Answer:
a=9 , b=14
Step-by-step explanation:
Just do the operation (x+7)(x+2)
x(x)+x(2)+7(x)+7(2)
x^2+2x+7x+14
x^2+9x+14
So a=9 and b=14
While it says not to state it, I will state which one is which, just for clarification.
Linear Pattern: A person is paid $10 for every hour they work. Before they start working, they are given an additional $5. They receive no raises in their pay.
This is linear because the pay is constant, and they aren't receiving any additional money. The equation for this would be y = 10x+5, x is the amount of hours they work.
Non-Linear Pattern: A person is paid $10 for every hour they work. Before they start working, they get are given an additional $5. For every 30 minutes they work after hour 4, they receive a $1 raise.
This is non-linear because the pay, after a certain amount of time, would go up, and the graph would soon start going higher after hour 4.
An ordered pair for the linear would be: (5, 55)
After working 5 hours, they would have $55.
An ordered pair for the non-linear would be (5, 56)
After working for 5 hours, they would have $56.
<em>If f(1) = 1 that means c is -2 because when you substitute x = 1 and when c = -2, you'll get f(1) = -2(1)+3 = -2+3 = 1</em>
<em>So the constant c is -2 and that means the value of f(-4) is</em>
<em>f(-4)=-2(-4)+3=8+3=11</em>
<em />
<em>Thus, the value of f(-4) is 11.</em>
<em />
<em>About why does "c" have to be -2, here's the proof.</em>
<em>Given y = f(x), therefore.</em>
<em>y=cx+3</em>
<em>Since when x = 1 and y = 1, then Substitute x = 1 and y = 1, thus 1 = c+3</em>
<em>1 - 3 = c and therefore, -2 = c #</em>
<em>So this is the proof that c = -2</em>
Integration by parts will help here. Letting

and

, you end up with

and

. Now


For the remaining integral, setting

gives

, so

Putting everything together, you end up with
Answer:
Using the estimate:
The car has to go for 1,200 miles but it consumes a gallon of gasoline for every 30 miles. The number of gallons it will need is therefore:
= 1,200 / 30
= 40 gallons
Each gallon costs $3.00 so the total cost is:
= 40 * 3
= $120
Without using the estimate:
The car has to go for 1,211 miles but it consumes a gallon of gasoline for every 29 miles. The number of gallons it will need is therefore:
= 1,211 / 29
= 41.76 gallons
Each gallon costs $3.40 so the total cost is:
= 41.76 * 3.40
= $141.98
<em>Using the estimate provides a lower cost of gasoline for the trip. </em>