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nordsb [41]
3 years ago
10

PLZ help!!

Mathematics
1 answer:
Paladinen [302]3 years ago
5 0

Answer:

Step-by-step explanation:

At the self employed store, her monthly expense would be

y = $835

Which would plot as a horizontal line

At the franchise store here expense would be

y = 5x where x is the number of haircuts completed.

This would plot as a straight line of slope 5

The two would intersect when the two y values are equal

5 x = 835

so the same cost per month would occur at y = 835

at the franchise, she would have completed 835/5 = 167 haircuts.

If she plans on doing fewer than 167 haircuts per month, she nets more money at the franchise,

If she completes more than 167 haircuts per month, the self employed store deal keeps more money in her pocket.

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ohaa [14]

Answer:

9\, w^{2} - 100 = (3\, w - 10) \, (3\, w + 10).

Step-by-step explanation:

Fact:

\begin{aligned} & (a - b)\, (a + b)\\ =\; & a^{2} + a\, b - a\, b - b^{2} \\ =\; & a^{2} - b^{2} \end{aligned}.

In other words, (a^{2} - b^{2}), the difference of two squares in the form a^{2} and b^{2}, could be factorized into (a - b)\, (a + b).

In this question, the expression (9\, w^{2} - 100) is the difference between two terms: 9\, w^{2} and 100.

  • 9\, w^{2} is the square of 3\, w. That is: (3\, w)^{2} = 9\, w^{2}.
  • On the other hand, 10^{2} = 100.

Hence:

9\, w^{2} - 100 = (3\, w)^{2} - (10)^{2}.

Apply the fact that a^{2} - b^{2} = (a - b) \, (a + b) to factorize this expression. (In this case, a = 3\, w whereas b = 10.)

\begin{aligned}& 9\, w^{2} - 100 \\ =\; & (3\, w)^{2} - (10)^{2} \\ = \; & (3\, w - 10)\, (3\, w + 10)\end{aligned}.

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