The function g is defined by g(x)=ax−7, where a is a constant. find a, if the graph of g passes through the point ( 1/3 ,−2).

a = 15

Step-by-step explanation:

The graph of function g(x) is described by g(x)=ax−7, or y = ax−7.

y = g(x)=ax−7 passes through (1/3, -2).  We can subst. -2 for y and 1/3 for x to determine the value of the coefficient a:

-2 = g(1/3) = a(1/3) - 7

Solve for a.  First, add 7 to both sides:  5 = a(1/3).

Next, multiply both sides by 3:  15 = a, or a = 15.

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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