Find the pair of numbers whose sum is 46 and whose product is a maximum.

To solve this problem you must apply the proccedure shown below:

 1. Let's call:

 x the first number and and the other number 46-x

 2. Then, the product of both numbers is:

 y=x(46-x)

 3. When you apply the distributive property, you obtain:

 y=46x-x^2

 4. As you can see, the coefficient of x^2 is negative, this means that the maximun value is at the vertex of the parabola.

 5. Then, you have:

 h=-b/2a
 h=-46/2(-1)
 h=23   (x coordinate)

 6.Then:

  y=46x-x^2
 y=46(23)-(23)^2
 y=529

 Therefore the answer is: 23 and 529.

 

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c