Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a Not-equals 1 and b Not-equals 1?

log Subscript x Baseline x
StartFraction log Subscript b Baseline x Over log Subscript b Baseline a EndFraction
StartFraction log Subscript b Baseline a Over log Subscript b Baseline x EndFraction
StartFraction log Subscript a Baseline b Over log Subscript x Baseline b EndFraction
StartFraction log Subscript a Baseline x Over log Subscript b Baseline x EndFraction

Polygon mnopq is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image m′n′o′p′q′. the coordinates of point m are (2, 4), and the coordinates of point n are (3, 5). the slope of is .

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.

    choose the correct definition for  extremo.  a.  end      b.  extra      c.  extract      d.  eventual