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4 years ago

Factor the expression. 15n−18

Mathematics

2 answers:

Taya2010 [7]4 years ago

6 0

Divide each term by 3...
15n - 8 = 3(5n - 6)

Alex17521 [72]4 years ago

5 0

I saw that you put this question here twice so here's my answer again with the math.

Factor 15n−18
15n−18
=3(5n−6)

3(5n−6)

5n-18 factored is 3(5n−6)

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The perimeter of a rectangle is 202. The length is 26 more than 4 times the width. Find the dimensions

jek_recluse [69]

Answer:

$P = 2*(26+4y) + 4y$

And if we solve for y we got:

$202= 52 +8y +4y$

$202= 52 +12 y$

And replacing we got:

$150 = 12y$

And we got:

$y = \frac{150}{12}= 12.5$

And for x we got:

$x = 26 +4*12.5 = 76$

So then the length would be 76 and the width we got 12.5

Step-by-step explanation:

For this case we have a rectangle. The perimeter is given by:

$P= 2x+2y$

Where x represent the length and y the the width. We can set the following conditions:

$x = 26 +4y$

And if we replace the conditions we got:

$P = 2*(26+4y) + 4y$

And if we solve for y we got:

$202= 52 +8y +4y$

$202= 52 +12 y$

And replacing we got:

$150 = 12y$

And we got:

$y = \frac{150}{12}= 12.5$

And for x we got:

$x = 26 +4*12.5 = 76$

So then the length would be 76 and the width we got 12.5

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Answer:

Part (A) The required ways are 792.

Part (B) The required ways are 101376.

Step-by-step explanation:

Consider the provided information.

Part (A) The alphabet {a, b}

The length of strings is 12 that containing exactly five a's.

The number of ways are: $\frac{12!}{5!7!}$

After filling "a" we have now 7 places.

For 7 places we have "a" and "b" alphabet but we already select a's so now the remaining place have to fill by "b" only.

Thus, the required ways are: $\frac{12!}{5!7!}\times 1=792$

Part (B) The alphabet {a, b, c}

We have selected five a's now we have now 7 places.

For 7 places we have "b" and "c".

Thus, there are 2 choices for each 7 place that is $2^7$

Therefore the total number of ways are: $792\times 2^7=101376$

Thus, the required ways are 101376.

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4 years ago