Answer:
x - 3 ≥ 1
Step-by-step explanation:
Solving each of the inequalities
x + 3 ≥ 1 ( subtract 3 from both sides )
x ≥ - 2
3x ≥ 1 ( divide each inequality by 3 )
x ≥
x - 3 ≥ 1 ( add 3 to both sides )
x ≥ 4 ← required solution
What is the circumference (in inches) of a circle with radius of 5 inches? Use 3.14 for π.
2 answers:
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9514 1404 393
Answer:
n = 8
Step-by-step explanation:
"By inspection" is an appropriate method.
We are asked to compare the expressions
n·n
8·n
and find the value(s) of n that makes them equal. <em>By inspection</em>, we see that n=8 will make these expressions equal. We also know that both expressions will be zero when n=0.
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More formally, we could write ...
n^2 = 8n . . . . the two formulas give the same value
n^2 -8n = 0 . . . . rearrange to standard form
n(n -8) = 0 . . . . . factor
Using the zero product rule, we know the solutions will be the values of n that make the factors zero. Those values are ...
n = 0 . . . . . makes the factor n = 0
n = 8 . . . . . makes the factor (n-8) = 0
Generally, we're not interested in "trivial" solutions (n=0), so the only value of n that is of interest is n = 8.
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A lot of times, I find a graphing calculator to be a quick and easy way to find function argument values that make expressions equal.
