If my question is 375 + (-5t) = 25 + 2t

Question

What does t equal

Answer 1

To solve the equation \(375 + (-5t) = 25 + 2t\), we can start by simplifying it:

1. Rewrite the equation: \[ 375 - 5t = 25 + 2t \]

2. Add \(5t\) to both sides to get all the \(t\) terms on one side: \[ 375 = 25 + 2t + 5t \] This simplifies to: \[ 375 = 25 + 7t \]

3. Next, subtract \(25\) from both sides to isolate the term with \(t\): \[ 375 - 25 = 7t \] This simplifies to: \[ 350 = 7t \]

4. Then, divide both sides by \(7\) to solve for \(t\): \[ t = \frac{350}{7} = 50 \]

So, \(t\) equals \(50\).

Answer 2

If my question is 56 + 12t = 33 + 14t
What does t equal?

Answer 3

To solve the equation \(56 + 12t = 33 + 14t\), we can follow these steps:

1. Start with the original equation: \[ 56 + 12t = 33 + 14t \]

2. Subtract \(12t\) from both sides to get all the \(t\) terms on one side: \[ 56 = 33 + 14t - 12t \] This simplifies to: \[ 56 = 33 + 2t \]

3. Next, subtract \(33\) from both sides to isolate the term with \(t\): \[ 56 - 33 = 2t \] This simplifies to: \[ 23 = 2t \]

4. Finally, divide both sides by \(2\) to solve for \(t\): \[ t = \frac{23}{2} = 11.5 \]

So, \(t\) equals \(11.5\).

Answer 4

If plant A starts at 56cm and grows 12cm every month and plant B starts at 33cm and grows 14cm every month
At 11.5 months they will be

Answer 5

To find the heights of Plant A and Plant B after 11.5 months, we can use the following equations:

1. For Plant A:

   • Starting height: 56 cm
   • Growth rate: 12 cm per month

   The height of Plant A after \( t \) months is given by: \[ \text{Height of Plant A} = 56 + 12t \]

2. For Plant B:

   • Starting height: 33 cm
   • Growth rate: 14 cm per month

   The height of Plant B after \( t \) months is given by: \[ \text{Height of Plant B} = 33 + 14t \]

Now, let's calculate their heights after 11.5 months.

For Plant A:

\[ \text{Height of Plant A} = 56 + 12 \times 11.5 \] \[ = 56 + 138 = 194 \text{ cm} \]

For Plant B:

\[ \text{Height of Plant B} = 33 + 14 \times 11.5 \] \[ = 33 + 161 = 194 \text{ cm} \]

Summary

• Height of Plant A after 11.5 months: 194 cm
• Height of Plant B after 11.5 months: 194 cm

So, after 11.5 months, both Plant A and Plant B will be 194 cm tall.

Answer 6

-30 + (-10t) and -15 + (-12t)
After how many minutes will they be in the same elevation? T = time / minutes

Answer 7

To find the time \( t \) when the two expressions \(-30 - 10t\) and \(-15 - 12t\) are equal, we can set them equal to each other and solve for \( t \).

Step 1: Set the expressions equal to each other

\[ -30 - 10t = -15 - 12t \]

Step 2: Rearrange the equation

To isolate terms involving \( t \), first add \( 10t \) to both sides: \[ -30 = -15 - 12t + 10t \]

This simplifies to: \[ -30 = -15 - 2t \]

Next, add \( 15 \) to both sides: \[ -30 + 15 = -2t \] \[ -15 = -2t \]

Step 3: Solve for \( t \)

Now, divide both sides by \(-2\): \[ t = \frac{-15}{-2} = \frac{15}{2} = 7.5 \]

Conclusion

The two expressions will be at the same elevation after 7.5 minutes.

Answer 8

What elevation will they be at after 7.5 minutes

Answer 9

To find the elevation of both expressions at \( t = 7.5 \) minutes, we can substitute \( t = 7.5 \) into each expression:

Expression 1: \(-30 - 10t\)

\[ \text{Elevation}_1 = -30 - 10(7.5) \] \[ = -30 - 75 \] \[ = -105 \]

Expression 2: \(-15 - 12t\)

\[ \text{Elevation}_2 = -15 - 12(7.5) \] \[ = -15 - 90 \] \[ = -105 \]

Conclusion

After \( 7.5 \) minutes, both expressions will be at an elevation of -105.