# Georgemichels

#1
+8
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.

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.

May 17, 2023
#1
+8
0

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

a + ab = 250 ...(1)
a - ab = -240 ...(2)

(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.

May 13, 2023
#2
+8
+1

Hello,

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

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.

May 9, 2023