Look at the graph, here : https://www.desmos.com/calculator/xudd5o54ri
The points of intersection are
x = 0
x = 4
The easiest way to answer this is to look at a graph, here : https://www.desmos.com/calculator/2acf7auewz
Notice, whosmans, that this piecewise function appears to be continuous except at x = 0
So....the last answer is correct
Kinda' hard to see...but
( f * p ) ( x) = f(x) * p(x) = the revenue from selling f(x) frozen yogurts at a price of p(x) per yogurt
[ Quantity sold ] * [ Price per unit ] = Revenue
The 29th term is given by :
1st term + common difference * ( 29 - 1) =
-43 + 8*(28) = 181
The sum is given by
[ 1st term + 29th term ] * number of terms / 2 =
[ -43 + 181 ] * 29 / 2 =
[ 138 ] * 29 / 2 =
2001
That's a nice solution, Rom....!!!
That's a pretty unique method, Heureka.....where did you find it ????
OK......
"a" = x = 4
So
3(4) + 2y = 12
12 + 2y = 12 subtract 12 from both sides
2y = 0 divide by 2 on both sides
y = 0 = " b "
Here's one way to check your work for these...
Let x = 1 and let y = 1
We want to evaluate the original expression, first
3 [ 4(1) + 2(1) ] + 5(1)
3 [ 4 + 2 ] + 5
3[6] + 5 = 18 + 5 = 23
Now....evaluate the final answer
17(1) + 6(1) =
17 + 6 = 23
Since the answers are the same.....we have it correct
We are distributing the "3" over the terms in the parentheses
3(4x + 2y) + 5x =
3*4x + 3*2y + 5x =
12x + 6y + 5x [ combine like terms ]
17x + 6y
