Dominic works on the weekends and on vacations from school mowing lawns in his neighborhood. For every lawn he mows, he charges
$12. Complete the table. Then determine ordered pairs, and create a labeled graph. 1. How many lawns will Dominic need to mow in order to make $240? _________(blank 1) 2. How much money will he make if he mows 9 lawns? _________(blank 2) Question 1 options: Blank # 1 Blank # 2
1 answer:
Answer:
<em>See Attachment for Graph</em>
<em></em>
Step-by-step explanation:
Given
Solving (a): Number of lawns in $240
Multiply both sides by 20
Solving (b): Cost of mowing 9 lawns
Multiply both sides by 9
To create a graph, we need to generate a formula;
If
So:
<em>The graph formula is</em>
<em>See Attachment for Graph</em>
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Step 1 involves you listing out all the ways to multiply to 56, and then adding up those factors. For instance, the first row has 1 and 56 which add to 57 in the third column. The second row has -1 + (-56) = -57. The third row has 2+28 = 30. And so on. The idea is to fill out the table completely with the other ways to have factors of 56 added up. The table is shown in the attached image below.
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Step 2 then uses the table to figure out which pair of factors (of 56) add to -15. This would be -7 and -8. In other words,
-7 plus -8 = -15
-7 times -8 = 56
We have found the right pair of numbers. In the table I have provided, this is shown as the highlighted yellow row.
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Step 3 is then using those pair of numbers found in step 2 to set up the factorization. We would say that x^2-15x+56 factors to (x-7)(x-8). This is the same as (x-8)(x-7) as we can multiply two numbers in any order we want.
