The sum of 5 consecutive even numbers is 180 what is the first number in the sequence

First, a even number in general could be written as  2k for any k ( k is any integer number).

Let x_1, x_2, x_3, x_4, x_5 the 5 consecutive even numbers, then,

x_1 + x_2 + x_3 + x_4 + x_5 = 180. But for the first commentary, any of the x_i's are even numbers, so, are of the form 2k_i, but, they are consecutive, think about the sequence: 2,4,6,8,10, we could written as 2(1) + 2 (2) + 2(3) + 2(4) + 2(5), the numbers between (), are the k's and are consecutive, and we could write consecutive numbers as x, x+1, x+1 +1 = x+2, (x+2)+1, etc.

So, for the previous commentary, we rewrite

x_1 + x_2 + x_3 + x_4 + x_5 = 180

as

2k + 2(k+1) + 2(k+2) + 2(k+3) + 2(k+4)  = 180

is equivalent to (factorizing 2)

2 [k + k+1 + k+2 +k+3 +k+4 ] = 180

(divide both sides by 2)

[k + k+1 + k+2 +k+3 +k+4 ] = 90

(simplifyng the expression)

5k+10 = 90

(substracting 10 in both sides)

5k = 80

(divide both sides by 5)

k = 16

then, the first number is x_1 = 2k = 2(16) = 32

Now, we can check, the corresponding sequence was

32 + 34 +36 +38 +40 = 180.

i dont know sorry

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!