Question

Solve for t.
Give an exact answer.
3t – 18 = 41-3
3
-t
4

Answer 1

Using the quadratic formula, we find two solutions for t: t = 10 and t = -20 from the equation t² + 10t - 200 = 0. Since time can't be negative, the exact solution is t = 10 seconds.

Step-by-step explanation:

To solve for the time t using the quadratic formula, we will rearrange the equation to set it equal to zero, and then apply the formula. The quadratic formula is:

-b ± √(b² - 4ac) / (2a)

For the equation t² + 10t - 200 = 0, we identify a = 1, b = 10, and c = -200. Plugging these values into the quadratic formula, we get:

t = (-10 ± √((10)² - 4(1)(-200)))/(2(1))

This simplifies to:

t = (-10 ± √(100 + 800))/2

t = (-10 ± √900)/2

t = (-10 ± 30)/2

Yielding two solutions for t: t = (20/2) or t = (-40/2), which simplifies to t = 10 and t = -20. Since time cannot be negative, we discard t = -20 and keep t = 10 as the exact solution.

Answer 2

t = 1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define equation

3t - 18 = 4(-3 - 3/4t)

Step 2: Solve for t

1. Distribute 4: 3t - 18 = -12 - 3t
2. Add 3t to both sides: 6t - 18 = -12
3. Add 18 to both sides: 6t = 6
4. Divide 6 on both sides: t = 1

Step 3: Check

Plug in t into the original equation to verify it's a solution.

1. Substitute in t: 3(1) - 18 = 4(-3 - 3/4(1))
2. Multiply: 3 - 18 = 4(-3 - 3/4)
3. Subtract: -15 = 4(-15/4)
4. Multiply: -15 = -15

Here we see that -15 does indeed equal -15.

∴ t = 1 is a solution of the equation.