If $-3\le x+5 \le 8$ and $x$ is an integer, what is the sum of all the possible solutions?

-30

Step-by-step explanation:

The integers are the whole numbers and the opposite of the whole numbers.

That is {...,-3,-2,-1,0,1,2,3,...} is the set of integers.

If it is a number you count with or the opposite of a number you count with it or 0, then it is an integer.

So we need to solve the inequality first, and then just say all the integers included in that compound inequality. Last step is to add since it is asking for the sum of those integers.

Let's do this.

Subtract 5 on all sides:

Simplify all sides:

This inequality includes all numbers between -8 and 3, and both include -8 and 3 because of the equal part on both of the inequality parts.

So we have -8,-7,-6,-5,-4,-3,-2,-1,0,1,2, and 3 are the integer solutions of this inequality.

Let's add them. I'm going to put opposites together because I know they will zero out.

So I have this:

-8+-7+-6+-5+-4+-3+-2+-1+0+1+2+3

-8+-7+-6+-5+-4+(-3+3)+(-2+2)+(-1+1)+0

-8+-7+-6+-5+-4+0       +0        +0     +0

-8+-7+-6+-5+-4

-(8+7+6+5+4)

-([8+7]+[6+5]+4)

-([15]+[11]+4)

-(15+11+4)

-([15+11]+4)

-([26]+4)

-(26+4)

-(30)

-30

a ruler? idk

step-by-step explanation:

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841