9514 1404 393
Answer:
3 < x < 6
Step-by-step explanation:
Use the perimeter formula to write an expression for the perimeter. Then put that in an inequality with the given limits. Solve for x.
P = 2(L +W)
P = 2((4x) +(2x +1)) = 2(6x +1) = 12x +2 . . . . . fill in the given values; simplify
The perimeter wants to be between 38 and 74 cm, so we have ...
38 < 12x +2 < 74
36 < 12x < 72 . . . . . subtract 2
3 < x < 6 . . . . . . . . . divide by 6
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<em>Additional comment</em>
Solving a compound inequality is very much like solving a single inequality. You need to "undo" what is done to the variable. The rules of equality (ordering) still apply. If you were to multiply or divide by a negative number, the direction (sense) of the inequality symbols would reverse in the same way they do for a single inequality.
Here, our first step was to subtract 2 from all parts of the inequality:
38 -2 < 12x +2 -2 < 74 -2 ⇒ 36 < 12x < 72
The division by 12 worked the same way: all parts are divided by 12.
36/12 < (12x)/12 < 72/12 ⇒ 3 < x < 6
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If it makes you more comfortable, you can treat the perimeter limits as two separate inequalities: 38 < 12x+2 and 12x+2 < 74. Both restrictions apply, so the solution set is the intersection of the solution sets of these separate inequalities.
Answer:
or 0.25 or 25%. Answer as instructed in the question.
Step-by-step explanation:
There are four equal parts and since the spinner is unbiased, the probabilities will be equal.
2 over 2 down i beleive...
so 2/-2
Here we're discussing the "nth partial sum of a geom series."
1 - r^n
The formula for that is s(n) = a(1) ---------------
1-r
We can subst. the given values and see where that takes us:
1 - (-2)^6 1 - 64
105 = a(1)*---------------- = ----------*a(1) = -21*a(1)
1-(-2) 3
105
Solving this for a(1): a(1) = --------- = -5 (answer)
-21
Answer:
a=1.75
Step-by-step explanation:
Use the attachment posted