Which of the following is the solution set of –4 < 3t + 5 ≤ 20?
a)
{t | t < –3}
b)
{t | t < –3 or t ≥ 5}
c)
{t | –3 < t ≤ 5}
d)
{t | t < –3 and t ≤ 5}

Option C : {t|t>-3 and t≤5}

Step-by-step explanation:

The given question is:

–4 < 3t + 5 ≤ 20

It can be broken down to two inequalities

Inequality 1:

-4<3t+5

Subtracting 5 from both sides

-4-5<3t+5-5

-9<3t

Switching sides

3t>-9

Dividing both sides by 3

t >-3

Inequality 2:

3t + 5 ≤ 20

Subtracting 5 from both sides

3t+5-5 ≤ 20-5

3t ≤15

Dividing both sides by 3

t ≤ 5

So the solution is -3 < t ≤ 5

Hence the correct answer is:

{t|t>-3 and t≤5}

Option C is correct ..

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step-by-step explanation:

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)