3t^2=2t-18, is a quadratic equation, need help to solve.

t = 1/3 + (i sqrt(53))/3 or t = 1/3 - (i sqrt(53))/3

Step-by-step explanation:

Solve for t:

3 t^2 = 2 (t - 9)

Expand out terms of the right hand side:

3 t^2 = 2 t - 18

Subtract 2 t - 18 from both sides:

3 t^2 - 2 t + 18 = 0

Divide both sides by 3:

t^2 - (2 t)/3 + 6 = 0

Subtract 6 from both sides:

t^2 - (2 t)/3 = -6

Add 1/9 to both sides:

t^2 - (2 t)/3 + 1/9 = -53/9

Write the left hand side as a square:

(t - 1/3)^2 = -53/9

Take the square root of both sides:

t - 1/3 = (i sqrt(53))/3 or t - 1/3 = -(i sqrt(53))/3

Add 1/3 to both sides:

t = 1/3 + (i sqrt(53))/3 or t - 1/3 = -(i sqrt(53))/3

Add 1/3 to both sides:

t = 1/3 + (i sqrt(53))/3 or t = 1/3 - (i sqrt(53))/3

80 the answer is 80

step-by-step explanation:

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: