If you can only use 3 of these numbers once to find a sum of 30 without subtracting or adding additional numbers, what three numbers would you use out of 1, 3, 5, 7, 9, 11, 13, and 15? ()+()+()=30

The correct answer is

It is impossible to add odd numbers (1, 3, 5, 7, 9, 11, 13, and 15) and odd number of times (3) to get an even number (30)

Step-by-step explanation:

1, 3, 5, 7, 9, 11, 13, and 15 are all odd numbers and 30 is an even number

When odd numbers are added even times the answer is always even for example 3 + 5 = 8,  and when odd numbers are added odd times the answer is always odd for example 1 + 5 + 7 = 13

It is not possible to add three odd numbers to get an even number

Where x = odd therefore x + 1 = even = y say

hence  2 × x = 2×(y-1) = 2·y - 2 = even number

Also 3 × x = (3y -3) = odd number

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

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form