-|2x+3| > 2 and <span>-|2x+3| > - 2
</span>-2x+3 > 2
-2x > 2 - 3
-2x > -1
-2x / -2 > -1 / -2
x < 1/ 2
-|2x+3| > - 2
x < 5/2
<span>Part
A: Solve A = (x + 23) for x.
A = x + 23
=> A - 23 = x + 23 - 23
=> A - 23 = x
=> x = A - 23 <------- answer
Part B: Determine the value of x
when A = 108
Replace the value of A in the expression x = A - 23
x = 108 - 23 = 75
x = 75 <------- answer
Part C: Solve -np - 90 > 30 for n.
-np - 90 > 30
=> -np + np - 90 >30 + np
=> - 90 > 30 + np
=> -90 - 30 > 30 - 30 + np
=> -120 > np
=> np < - 120 <----- answer
</span>
Answer: NP = 9 inches
Step-by-step explanation:
In a parallelogram, the opposite sides are equal.
If the length of the longer side is MN, it means that the length of the two opposite longer sides is 2MN.
If the length of the shorter side is NP, it means that the length of the two opposite shorter sides is 2NP.
The perimeter is 2MN + 2NP
If the perimeter of MNPQ is 68 inches, it means that
2MN + 2NP = 68- - - - - - - - - - - -1
In parallelogram MNPQ, side MN is seven inches longer than twice the length of side NP. It means that
MN = 2NP + 7- - - - - - - - - - -2
Substituting equation 2 into equation 1, it becomes
2(2NP + 7) + 2NP = 68
4NP + 14 + 2NP = 68
4NP + 2NP = 68 - 14
6NP = 54
NP = 54/6
NP = 9 inches
Answer: Answers are in the steps read carefully!
Step-by-step explanation:
A) 3x^2 - 7x + 2 To factor this polynomial, you have to find two numbers that their product is 6 and their sum is -7. The numbers -1 and -6 works out because -6 times -1 is 6 and -6 plus -1 is -7.
Now rewrite the polynomial as
3x^2 - 1x - 6x + 2 Now group it
(3x^2 - 1x) (-6x+2) Factor it by groups
x (3x -1) -2(3x -1) Now factor out 3x-1
(3x -1) (x-2) Done!
B) 2x^2 - x -3 Now the same way.You will have two numbers that their product is -6 and their sum is -1. You may be wondering how I get -6 .I get -6 by multiply the leading coefficient 2 by the constant -3. The numbers -3 and 2 works out. Because -3 times 2 is -6 and -3 plus 2 is -1.
Rewrite the polynomial as
2x^2 +2x - 3x -3 GRoup them and factor them
(2x^2 + 2x) (-3x-3)
2x(x+1) -3(x+1) Factor out x+1
(x+1) (2x -3) Done!
C) 3x^2 - 16x - 12 Find two numbers that their product is -36 and their sum is -12. The numbers -18 and 2 works out because -18 times 2 is -36 and -18 plus 2 is -16.
Rewrite the polynomial
3x^2 +2x -18x - 12 GRoup them
(3x^2 + 2x) (-18x - 12) Factor them
x (3x +2) -6(3x +2) Factor out 3x+2
(3x+2) (x -6) Done !
