Mathematics, 19.01.2020 12:31 5001Je

The product of two consecutive positive integers is 812. what is the value of the lesser integer?

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The answer the question, let x be the smaller positive integer. With this, the greater integer may be represented as x + 1. The product of these integers is 812. The product may be written as,

(x)(x + 1) = 812

Solving for x in this problem gives x = 28 or x = -29. Since we are asked about positive integers only, x = -29 becomes an extraneous root. Thus, the lesser integer is 28.

Answer from: naomicervero

lets name the smaller integer as x

the consecutive integer is x + 1 as its the next number

the product of these 2 numbers are 812

you get the product once you multiply the 2 numbers

x * (x + 1) = 812

x² + 1x = 812

x² + x - 812 = 0

this a quadratic equation

we have to first find the factors of 812 * x² with a difference or sum of + x

the 2 factors are +29x and - 28x which have a product of 812x² and difference of +x

we substitute +x in the quadratic equation with +29x - 28x

x² + 29x -28x - 812 = 0

x(x + 29) -28(x + 29) = 0

(x+ 29)(x-28) = 0

so there are 2 possibilites for x

x + 29 = 0 or x - 28 = 0

x = -29 x = 28

since we are asked to find positive integers from the 2 possible values of x

x = 28 is the positive number

therefore smaller integer is 28

Answer from: Quest

do i do it on a graph?

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200. after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes 1800 - 6400 which gets you 11,600.

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