Answer:For number 6 I believe is x^12y^22
Answer:
![a + b \geq 30](https://tex.z-dn.net/?f=a%20%2B%20b%20%5Cgeq%20%2030)
![b - a \geq 10](https://tex.z-dn.net/?f=b%20-%20a%20%5Cgeq%20%2010)
Step-by-step explanation:
Given
Two integers a and b
The first statement in the question says, their sum is at least 30
The keyword "at least" means their sum can not fall below 30 and this is represented mathematically as
![a + b \geq 30](https://tex.z-dn.net/?f=a%20%2B%20b%20%5Cgeq%20%2030)
The next statement says their difference is at least 10 and b is greater;
The keyword "at least" means the same as used above (i.e. can not exceed); The second statement is represented as:
![b - a \geq 10](https://tex.z-dn.net/?f=b%20-%20a%20%5Cgeq%20%2010)
Hence, the system of inequality that represents the statements are:
![a + b \geq 30](https://tex.z-dn.net/?f=a%20%2B%20b%20%5Cgeq%20%2030)
![b - a \geq 10](https://tex.z-dn.net/?f=b%20-%20a%20%5Cgeq%20%2010)
Answer:
![\frac{4}{6} =\frac{6}{9}= \frac{8}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B6%7D%20%3D%5Cfrac%7B6%7D%7B9%7D%3D%20%5Cfrac%7B8%7D%7B12%7D)
Step-by-step explanation:
<em>I'm assuming this is asking for 3 separate fractions that are each equal to 2/3</em>
Remember, multiplying the top and bottom of a fraction by a number will not change the fraction.
![\frac{2}{3} *\frac{2}{2} =\frac{4}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%2A%5Cfrac%7B2%7D%7B2%7D%20%3D%5Cfrac%7B4%7D%7B6%7D)
![\frac{2}{3} *\frac{3}{3} =\frac{6}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%2A%5Cfrac%7B3%7D%7B3%7D%20%3D%5Cfrac%7B6%7D%7B9%7D)
![\frac{2}{3} *\frac{4}{4} =\frac{8}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%2A%5Cfrac%7B4%7D%7B4%7D%20%3D%5Cfrac%7B8%7D%7B12%7D)
These three fractions are all equal to 2/3
The two numbers are 23 and 16 and the method is shown algebraically using simultaneous equations in the photo