I have 2 problems that I need solved. Can someone please help me?
t+36t=0
second problem
T^2-7t+12=0 Can you show me the steps please?
Add.
37t = 0
Divide both sides by 37.
T = 0
T^2 - 7t + 12 = 0
Factor.
(t-3)(t-4) = 0
Set each factor = 0 and solve for t.
Of course! I'll be happy to help you solve both problems.
Problem 1: t+36t=0
To solve this equation, we'll combine the like terms on the left side of the equation:
t + 36t = 0
1t + 36t = 0
(1 + 36)t = 0
37t = 0
Now, we need to isolate the variable t. To do this, we divide both sides of the equation by 37:
37t/37 = 0/37
t = 0
So, the solution to the equation t+36t=0 is t = 0.
Problem 2: T^2-7t+12=0
This is a quadratic equation, and to solve it, we can use the factoring method. We need to find two numbers that multiply to give 12 and add up to -7.
The numbers that satisfy these conditions are -3 and -4 because (-3)*(-4) = 12 and (-3) + (-4) = -7.
Now, we can rewrite the equation by using these numbers:
T^2 - 3T - 4T + 12 = 0
Next, we group the terms:
(T^2 - 3T) + (-4T + 12) = 0
Now, we can factor by taking out the common factors from each group:
T(T - 3) - 4(T - 3) = 0
Notice that we have a common factor of (T - 3) in each group. So, we can factor it out:
(T - 3)(T - 4) = 0
Now, we have a product of two factors equal to zero. According to the zero product property, if a*b = 0, then either a = 0 or b = 0.
So, we set each factor equal to zero and solve for T:
T - 3 = 0 or T - 4 = 0
Adding 3 to both sides of the first equation and adding 4 to both sides of the second equation, we get:
T = 3 or T = 4
Therefore, the solutions to the equation T^2-7t+12=0 are T = 3 and T = 4.
I hope this helps! Let me know if you have any further questions.