Uncle ian spent $59 at a book store. he bought science fiction and mystery novels. the science fiction novels cost $7 apiece and the mystery novels cost $9 apiece. if uncle ian bought 7 novels, how many of each type did he buy?

2 science fiction and 5 mystery

Step-by-step explanation:

First, we will set up a system of equations.

x (science fiction) y (mystery)

x + y = 7 This is the total books bought.

7x + 9y = 59 The amount of each set to the total cost.

Now we solve.

(-7)x + y = 7 equals

-7x - 7y = -49

added to

7x + 9y = 59

this equals

2y = 10

y = 5

Now we know one. We can plug it in to find the other value.

x + 5 = 7

x = 2

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2