Carlos is 33 years younger than Kristen. 2 years ago, Kristen's age was 2 times Carlos's age. How old is Carlos now?

Carlos is 35 years old now

Step-by-step explanation:

Assume that Carlos is x years old now

∵ Carlos is x years old now

∵ Carlos is 33 years younger than Kristen

- Kirsten's age is the sum of x and 33

∴ Kirsten is x + 33 years old now

2 years ago

∵ Carlos's age = x - 2

∵ Kristen's age = x + 33 - 2 = x + 31

∵ Kristen's age was 2 times Carlos's age

- Equate Kristen's age by 2 times Carlos's age

∴ x + 31 = 2(x - 2)

- Simplify the right hand side

∴ x + 31 = 2x - 4

- Subtract x from both sides

∴ 31 = x - 4

- Add 4 to both sides

∴ 35 = x

∵ x represents Carlos's age now

∴ Carlos is 35 years old now

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>