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4 years ago

the product of two consecutive even positive integers is 10 more than seven times the larger . find the integers?

1 answer:

4 0

2 consecutive even numbers.....x and x + 2

x(x + 2) = 7(x + 2) + 10
x^2 + 2x = 7x + 14 + 10
x^2 + 2x = 7x + 24
x^2 + 2x - 7x - 24 = 0
x^2 - 5x - 24 = 0
(x - 8)(x + 3) = 0

x - 8 = 0
x = 8

x + 3 = 0
x = -3...not this one because it is negative

x = 8
x + 2 = 8 + 2 = 10

so ur 2 consecutive even numbers are 8 and 10

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3 years ago

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2 years ago

Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every

Nutka1998 [239]

Answer:

25 seconds

Step-by-step explanation:

Hi there!

In order to answer this question, first we need to know how many bolts per second are produced by each machine, this can be known by dividing the number of bolts by the time it takes.

For machine A:

$A = \frac{120 bolts}{40 s}= 3 \frac{bolts}{s}$

For machine B:

$B = \frac{100 bolts}{20 s}= 5 \frac{bolts}{s}$

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Now, we need to know how much time it will take to producee 200 bolts, to find this out we need to divide the amount of bolts by the production rate:

$t = \frac{bolts}{ProductionRate}= \frac{200 bolts}{8 \frac{bolts}{s} }$

The <em>bolts</em> unit cancell each other and we are left with <em>seconds</em>

$t = \frac{200}{8} s = 25 s$

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Greetings!

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3 years ago

Read 2 more answers

Paul owes Paula 35 cents and has a pocket full of 5-cent coins, 10-cent coins, and 25-cent coins that he can use to pay her. Wha

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So, what is the case in which he uses the least coins? can he use 1 coin? no, there isn't a 35 cent coin. can he use 2 coins? yes! he can use 25+10 cent coins!

now, the largest number of coins means the coins of the smallest value: so using only 5 cent coins. How many would this be?

we have to divide:

35/5=7

so we would use 7 coins.

And the difference is 5: 7-2 is 5.

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3 years ago