Factoring by grouping usually pairs up the first 2 sets of expressions with the second 2 sets. Ours looks like this, then:
. If we factor out the common x-squared in the first set of parenthesis, along with factoring out the common 5 in the second set, we get this:
. Now the common expression that can be factored out is the (x-9). When we do that, here's what it looks like:
. I'm not sure how far you are going with this. You could set each of those equal to 0 and solve for x in each case. The first one is easy. If x - 9 = 0, then x = 9. The second one involves the imaginary i since x^2 = -5. In that case,
. Hopefully, in what I have given you, you can find what you're looking for.
Answer:
1
Step-by-step explanation:
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Answer:
- shortest: 11 1/8 in
- longest: 11 3/8 in
Step-by-step explanation:
It should be no surprise that the shortest allowable length is the nominal length less the full allowed tolerance:
11 1/4 - 1/8 = 11 1/8 . . . inches
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Likewise, the longest allowable length is the nominal length plus the maximum tolerance:
11 1/4 + 1/8 = 11 3/8 . . . inches
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Of course, you know that 1/4 = 2/8, so adding or subtracting 1/8 gives the fractions shown above.
100 notes were altogether
<em><u>Solution:</u></em>
Given that ratio of the number of $2 notes to the number of $5 notes was 4 : 1
number of $2 notes : number of $5 notes = 4 : 1
Let 4x be the number of $ 2 notes
Let 1x be the number of $ 5 notes
Given that total value of notes is $ 260
Therefore,
$ 2 (number of $ 2 notes ) + $ 5(number of $ 5 notes ) = $ 260
$ 2(4x) + $ 5(1x) = $ 260
8x + 5x = 260
13x = 260
x = 20
<em><u>Thus number of notes altogether is given as:</u></em>
4x + 1x = 4(20) + 1(20) = 80 + 20 = 100
Thus 100 notes were altogether
