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Fynjy0 [20]
3 years ago
8

Find Two consecutive positive integers such that the square of the larger integer is nineteen more than nine times the smaller i

nteger
Mathematics
1 answer:
Kamila [148]3 years ago
5 0

Answer:

9 and 10

Step-by-step explanation:

To start, let's have what we know:

a and b are two consecutive positive integers

a = first integer

b = second integer, 1 greater than variable a

b = a + 1

b^2 = 19 + 9a

To solve this, we would only have to substitute values in

b^2 = 19 + 9a

(a+1)^2 = 19 + 9a

a^2 + 2a +1     = 19 + 9a

       -9a -19    -19 - 9a

a^2 -7a - 18 = 0

a^2 + 2a - 9a - 18

a(a + 2) - 9(a+2) = 0

(a - 9)(a + 2) = 0

So solving this, we would get a = 9 or a = -2. Since this is supposed to be a positive integer, a will be 9.

Solving for b,

b = a + 1

  = 9 + 1

  = 10

Let me know in the comments if you have any questions! If you could mark this answer as brainliest, I would very much appreciate it!

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Step-by-step explanation:

. Set up the following proportion: Pens are 3 for $0.69 at the supply store. What proportion can be used to find p, the amount it will cost Mrs. Faber to buy 180 pens? . Set up the following proportion: Pens are 3 for $0.69 at the supply store. What proportion can be used to find p, the amount it will cost Mrs. Faber to buy 180 pens? . Set up the following proportion: Pens are 3 for $0.t up the following proportion: Pens are 3 for $0.69 at the supply store. What proportion can be used to find p, the amount it will cost Mrs. Faber to buy 180 pens? . Set up the following proportion: Pens are 3 for $0.69 at the supply store. What proportion can be used to find p, the amount it will cost Mrs. Faber to buy 180 pens? . Set up the following proportion: Pens are 3 for $0.69 at the supply store. What proportion can be used to find p, the amount it will cost Mrs. Faber to buy 180 pens? . Set up the followie supply store. What proportion can be used to find p, the amount it will cost Mrs. Faber to buy 180 pens?

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Read more about equivalent expressions at:

brainly.com/question/2972832

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