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Thepotemich [5.8K]
3 years ago
10

Igloos unlimited charges $150 per night with a 50% discount for every night after the third night .if you stay for days how much

will you pay?
Mathematics
1 answer:
Marina CMI [18]3 years ago
6 0

Answer:

150x,       (x<=3)

225+75x,   (x>3)

*x is the number of nights stayed.

Step-by-step explanation:

-Let the number of days stayed be x.

#If the number of days is equal to or less than 3 days, the cost is:

Cost=C_d\times Days\\\\=150x

Hence, the cost for x>3 is given by 150x

#If the number of days is greater than 3, the the cost is calculated as:

\#First \ 3 \ Days.\\Cost=C_d\times Days\\\\\\=150\times 3\\\\=450\\

\\\#Next \ number \ of \ days\\\\Cost=C_d\times Days\\\\=0.5(150)\times (x-3)\\\\=75(x-3)

We sum the two costs for x>3

\sum{Costs}=450+75(x-3)\\\\=225+75x

Hence, the cost for x>3 is given by 225+75x

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The partial factorization of x2 – x – 12 is modeled with algebra tiles.
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Answer:

x² – x – 12 = (x – 4)(x + 3)

Step-by-step explanation:

Identify two numbers that add to -1 and multiply to -12, let's call them p and q.

So ax² + bx + c = (x + p)(x + q)

pq = c

p + q = b.

It is easier to find these numbers by finding factors of -12.

This can be done by splitting the number up until all the numbers are prime.

-12 → 6 × -2 or -6 × 2 → -(3 × 2 × 2)

There can only be two numbers so the only options we have are 6 and -2, -6 and 2, 3, and -4, or -3 and 4.

We can eliminate them by adding them up.

6 + -2 = 4 ≠ -1 so that can't be it.

-6 + 2 = -4 ≠ -1 so that can't be it either.

-3 + 4 = 1 ≠ -1

therefore p and q are 3 and -4 because 3 + -4 = -1.

so x² – x – 12 = (x – 4)(x + 3)

p = -4, and q = 3.

(x – 4)(x + 3) = x(x + 3) – 4(x + 3) = x² + 3x – 4x + 12 = x² – x – 12

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