M(t)M, left parenthesis, t, right parenthesis models the distance (in millions of \text{km}kmstart text, k, m, end text) from Ma
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11. c) 7x² +5x +8 remainder 7.
12. d) 6x² -6x +3 remainder 2x.
Step-by-step explanation:
Step 1; By dividing 7x³ -2x² +3x -1 with x -1 we get the following calculations. We multiply 7x² with x-1 and get 7x³ - 7x². We subtract this from 7x³ -2x² and get 5x². Now we add this with the 3x in 7x³ -2x² +3x -1. We get 5x² +3x. We multiply x -1 with 5x and get 5x² -5x and subtract it from 5x² +3x and get 8x. We multiply the x -1 with 8 and get 8x -8. We subtract this from 8x -1 and get a remainder of 7. So the quotient is 7x² +5x +8 with a remainder of 7.
Step 2; By dividing 6 +0x³ -3x² +5x with x² +x we get the following calculations. We multiply 6x² with x² +x and get 6
+6x³. We subtract this from 6
+0x³ and get -6x³. Now we add this with the -3x² in 6
+0x³ -3x² +5x. We get -6x³ -3x². We multiply x² +x with -6x and get -6x³ -6x² and subtract it from -6x³ -3x² and get 3x². We multiply the x² +x with 3 and get 3x² +3x. We subtract this from 3x² +5x and get a remainder of 2x. So the quotient is 6x² -6x +3 with a remainder of 2x.
Madison worked for 7.5 hours before school and 15 hours after school
<em><u>Solution:</u></em>
Given that, Madison works a job before and after school
Amount earned before school = $ 11.50 per hour
Amount earned after school = $ 11.75 per hour
Amount earned last week = $ 262.50
Let "x" be the hours worked before school
Given that, she worked twice as many hours after school
So, number of hours worked after school = 2x
Therefore, we can say,
Total amount earned = (Amount earned before school)(number of hours) + (Amount earned after school)(number of hours)
Number of hours worked after school = 2x = 2(7.5) = 15
Thus Madison worked for 7.5 hours before school and 15 hours after school