10:12
15:18
i got this from doubling the first to make 5 = 10 and then that made 6 = 12. the second one was the same but tripled to make 6 = 18 and then that made 5 = 15
A(1) = - 3 ;
a(2) = a(1) + ( 2 - 1 )d ;
3 = -3 + d ;
d = 6 ;
a(3) = a(1) + ( 3 - 1)d;
9 = - 3 + 2d ;
12 = 2d ;
d = 6 ;
a(4) = a(1) + ( 4 - 1 )d ;
15 = -3 + 3d ;
18 = 3d ;
d = 6 ;
Then, a(n) = - 3 + ( n- 1 )6 ;
a(n) = - 3 + 6n - 6 ;
a(n) = 6n - 9 is an explicit functin rule for the sequence -3, 3, 9, 15, ...
Answer:
x = 20/32
Step-by-step explanation:
you have to distribute first.
1) times 4 by all the nubmers and figures inside the pharanthesese and so you get 32x + 20
2) you have to solve for x and so you move the 20 to the other side and get 32x = 20
3) you then divided both sides by 32 to get x by itself and you get x = 20/32
Answer:
son age: X
man_age= 5X
in 3 years: we have: (man_age+3)(X+3)=380
we can replace the man age by 5X and we get :
(5X+3)(X+3)=380
it is a quadratic equation with 2 solutions. One negative and 7
The solution is thus 7, since age can not be negative.
The son is thus 7 and the dad 5 times more 35
Step-by-step explanation:
Answers:
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Explanation:
7+6 = 13. Divide this over 5 to get 13/5 = 2 remainder 3. The quotient 2 is something we don't care about. <u>We only worry about the remainder</u>. Therefore 7+6 = 3 (mod 5)
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2+1 = 3 (mod 5) for similar reasoning as above. 3/5 = 0 remainder 3.
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20 = 9 (mod 11) since 20/11 = 1 remainder 9. Imagine you had 20 cookies and 11 friends. Each friend would get 1 whole cookie (quotient) and there could be 9 left over (remainder).
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35/11 = 3 remainder 2
Or you could use repeated subtraction like so to find the remainder
35-11 = 24
24-11 = 13
13-11 = 2
The last result (2) is smaller than 11, so we stop here and this is the remainder.
Therefore, 35 = 2 (mod 11)
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Here's another way to think of it. Consider you have $35 in your pocket. Let's say a store is selling trinkets for $11 each. We can pose these key questions:
- What is the most number of trinkets you can buy?
- If you buy that max amount, how much will you have left over?
The answer to the first question is 3 trinkets because 3*11 = 33 dollars is under the budget of $35. The amount left over is 35-33 = 2 dollars which is the remainder. It's not larger than 11, so we cannot buy any more trinkets at this point.
