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Add the fractions to get \({26 \over t}\)

So, t must be 1 of the \(\color{brown}\boxed{4}\) divisors of 26 (1,2,13,26)

I asked you to list them Doremy.

Why have you not done so.

Thanks guys, you are right :)

Except last time the meaning was made clear, this time it was not :)

Não sei se é isso que está perguntando.

\(\frac{1}{4}\;\times\;60\;=15\)

Hint: Draw a perpendicular line from point C to segment DA. This creates a 30-60-90 triangle. 

Thanks! But how did you get that?

Solve for a:
1/(a^3 + 7) - 7 = 5 - a^3/(a^3 + 7)

Bring 1/(a^3 + 7) - 7 together using the common denominator a^3 + 7. Bring 5 - a^3/(a^3 + 7) together using the common denominator a^3 + 7:
(-7 a^3 - 48)/(a^3 + 7) = (4 a^3 + 35)/(a^3 + 7)

Multiply both sides by a^3 + 7:
-7 a^3 - 48 = 4 a^3 + 35

Subtract 4 a^3 - 48 from both sides:
-11 a^3 = 83

Divide both sides by -11:
a^3 = -83/11

Taking cube roots gives (-83/11)^(1/3) times the third roots of unity:

a = (-83/11)^(1/3)    or a = -(83/11)^(1/3)    or a = -(-1)^(2/3) (83/11)^(1/3)

Do you understand now nerdiest? 

You are a good student here and you never should be worried about saying clearly when you do, or do not fully understand.

I put an emphasis on the work 'clearly'

Thanks to the three of you who have helped here :)

I have just looked at your posting history.

You are only hear to collect answers and on occasion you give abuse.

You have never thanks anyone for trying to help you nor have your ever interacted properly with an answerer. 

You have however abused an answer once.

So how about you just go away?

hint

\(\displaystyle \boxed{r=\frac{a_n}{a_{n-1}}=\frac{a_2}{a_{1}}=\frac{a_3}{a_{2}}=etc}\)

cards originally had by adam = x, cards originally had by claire = y.

7/4 y = x from sentence 1

1/2y = x - 35(I'm assuming your questions means that Adam did not give the postcards away to claire here)

7/4y - x = 0

1/2y - x = -35

equation 1 - equation 2 to get

5/4y = 35

Thus

y = 28, and

x = 49

Adam originally had 49 cards, and Claire originally had 28 cards

2^10 ==1024

{1} | {2} | {3} | {4} | {5} | {11} | {12} | {13} | {14} | {15} | {1, 2} | {1, 3} | {1, 4} | {1, 5} | {1, 11} | {1, 12} | {1, 13} | {1, 14} | {1, 15} | {2, 3} | {2, 4} | {2, 5} | {2, 11} | {2, 12} | {2, 13} | {2, 14} | {2, 15} | {3, 4} | {3, 5} | {3, 11} | {3, 12} | {3, 13} | {3, 14} | {3, 15} | {4, 5} | {4, 11} | {4, 12} | {4, 13} | {4, 14} | {4, 15} | {5, 11} | {5, 12} | {5, 13} | {5, 14} | {5, 15} | {11, 12} | {11, 13} | {11, 14} | {11, 15} | {12, 13} | {12, 14} | {12, 15} | {13, 14} | {13, 15} | {14, 15} | {1, 2, 3} | {1, 2, 4} | {1, 2, 5} | {1, 2, 11} | {1, 2, 12} | {1, 2, 13} | {1, 2, 14} | {1, 2, 15} | {1, 3, 4} | {1, 3, 5} | {1, 3, 11} | {1, 3, 12} | {1, 3, 13} | {1, 3, 14} | {1, 3, 15} | {1, 4, 5} | {1, 4, 11} | {1, 4, 12} | {1, 4, 13} | {1, 4, 14} | {1, 4, 15} | {1, 5, 11} | {1, 5, 12} | {1, 5, 13} | ............. (total: 1024)

1024  -  5==1019  - number of unique integers.

4 3 2 1, is the original partition of 10. However, we can have a hidden "0" at the end, making it 4,3,2,1,0 for our use in calculating the partitions of 12.

For 12, we can place two extra 1's into the five existing slots (4 3 2 1 0), in other words five choose two places. Note that five choose two = 10.

At this point the answer seems like 10 but there are two additional cases not counted, which are to place both extra 1's into the same place AND to create 2 new slots at the end instead of one. There are two ways to do so, leaving us with respectively 6,3,2,1 and 4,3,2,1,1,1

So the answer is 10+2 = 12. I was originally kinda stuck but figured it out later.

Idk if this is faster than just listing everything out but its probably more elegant

Thank you. 

The perimeter is 64.

Let the number ==N

5N / [N + 7] ==7

5N ==7N + 49

5N  -  7N == 49

 - 2N == 49

N ==49 / -2 == - 24.5

1 - 0.4 ==0.6

0.6^3==0.216

1  -  0.216 ==78.4% percentage decrease in volume

5 x 5 x 6 x 8 ==1,200

So, the smallest such number==5568.

t==1 ,2 ,13 ,26==4 such positive integers.

6000  -  5000 ==$1,000 - simple interest earned over 8 years.

1,000 / 8 ==$125 - simple interest earned over 1 year

125 / 5000 ==0.025  x  100 ==2.5% simple interest rate per year.

The answer is 3x - 5y >= -2.

The answer is 72%.

15% I think.

Solve the inequality

Hello Guest!

\(-4(x + 4) > x + 7 + 5(x + 2)\\ -4x-16>x+7+5x+10\\ -10x>33\\ \color{blue}x<-3.3\)

\(\color{blue}x\in \mathbb R \ |\ \) \(\color{blue}-\infty\) < x < -3.3

  !