I am attaching a sketch for reference, the quadrilateral that is formed is the red area ABDC. First of all, we have that the quadrilateral has all of its sides equal. We also know that the crosswalks are parallel in pairs, because they are both normal to the same two parallel lines (that define a road in our sketch). AB is parallel to CD this way and AC is parallel to BD (in Euclidean Geometry, two lines normal to the same line are parallel). Thus, ABDC is a parallelogram with equal sides. It is either a square or a rhombus. It cannot be a square since one of its angles is 30 degrees, thus it is a rhombus (also called an equilateral quadrilateral).
Answer:
calculate the perimeter of the garden
Just plug in x = -5
f(-5) = 6 - 2(-5) = 6+10 - 16.
(2x + 3)⁵
(2x + 3)(2x + 3)(2x + 3)(2x + 3)(2x + 3)(2x + 3)
(2x(2x + 3) + 3(2x + 3))(2x(2x + 3) + 3(2x + 3)(2x + 3)
(2x(2x) + 2x(3) + 3(2x) + 3(3))(2x(2x) + 2x(3) + 3(2x) + 3(3))(2x + 3)
(4x² + 6x + 6x + 9)(4x² + 6x + 6x + 9)(2x + 3)
(4x² + 12x + 9)(4x² + 12x + 9)(2x + 3)
(4x²(4x² + 12x + 9) + 12x(4x² + 12x + 9) + 9(4x² + 12x + 9))(2x + 3)
(4x²(4x²) + 4x²(12x) + 4x²(9) + 12x(4x²) + 12x(12x) + 12x(9) + 9(4x²) + 9(12x) + 9(9))(2x + 3)
(16x⁴ + 48x³ + 36x² + 48x³ + 144x² + 108x + 36x² + 108x + 81)(2x + 3)
(16x⁴ + 48x³ + 48x³ + 36x² + 144x² + 36x² + 108x + 108x + 81)(2x + 3)
(16x⁴ + 96x³ + 216x² + 216x + 81)(2x + 3)
16x⁴(2x + 3) + 96x³(2x + 3) + 216x²(2x + 3) + 216x(2x + 3) + 81(2x + 3)
16x⁴(2x) + 16x⁴(3) + 96x³(2x) + 96x³(3) + 216x²(2x) + 216x²(3) + 216x(2x) + 216x(3) + 81(2x) + 81(3)
32x⁵ + 48x⁴ + 184x⁴ + 288x³ + 432x³ + 648x² + 432x² + 648x + 162x + 243
32x⁵ + 232x⁴ + 720x³ + 1080x² + 810x + 243
Domain is {-2,0,2}.
The ends of the arrows give us a range.
Range is {0,4}.
Answer: <span>c. domain: {–2, 0, 2}, range: {4, 0}</span>