I am less than 6 feet tall but more than 2 feet tall. my height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. what is my height in inches

  56

Step-by-step explanation:

The difference between 6 and 7 is 1, so the difference between 2×6 = 12 and 2×7 = 14 will be 2×1 = 2.

The solutions to

  6a +2 = 7b

for integers a and b will be of the form ...

  a = 7n +2

  b = 6n +2

Which makes ...

  7b = 7(6n +2) = 42n +14

The value of n that gives a value of 7b in the range of 24 to 72 is n = 1.

For that value, the height in inches is ...

  42×1 +14 = 56 . . . . inches

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Check

56 = 7×8, a multiple of 8

56 = 54 +2 = 6×9 +2. This is 2 more than a multiple of 6

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.