which expression is equivalent to 6x2– 19x – 55?

( 6x + 11 ) ( x - 5 )

Step-by-step explanation:

Let

6x2 - 19x - 55 = 0

6x2 - (30-11)x - 55 = 0

6x2 - 30x + 11x - 55 = 0

6x ( x - 5 ) + 11 ( x - 5 ) = 0

( 6x + 11 ) ( x - 5 ) = 0

Therefore, ( 6x + 11 ) ( x - 5 ) = 6x2 - 19x - 55

The upper vertices are (9 , 2) and (-6 , 2)

Step-by-step explanation:

* Lets explain the information in the problem

- The welcome sign is a rectangle

- The height of it is 5 feet

- He has drawn a sketch on a coordinate grid

# On the sketch

- The lower vertices of the rectangle are (9 , -3) and (6 , -3)

- The lower vertices have the same y-coordinates

- The upper vertices will have the same y-coordinates which are greater

 than the y-coordinates of the lower vertices by 5 units, because the

 height of the sign is 5 feet

- The x-coordinates of the upper vertices have the same x-coordinates

 of the lower vertices because the sides of the rectangle perpendicular

 to each other

* Lets solve the problem

∵ The lower vertices are (9 , -3) and (-6 , -3)

∵ The x-coordinates of the lower vertices are 9 , -6

∴ The x-coordinates of upper vertices are 9 , -6

∵ The height of the sign is 5 units in the sketch

∴ We will add the y-coordinates of the lower vertices by 5

∵ The y- coordinates of the lower points are -3 and -3

∴ The y-coordinates of the upper vertices are -3 + 5 = 2 and -3 + 5 = 2

* Lets write the upper vertices

∵ The x-coordinates of upper vertices are 9 and -6

∵ The y-coordinates of upper vertices are 2 and 2

∴ The upper vertices are (9 , 2) and (-6 , 2)