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Y_Kistochka [10]
3 years ago
9

A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of the house

Mathematics
1 answer:
Nina [5.8K]3 years ago
8 0

Answer:

(15,18)

Step-by-step explanation:

write two equations with the information provided.

2x + 3y = 84

x + 4y = 87

use the property of substitution to answer.

x + 4y = 87,   x = 87 - 4y

2(87 - 4y) + 3y = 84

174 - 8y + 3y = 84

174 - 84 = 8y - 3y

90 = 5y

90/5 = y

y = 18

Add the value of Y to an original equation. Solve for X

2x + 3(18) = 84

2x + 54 = 84

2x = 84 - 54

2x = 30

x = 30/2

x = 15

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If the 5th term of a geometric progression is 162 and the 8th term is 4374, find the (i) 1st three terms of the sequence; (ii) s
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Answer:

see explanation

Step-by-step explanation:

The nth term of a geometric progression is

a_{n} = a₁r^{n-1}

where a₁  is the first term and r the common ratio

Given a₅ = 162 and a₈ = 4374 , then

a₁r^{4} = 162 → (1)

a₁r^{7} = 4374 → (2)

Divide (2) by (1)

\frac{a_{1}r^{7}  }{a_{1}r^{4}  } = \frac{4374}{162}

r³ = 27

r = \sqrt[3]{27} = 3

Substitute r = 3 into (1) and solve for a₁

a₁(3)^{4} = 162

81a₁ = 162

a₁ = \frac{162}{81} = 2

Then

a₂ = a₁ × 3 = 2 × 3 = 6

a₃ = a₂ × 3 = 6 × 3 = 18

The first 3 terms are 2, 6, 18

(ii)

The sum to n terms of a geometric progression is

S_{n} = \frac{a_{1}(r^{n}-1)  }{r-1} , then

S_{10} = \frac{2(3^{10}-1) }{3-1}

     = \frac{2(59049-1)}{2}

     = 59049 - 1

     = 59048

   

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