The only factoring you need to do is already done for you:
<em>x</em>² + <em>x</em> - 12 = (<em>x</em> + 4) (<em>x</em> - 3)
What you're asked to do is decompose
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12)
into partial fractions, i.e. find <em>a</em> and <em>b</em> such that
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = <em>a</em> / (<em>x</em> + 4) + <em>b</em> / (<em>x</em> - 3)
Multiply both sides by <em>x</em>² + <em>x</em> - 12 :
3<em>x</em> - 4 = <em>a</em> (<em>x</em> - 3) + <em>b</em> (<em>x</em> + 4)
3<em>x</em> - 4 = (<em>a</em> + <em>b</em>) <em>x</em> + (-3<em>a</em> + 4<em>b</em>)
So we have
<em>a</em> + <em>b</em> = 3
-3<em>a</em> + 4<em>b</em> = -4
and solving this system gives
<em>a</em> = 16/7 and <em>b</em> = 5/7
so you should submit the numbers in bold:
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = 16 / (7 (<em>x</em> + 4)) + 5 / (7 (<em>x</em> - 3))
Answer: $18 a week
Step-by-step explanation: hope it helps
Domain is the x-values.
Scenarios where positive integers are appropriately used for the domain of the function:
<span>The function c(p) represents The cost for P people to attend the movies. (number of people can either be 0 going upwards)
</span><span>the function m(t) represents the miles driven over T hours (hours always start with 1.)
</span><span>the function t(m) represents the average high temperature for a given number of months (number of months always start with 1)
</span><span>the function p(w) represents the prophet of a farmer who sells whole watermelons (count of whole watermelon starts with 1)
</span>
<span>the function h(n) represents the number of person-hours it takes to assemble n engines in a factory (number of engines always start with 1)</span>
Answer: B I believe
Step-by-step explanation:
Answer:
<em>This is a guess but is it : A Shadow ?</em>
<em>Hope this helps..</em>
<em>Also, may I have Brainliest if correct..?</em>
<em>Have a nice day!</em>
