Ashort necklace has 32 gold beads and 8 black beads.
a long necklace has a total of 60beads.
both necklaces have the same ratio of gold beads to black beads
how many black beads are on the long necklace?

Rhombus adef is inscribed into a triangle abc so that they share angle a and the vertex e lies on the side bc . what is the length of the side of the rhombus if ab=c, and ac=b.

Examine the paragraph proof. which theorem does it offer proof for? prove jnm – nmi according to the given information in the image. jk | hi while jnm and lnk are vertical angles. jnm and lnk are congruent by the vertical angles theorem. because lnk and nmi are corresponding angles, they are congruent according to the corresponding angles theorem. finally, jnm is congruent to nmi by the transitive property of equality alternate interior angles theorem gorresponding angle theorem vertical angle theorem o same side interior angles theorem

Find the volume of the solid bounded by the plane z=0 and the paraboloid z=1-x^2 –y^2