9a-3(a-6)=-6
9a-3a+18=-6
6a+18=-6
6a=-24
a=-4
The expression 15t – 2t not equivalent to 2t – 15t because the negative sign in 15t – 2t belongs to the term 2t.
Solution:
Given expressions are 15t – 2t and 2t – 15t.
To determine 15t – 2t is equivalent to 2t – 15t or not.
Substitute t = 2 in above two expressions.
15t – 2t = 15(2) – 2(2)
= 30 – 4
= 26
2t – 15t = 2(2) – 15(2)
= 4 – 30
= –26
The values of the expressions are different when t = 2.
So, 15t – 2t is not equivalent to 2t – 15t.
Hence the expression 15t – 2t not equivalent to 2t – 15t because the negative sign in 15t – 2t belongs to the term 2t.
20: Let 
be the amount of money. If this amount is shared between 8 people, each person will get x/8 dollars. But there actually are 6 people, so everyone is getting x/6 dollars. We know that this difference results in 30 dollars more, so we have
Rearrange the left hand side as
And multiply both sides by 24 to get
21: Let 
and 
be the number of marbles owned by Mike and Judy, respectively. At the beginning, we have
If they both get 9 more marbles, Mike will have 
marbles, and Judy will have 
marbles. So, we have
Plug this value in the first equation and we have
And we deduce
So, the difference is
22: Let 
be the number of $10, $20 and $50 coupon, respectively. We're given:
![\begin{cases}x=2y+3\\z=\frac{1}{2}y\\x+y+z=38\end{cases} We can write the third equation by substituting the expressions for x and z: [tex]x+y+z=(2y+3)+y+\left(\dfrac{1}{2}y\right)=38](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dx%3D2y%2B3%5C%5Cz%3D%5Cfrac%7B1%7D%7B2%7Dy%5C%5Cx%2By%2Bz%3D38%5Cend%7Bcases%7D%0A%3C%2Fp%3E%3Cp%3EWe%20can%20write%20the%20third%20equation%20by%20substituting%20the%20expressions%20for%20x%20and%20z%3A%0A%3C%2Fp%3E%3Cp%3E%5Btex%5Dx%2By%2Bz%3D%282y%2B3%29%2By%2B%5Cleft%28%5Cdfrac%7B1%7D%7B2%7Dy%5Cright%29%3D38)
Rearrange as follows:
And now we can deduce the number of the other coupons:
So, the total value is
23: a) In order to find the first three terms of the sequence, you just need to plug n=1,2,3:
b) We have
c) 105 is a term of the sequence if and only if there exists an integer k such that
So, 105 is not a term of the sequence.
Answer:
El cuadrado de la suma de dos números cualquiera
Step-by-step explanation:
Hope this helps
