C is the incenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABC and DBC are congruent? It is given that C is the incenter of triangle ABD, so segment BC is an altitude of angle ABD. Angles ABC and DBC are congruent according to the definition of an angle bisector. Segments AB and DB are congruent by the definition of an isosceles triangle. Triangles ABC and DBC share side BC, so it is congruent to itself by the reflexive property. By the SAS postulate, triangles ABC and DBC are congruent. Triangle ABD with segments BC, DC, and AC drawn from each vertex and meeting at point C inside triangle ABD. A. There is an error in line 1; segment BC should be an angle bisector.

B. The proof is correct.

C. There is an error in line 3; segments AB and BC are congruent.

D. There is an error in line 5; the ASA Postulate should be used.

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. increase the area of the base of the square pyramid by a factor of ten. increase the height of the cylinder by a factor of ten. increase the radius of the cone by a factor of ten. increase the radius of a sphere by a factor of ten. juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a cube with a side length of 12 feet a cone with a diameter of 12 feet and a height of 10 feet a square pyramid with a base side length of 12 feet and a height of 9 feet a hemisphere with a diameter of 12 feet marion has a bicycle that she is planning to take for a ride. the rim of the rear wheel lies 41 cm from the center of the wheel. the tire itself has a thickness of 3 cm.in order to marion to ride her bicycle 96,712 cm, approximately how many rotations will the rear wheel make? 350 15.9 376 5133 an isosceles trapezoid has perimeter of 42 inches. each of the congruent nonparallel sides is 5 inches long, and the trapezoid is 3 inches tall. how long are the two parallel sides? 10 inches and 16 inches 12 inches and 20 inches 16 inches and 16 inches 10 inches and 22 inches

For [tex]f(x) = 4x + 1[/tex] and (x) = [tex]g(x)= x^{2} -5,[/tex] find [tex](\frac{g}{f}) (x)[/tex]a. [tex]\frac{x^{2} - 5 }{4x +1 },x[/tex] ≠ [tex]-\frac{1}{4}[/tex]b. x[tex]\frac{4 x +1 }{x^{2} - 5}, x[/tex] ≠ ± [tex]\sqrt[]{5}[/tex]c. [tex]\frac{4x +1}{x^{2} -5}[/tex]d.[tex]\frac{x^{2} -5 }{4x + 1}[/tex]

Acompany made a profit of 75000 over a period of 6 years on an initial investment of 15000 what is the annual roi