Lines are perpendicular if the slope of one is the negative reciprocal of the other. In this case the slopes are -8/3 and 8/3, so while negative they are not reciprocal. So no, the two lines intersect but are not perpendicular.
Each new term of this arith. seq. is obtained by adding 4 to the previous term. Hence, 15 = 11+4; 19=15+4, and so on. Add 4 to 19 to get the next term. Keep going until you have 4 new terms for the arith. seq. 11, 15, 19, .....
Let the number of children be c, and the number of adults be a.
c + a = 170 (total number of tickets)
Then the cost of each is: $5.90/child, $9.60/adult:
5.9c + 9.6a = 1269.40 (total sales)
Solving as 2 simultaneous equations, we first transform the first equation:
a = 170 - c
Substitute into the 2nd equation:
5.9c + 9.6(170 - c) = 1269.40
Solving gives c = 98, and a = 170 - 98 = 72. This means that 72 adult tickets were sold that day.
Answer:
Vertical and supplementary
(2a+2)(4a+4)
8a^2+8a+8a+8
The answer is 8a^2+16a+8
