The answer to the question provided is 10.
Step-by-step explanation:
☆Cross multiply.
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It helps to first clarify that the notation (f - g)(x) simply means f(x) - g(x). Given that, let's look at our f(x) and our g(x) here, and use their definitions to find their difference.
When we're taking (f - g)(x), we simply substitute the expression 3x + 1 for f(x) and the expression x² - 6 for g(x) to obtain:
Or, ordering the polynomial from highest power to lowest and combining the constants:
Edit: By request, here's what would happen if you had something instead like:
In this case, you'd have to *multiply* the two function expressions together. Here's what that would look like:
Using the distributive property, we can distribute the expression
to the terms 
and 
:
Distributing again, we get:
And we're done.
When we're taking (f - g)(x), we simply substitute the expression 3x + 1 for f(x) and the expression x² - 6 for g(x) to obtain:
Or, ordering the polynomial from highest power to lowest and combining the constants:
Edit: By request, here's what would happen if you had something instead like:
In this case, you'd have to *multiply* the two function expressions together. Here's what that would look like:
Using the distributive property, we can distribute the expression
Distributing again, we get:
And we're done.
Answer:
$53
Step-by-step explanation:
Given that, two type of clothes nylon and wool carpet.
Let the price of one yard of nylon carpet = $
Let the price of one yard of wool carpet = $
Price for 16 yd of nylon carpet and 22 yd of wool carpet = $1902
Price for 20 yd of nylon carpet and 21 yd of wool carpet = $2033
Writing equations as per given statement:
Here, we have to find the value of .
By equation (1), we get:
Putting the value from equation (3) to equation (2):
Therefore, the cost per yard for the wool carpet is $<em>53.</em>