Which of the following equations is true?
1. (3 + 4)2 + 23 = 57
2. (3 + 4)2 + 23 = 53
Which of the following equation is true at a=2?
adding in some exponents, we have
(3+4)^2 + 2^3 = 7^2 + 2^3 = 49+8 = 57
To check which equation is true, let's simplify both expressions:
1. (3 + 4)2 + 23 = 57
This simplifies to:
7 * 2 + 23 = 57
14 + 23 = 57
37 = 57 (which is not true)
2. (3 + 4)2 + 23 = 53
This simplifies to:
7 * 2 + 23 = 53
14 + 23 = 53
37 = 53 (which is also not true)
Neither of the equations is true.
To determine which of the equations is true, we need to solve both equations and check if the left side of each equation equals the right side.
Let's evaluate the equations one by one:
1. (3 + 4)2 + 23 = 57
- First, evaluate the expression within the parentheses: (3 + 4) = 7.
- Then, multiply 7 by 2: 7 * 2 = 14.
- Finally, add 14 to 23: 14 + 23 = 37.
So, the left side of the equation is 37, while the right side is 57. Since these values are not equal, equation 1 is NOT true.
2. (3 + 4)2 + 23 = 53
- Again, evaluate the expression within the parentheses: (3 + 4) = 7.
- Then, multiply 7 by 2: 7 * 2 = 14.
- Finally, add 14 to 23: 14 + 23 = 37.
In this case, the left side of the equation is 37, while the right side is also 37. Therefore, equation 2 is true.
Therefore, the correct equation is number 2: (3 + 4)2 + 23 = 53.