Determine whether the conclusion is valid. If not, identify the additional information needed to make it valid.

Given: DE∥GF , EF∥DG

Conclusion: DEFG is a rhombus.

Not valid: DF is perpendicular to EG (2nd)

Step-by-step explanation:

Not all parallelograms whose opposite sides are parallel is a rhombus. A rhombus's special characteristic is that their diagonals are perpendicular to each other.

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)