(x-6)(3x+7)
Expand and simplify

3x^2 − 11x − 42

Step-by-step explanation:

Simplify  (x − 6) (3x + 7)

Expand (x − 6) (3x + 7) using the  FOIL Method.

Apply the distributive property.

  x (3x + 7) − 6 (3x + 7)  

Apply the distributive property.

  x (3x) + x ⋅ 7 − 6 (3x + 7)

Apply the distributive property.

  x (3x) + x ⋅ 7 − 6 (3x) − 6 ⋅ 7

Simplify and combine like terms.

Rewrite using the commutative property of multiplication.

  3x ⋅ x + x ⋅ 7 − 6 (3x) − 6 ⋅ 7

Multiply x by x by adding the exponents.

Move x.

  3 (x ⋅ x) + x ⋅ 7 − 6 (3x) − 6 ⋅ 7

Multiply x by x.

  3x^2 + x ⋅ 7 − 6 (3x) − 6 ⋅ 7

Move 7 to the left of x.

  3x^2 + 7 ⋅ x − 6 (3x) − 6 ⋅ 7

Multiply 3 by −6.

  3x^2 + 7x − 18x − 6 ⋅ 7

Multiply −6 by 7.

  3x^2 + 7x − 18x − 42

Subtract 18x from 7x.

  3x^2 − 11x − 42

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .