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Vesna [10]
3 years ago
8

The owner of the Outdoor Furniture Center decides to use the 120% markup. At the end on

Mathematics
1 answer:
lana66690 [7]3 years ago
6 0

Answer: The total price of a bench is 1.008x.

Step-by-step explanation:

Since we have given that

Let the cost price be 'x'.

Mark up % = 120%

So, Mark up value would be

\dfrac{120}{100}x\\\\=1.20x

Discount % = 20%

Amount of discount is given by

\dfrac{20}{100}\times 1.2x\\\\=0.2\times 1.2x\\\\=0.24x

So, it becomes,

Amount after discount is given by

1.2x-0.24x\\\\=0.96x

Sales tax = 5%

Amount of sales tax would be

\dfrac{100+5}{100}\times 0.96x\\\\=\dfrac{105}{100}\times 0.96x\\\\=1.05\times 0.96x\\\\=1.008x

Hence, the total price of a bench is 1.008x.

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That's not a linear system, but you have an awesome school system for giving you this problem.

\dfrac 5 y - \dfrac 2 x = \dfrac{13}6

Multiply by 6xy to clear the fractions.

30x - 12y = 13 xy

That's a second degree equation, also known as a conic.  That one happens to be a hyperbola.  

30x = y(13 x +12)

y = \dfrac{30x}{13 x + 12}

Let's clear the fractions from the second equation, multiplying out common denominator xy:

\dfrac {36} x - \dfrac {24} y = 1

36y - 24 x = xy

We are being asked to find the meet of two hyperbolas, so we expect two answers, a quadratic equation.

Substituting,

36 \left( \dfrac{30x}{13 x + 12} \right) - 24 x = x \left( \dfrac{30x}{13 x + 12} \right)

36(30x) -24 x(13x + 12) = 30x^2

1080 x - 312 x^2- 288 x = 30x^2

x(792 - 342 x)= 0

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We have to rule out x=0 because it's in the denominator.

y = \dfrac{30x}{13 x + 12} = \dfrac{30(44/19)}{13(44/19)+12}

y = \dfrac{33}{20}

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3 years ago
Find the 8th term of the geometric sequence 5, -15, 45
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Answer:

a₈ = - 10935

Step-by-step explanation:

the nth term of a geometric sequence is

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a₈ = 5 × (-3)^{7} = 5 × - 2187 = - 10935

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