Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
<u>Algebra II</u>
- Distance Formula:

Step-by-step explanation:
*Note:
The distance formula is derived from the Pythagorean Theorem.
<u>Step 1: Define</u>
<em>Identify</em>
Point (5, 10)
Point (10, 12)
<u>Step 2: Find distance </u><em><u>d</u></em>
- Substitute in points [Distance Formula]:

- [√Radical] (Parenthesis) Subtract:

- [√Radical] Evaluate exponents:

- [√Radical] Add:

Answer:
c) x = 11
Step-by-step explanation:
Given equation: 7x - 9 = 28 + 4(x - 1)
<u><em>Steps:</em></u>
1. Distribute 4 through the parentheses:
7x - 9 = 28 + 4(x) + 4(-1)
7x - 9 = 28 + 4x - 4 [simplify]
7x - 9 = 24 + 4x
2. Subtract 4x from both sides:
7x - 4x - 9 = 24 + 4x - 4x
3x - 9 = 24
3. Add 9 to both sides:
3x - 9 + 9 = 24 + 9
3x = 33
4. Divide both sides by 3:
3x ÷ 3 = 33 ÷ 3
x = 11
5. Check your work:
7x - 9 = 28 + 4(x - 1) [substitute 11 for x]
7(11) - 9 = 28 + 4(11 - 1) [simplify]
77 - 9 = 28 + 4(10) [simplify]
68 = 28 + 40 [add]
68 = 68 ✔
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Answer:
The value of the proposition is FALSE
Step-by-step explanation:
~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ ~X) v (B ⊃ X)]
Let's start with the smallest part: ~X. The symbol ~ is negation when X is true with the negation is false and vice-versa. In this case, ~X is true (T)
~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ T) v (B ⊃ X)]
Now the parts inside parenthesis: (A ⊃ Y),(X ⊃ B),(A ≡ T) and (B ⊃ X). The symbol ⊃ is the conditional and A ⊃ Y is false when Y is false and A is true, in any other case is true. The symbol ≡ is the biconditional and A ≡ Y is true when both A and Y are true or when both are false.
(A ⊃ Y) is False (F)
(X ⊃ B) is True (T)
(A ≡ T) is True (T)
(B ⊃ X) is False (F)
~[(F) v ~(T)] ⋅ [~(T) v (F)]
The two negations inside the brackets must be taken into account:
~[(F) v F] ⋅ [F v (F)]
The symbol left inside the brackets v is the disjunction, and A v Y is false only with both are false. F v (F) is False.
~[F] ⋅ [F]
Again considerating the negation:
T⋅ [F]
Finally, the symbol ⋅ is the conjunction, and A v Y is true only with both are true.
T⋅ [F] is False.
Answer:
Step-by-step explanation:
first fit:
115 -> 300
500-> 600
358 -> 750
200 -> 350
375 -> not able to allocate
Best fit:
115 -> 125
500 -> 600
358 -> 750
200 -> 200
375 -> not able to allocate
worst fit:
115 -> 750
500 -> 600
358 -> not able to allocate
200 -> 350
375 -> not able to allocate