Given the figure, if ∠abc is 20° and c is the center of the circle, what is the measure of the central angle ∠acb? a) 40° b) 70° c) 100° d) 140°

D) 140°

Step-by-step explanation:

The total number of degrees in a triangle is 180. Since both sides of the triangle are the radius of the circle, the triangle is isosceles. Therefore the two opposite angles are equal. Thus, the central angle is 180° − 2(20°) = 140°.

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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