Ab and ac are tangent segments of circle k(o). what is the measure of the angle ∠bac, if midpoint of ao lies on the circle k(o)?
m∠bac=

  60°

Step-by-step explanation:

B and C are the points of intersection of the circle with diameter AO with circle O. If the midpoint of AO is X on circle O, then XO = XB = XC and ΔXOB and ΔXOC are equilateral triangles. That makes ∠BOC = 120° and its supplement, ∠BAC, equal to 60°.

13

step-by-step explanation:

divide the cost of the total of sodas you bought by the cost of one soda, for example:

$24.57 divided by $1.89 is 13 which means you bought 13 sodas

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)