Select the correct answer from each drop-down menu. the equation of a hyperbola is -4x2 + y2 + 16x + 12y + 16 = 0. the center of the hyperbola is (2, -, 2)(0, 0), and its vertices are (-4, 2)(2, -4)(2, 6) and (-8, 2)(2, -8)(2, -6)

Step-by-step explanation:

Rearranging the equation to standard form helps answer this question.

... -4(x^2 -4x) +(y^2 +12y) = -16 . . . subtract the constant, group x-terms, y-terms

... -4(x^2 -4x +4) +(y^2 +12y +36) = -16 -4(4) +36

... -4(x -2)^2 +(y +6)^2 = 4 . . . . write as squares

... ((y +6)/2)^2 -(x -2)^2 = 1 . . . . divide by 4

Now, this is in the form ...

... ((y -k)/a)^2 -((x -h)/b)^2 = 1

which has center (h, k) and vertices (h, k±a).

This form tells you the center is (x, y) = (2, -6), and the vertices are (2, -4) and (2, -8).

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.