Answer:
2563
Step-by-step explanation:
Kgr7q wtbej iw ku3yf kuey wuyr icnt gje eruyg eurygb ekuv ekght kicu dkyg
Answer: 8/9
Step-by-step explanation: 0.888... can be simplified to 8/9.
Answer:
1. YES 2. NO
Step-by-step explanation:
1. Since x=0.121212... and the question is asking for 100x, we need to multiply each side by 100. 0.121212... multiplied by 100 is 12.1212... So YES, 100x is still a repeating decimal.
2. 12.121212... minus 0.121212... would just be 12. This is because if we know that all the numbers behind the decimal point is 0.121212 and so on, 12.121212... minus 0.121212... the numbers behind the decimal would cancel out. So we are left with 12. So NO, the answer for 99x is NOT a repeating decimal.
Let the length of maria's book be a and that of Brandon's be b.
So, by the question,
the difference in length of books is 56
i.e. a-b=56------(1)
and the length of books all together is 348
i.e. a+b=348------(2)
Adding (1) and (2);
(a-b)+(a+b)=56+348
or, a-b+a+b=404
or, 2a=404
or, a=202
substitutting the value of a in (2),
202+b=348
or, b=146
therefore, the length of Maria's book is 202
and the length of Brandon's book is 146.
Answer:
![\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B6%7D%5C%5C-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B3%7D%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
If a 2x2 matrix is given as:
![\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D)
The inverse is:
![\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bad-bc%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Our matrix given is:
![\left[\begin{array}{cc}-4&2\\-6&6\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-4%262%5C%5C-6%266%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<em />
<em>Using the formula, let's find the inverse:</em>
<em>![\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]\\=\frac{1}{(-4)(6)-(-6)(2)}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\frac{1}{-12}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bad-bc%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%5Cfrac%7B1%7D%7B%28-4%29%286%29-%28-6%29%282%29%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%26-2%5C%5C6%26-4%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%5Cfrac%7B1%7D%7B-12%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%26-2%5C%5C6%26-4%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B6%7D%5C%5C-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B3%7D%5C%5C%5Cend%7Barray%7D%5Cright%5D)
</em>
