The key concept you must have to remember is that, the rate is kept constant, as what is specified in the problem. Our basis for the rate is the first situation.
Rate = 20 facts/ 1 min.
Let's equate this to the second situation using x as the time unknown.
20/1 = 35/x
Solving for x,
<em>x = 1.75 minutes</em>
Answer:
x = 2
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
-3(x - 1) = x - 5
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute -3: -3x + 3 = x - 5
- Add 3x to both sides: 3 = 4x - 5
- Add 5 to both sides: 8 = 4x
- Divide 4 on both sides: 2 = x
- Rewrite: x = 2
<u>Step 3: Check</u>
<em>Plug in x to verify it's a solution.</em>
- Substitute: -3(2 - 1) = 2 - 5
- Subtract: -3(1) = -3
- Multiply: -3 = -3
Here we see that -3 does indeed equal -3.
∴ x = 2 is a solution of the equation.
Answer:
x = -5 ±4sqrt(3)
Step-by-step explanation:
(x + 5)^2 = 48
Take the square root of each side
sqrt((x + 5)^2) = ±sqrt(48)
x+5 = ±sqrt(16*3)
x+5 = ±4sqrt(3)
Subtract 5 from each side
x = -5 ±4sqrt(3)
There are 12 letters in P H I L A D E L P H I A AND THERE AE:
2 P, 2 H, 2 A, 2 I
Permutation of ¹²P₁₂ = 12! , but mind you there are repeated letters so
the final Permutation: 12!/(2!)(2!)(2!)(2!) = 29 937 600 ways of arranging letters
