  3      --->  x + 2  =  5      and     x + 4  =  7

Volume  =  length x width x height

18 3/5  =  16.6

22 1/4  =  22.25

Volume  =  22.25 x 18.6 x 2                 <---  answer!