Olivia evaluated an expression and showed her work. which comment about olivia's solution is correct? problem: evaluate 27-15t for t=4 olivia's solution: 27-15×4=12×4=48 (a)she followed the order of operations, but she multiplied incorrectly. (b)she did not follow the order of operations. she should have multiplied before subtracting. (c)she did not follow the order of operations. she should have substituted for t after she subtracted, not before. (d)she followed the order of operations because she went from left to right.

  (b)  She did not follow the order of operations. She should have multiplied before subtracting

Step-by-step explanation:

The answer is self-explanatory.

There are a couple of mnemonics in use to help you remember the order of operations: PEMDAS, or BEDMAS, or BIDMAS. They mean ...

  P or B -- Parentheses or Brackets: evaluate any expressions in parentheses according to the order of operations before anything else

  E or I -- Exponents or Indices: next, evaluate any terms with an exponent (or index). Exponents are evaluated right to left, so that a^b^c means a^(b^c).

  MD or DM -- Multiplication and Division: These operations are performed next, left to right in the order of appearance. Any interpretation that says multiplication is performed before division (or vice versa) is incorrect.

  AS -- Addition and Subtraction: These operations are performed next (after multiplication and division), in order of appearance, left to right.

Theses mnemonics also have associated mnemonic sentences, such as "Please Excuse My Dear Aunt Sally" for PEMDAS.

Among other things, this means you need to be careful to use grouping symbols where required.

  a + b/c + d ≠ (a + b)/(c + d)

  1/x(x+a) = (x+a)/x ≠ 1/(x(x+a))

  x^1/2 ≠ x^(1/2)

  √3x = (√3)x ≠ √(3x)

  sin 2 pi = (sin(2))·pi ≠ sin(2·pi)

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Function arguments are evaluated according to the order of operations, and functions are applied, pretty much before anything else. See the last example above. This is why it is important to identify the arguments of a function using grouping symbols (parentheses/brackets).

The above describes the strict Order of Operations. Many calculators observe this order. Some calculators and some spreadsheets do not. (Beware!) Some observe it within limits (depth of parentheses) that may or may not be an issue for a given calculation. The Google on-line calculator reliably observes the Order of Operations.

In actual practice, it is often useful to take advantage of the commutative and associative properties of addition and multiplication. In using these properties, division can be treated as multiplication by a reciprocal, and subtraction can be treated as addition of a negative number.

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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