Determine if the sequence is arithmetic (yes or no). if it is, find the common difference. 1. 35, 32, 29, 2. -30, -40, -50, -

yes to both

Step-by-step explanation:

If the sequences are arithmetic then the common difference d, between adjacent  terms will be equal.

35, 32, 29, 26, ...

d = 32 - 35 = 29 - 32 = 26 - 29 = - 3

Hence sequence is arithmetic

- 30, - 40, - 50, - 60,

d = - 40 - (- 30) = - 40 + 30 = - 10

d = - 50 - (- 40) = - 50 + 40 = - 10

d = - 60 - (- 50) = - 60 + 50 = - 10

Hence sequence is arithmetic

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

~

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240