How to find it is related to the opposite angle in a cyclic quadrilateral is equal to 180 degeres

The measure of ∠BEF=110°.

Step-by-step explanation:

Given: In cyclic quadrilateral ABCD, ∠C = 110°

Then, ∠A+∠C=180°  [The sum of opposite angles in a cyclic quadrilateral is 180 degrees.]

⇒ ∠A+ 110°=180°

⇒ ∠A = 180°  - 110°

⇒ ∠A = 70°

In cyclic quadrilateral ABEF,

∠A+∠E=180°   [The sum of opposite angles in a cyclic quadrilateral is 180 degrees.]

⇒ 70° + ∠E=180°

⇒∠E=110°

Hence, the measure of ∠BEF=110°.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

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)