A student makes money by watching the neighbors' dog. The situation is modeled in the graph below. Money Made 130 120 110 100 90
80 Fee (dollars) 70 60 50 40 30 20 10 0 1 2 3 7 8 9 4 5 6 Time (days) 10 Select the statement that describes the relationship between the amount of money the student makes and time in days. The student charges $11 plus an additional $20 per day, The student charges $20 plus an additional $11 per day. The student charges $20 plus an additional $10 per day.
1 answer:
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These numbers are 12 and 14.
Answer:
Part A : 2y( x³ + 9x - 5x² - 45 ), Part B : 2y( x - 5 )( x² + 9 )
Step-by-step explanation:
Part A : Let's break every term down here to their " prime factors ", and see what is common among them,
2x³y + 18xy − 10x²y − 90y -
2x³y = 2 x³
y,
18xy = 2 3
3
x
y,
− 10x²y = 2 - 5
x²
y, - so as you can see for this example I purposely broke down - 10 into 2 and - 5. I could have placed the negative on the 2, but as that value was must likely common among all the terms, I decided to place it on the 5. The same goes for " − 90y. " I placed the negative there on the 5 once more.
− 90y = 2 - 5
3
3
y
The terms common among each term are 2 and y. Therefore, the GCF ( greatest common factor ) is 2x. Let's now factor the expression using this value.
2y( x³ + 9x - 5x² - 45 )
Part B : Let's simply factor this entire expression. Of course starting with the " factored " expression : 2y( x³ + 9x - 5x² - 45 ),
- Factor out "
" by grouping,
- Factor 9 from 9x - 45 and x² from x³ - 5x²,
- Factor out common term x - 5,
- And our solution is thus 2y( x - 5 )( x² + 9 )