Question

Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.

Which equation can be used to find m, the midpoint of the two numbers?

Answer 1

@acxbox22

Answer 2

is it (x-10)(x+10)=-99?

Answer 3

"Two numbers are 10 units away in different directions from their midpoint, m, on a number line"

so these two numbers are 20 units apart (2*10 = 20)

if x and y are the two numbers, then x-y = 20 where x is the larger number

we also know that x*y = -99

so one of the numbers is positive while the other is negative

Answer 4

x-y = 20

x-y+y = 20+y

y+20 = x

y = x - 20

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x*y = -99

x*(x-20) = -99

solve for x and use this to find y

Answer 5

how do i find the equation out of that?

Answer 6

(m – 5)(m + 5) = 99
(m – 10)(m + 10) = 99
m2 – 25 = –99
m2 – 100 = –99
these are my options.
i thought it was b but then i realized it has to equal -99

Answer 7

oh they want it in terms of m

Answer 8

let me think

Answer 9

ok if m is our reference point, then the first number is m+10 (since you count 10 units above the midpoint) and the second number is m-10

agreed so far?

Answer 10

yeah

Answer 11

do yo multiply them together?

Answer 12

so (m-10)*(m+10) is the product of the two numbers

we can FOIL that out to get m^2 - 10m + 10m - 100 = m^2 - 100

Answer 13

or you can use the difference of squares rule as a shortcut

Answer 14

okay

Answer 15

so that's why the answer is m^2 - 100 = -99

Answer 16

i understand

Answer 17

thanks

Answer 18

you're welcome