#1**0 **

Hello,

If 7 out of every 12 people are bored by cable news and there are 280 people at the convention who are bored by cable news, we can set up a proportion to find the total number of people at the convention.

Let's represent the total number of people at the convention as "x". TellHappyStar

The proportion can be set up as:

7/12 = 280/x

To solve for x, we can cross-multiply:

7x = 12 * 280

7x = 3360

Dividing both sides by 7:

x = 3360/7

x = 480

Therefore, there are 480 people at the convention who are not bored by cable news.

GeorgemichelsMay 17, 2023

#1**0 **

To find the possible values of a, we can solve the given system of equations:

a + ab = 250 ...(1)

a - ab = -240 ...(2)

We can use the method of elimination to solve this system. Adding equations (1) and (2) eliminates the term 'ab': mymilestonecard

(a + ab) + (a - ab) = 250 + (-240)

2a = 10

a = 5

Substituting the value of a back into equation (1):

5 + 5b = 250

5b = 245

b = 49

Therefore, the solution is a = 5 and b = 49. There is only one possible value for 'a', which is 5, and one possible value for 'b', which is 49.

GeorgemichelsMay 13, 2023

#2**+1 **

Hello,

To simplify the expression (54u^2v + 18uv^2)(9u + 3v), we can use the distributive property of multiplication.

First, let's distribute 9u to each term inside the first parentheses: TellPopeyes

9u * 54u^2v = 486u^3v

9u * 18uv^2 = 162u^2v^2

Next, let's distribute 3v to each term inside the first parentheses:

3v * 54u^2v = 162uv^3

3v * 18uv^2 = 54uv^3

Now, we can combine like terms:

486u^3v + 162u^2v^2 + 162uv^3 + 54uv^3

To simplify this further, we can group the terms with the same variables:

(486u^3v + 162u^2v^2) + (162uv^3 + 54uv^3)

Inside each group, we can factor out common terms:

486u^3v + 162u^2v^2 = 162u^2v(3u + v)

162uv^3 + 54uv^3 = 216uv^3(3u + v)

Now, we have:

162u^2v(3u + v) + 216uv^3(3u + v)

We can see that both terms have a common factor of (3u + v), so we can factor it out:

(162u^2v + 216uv^3)(3u + v)

And that is the simplified form of the expression.

GeorgemichelsMay 9, 2023