Tenemos un rectángulo cuya área es (15n + 9nx) cm 2 y su base mide (3n) cm. Existe también un cuadrado con la misma altura del rectángulo, tal que si al área del cuadrado se le disminuye (9x 2 ) cm 2 , ésta medirá 1825 cm 2 . ¿Cuánto mide el área original del cuadrado?

El área original del cuadrado es 34225 cm²

Step-by-step explanation:

Los parámetros dados son;

El área del rectángulo = (15·n + 9·n·x) cm²

La longitud de la base del rectángulo = (3·n) cm

La altura del cuadrado = La altura del rectángulo

El área original del cuadrado - 9·x² cm² = 1825 cm²

La altura del rectángulo = (El área del rectángulo) / (La longitud de la base del rectángulo)

∴ La altura del rectángulo = (15·n + 9·n·x) / (3·n) = 5 + 3·x

La altura del rectángulo = 5 + 3 · x = La altura del cuadrado

El área del cuadrado = Lado × Lado = Altura × Altura = (5 + 3·x) × (5 + 3·x)

∴ El área del cuadrado = (5 + 3·x) × (5 + 3·x) = 9·x² + 30·x + 25

Del área original del cuadrado - 9·x² cm² = 1825 cm², tenemos;

9·x² + 30·x + 25 - 9·x² = 1825

30·x + 25 = 1825

30·x = 1825 - 25 = 1800

x = 1800/30 = 60

x = 60

El área original del cuadrado - 9·x² cm² = 1825 cm²

El área original del cuadrado = 1825 cm² + 9·x² cm² = 1825 cm² + 9 × 60² cm² = 34225 cm²

El área original del cuadrado también se puede encontrar de la siguiente manera;

El área original del cuadrado = (5 + 3 × 60) × (5 + 3 × 60) = 34225 cm²

El área original del cuadrado = 34225 cm².

answer:

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payment for service including tax

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explanation:

service only with 20% tip  

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in the opening of the question the word 'service' is associated only with the pretax value.

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so technically the answer is  

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however, the intention of the question provider may have been that your answer is to be  

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'

payment just for service  

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payment for service including tax

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tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

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related questions

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.