Area of ​​the painted part

59.73 cm²

Step-by-step explanation:

2 × π × 7

2 × 3.14 × 7

43.96 ÷ 4

10.99 cm²

11 cm - 7 cm = 4 cm

2 × π × 4

2 × 3.14 × 4

25.12 ÷ 4

6.28 cm²

10.99 cm² + 6.28 cm² = 17.27 cm²

7 cm × 11 cm = 77 cm²

77 cm² - 17.27 cm²

59.73 cm²

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

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)