List all of the elements of set a if a = {x|x is an integer and -6 ≤ x < 0} a. {-6, -5, -4, -3, -2, -1, 0} b. {-6, -5, -4, -3, -2, -1} c. {-5, -4, -3, -2, -1}

Option b - {-6, -5,-4,-3,-2,-1}            

Step-by-step explanation:

Given : Set  

To find : List all of the elements of set a ?

Solution :

In Set  

there is an equal sign so -6 includes in the set.

there is no equal sign so 0 is not include in the set.

From -6 to 0 the number lies in between are -5,-4,-3,-2,-1.

So, The elements of set are {-6, -5,-4,-3,-2,-1}

Therefore, Option b is correct.

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.

(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