7 = 2x + 5
7 - 5 = 2x
2 = 2x
x = 1 ← <span>the other half of the coordinate</span>
Answer:
3 foil, 6 latex
Step-by-step explanation:
First, you can put all of these words words into equations. We know there are 162 ballons (18 players)(9 bouquets). So we can put it in the equation
x + y = 162
Since each foil balloon costs $1.92 and each Latex balloon costs $.19 and they all cost $124.20. We can put it in an equation:
.19x + 1.92y = 124.20
You then get the systems of equations:
x + y = 162
.19x + 1.92y = 124.20
solving for the equation, you get x = 54 and y = 108. BUT, you have to be careful. The problem said "How many of each type of balloon did each <em>bouquet</em> include?" So we need to divide both by 18 for the player because each player recieved on bouquet.
3(a + b) and 3a + b - NOT EQUIVALENT because
3(a + b) = 3a + 3b
<em>used distributive property a(b + c) = ab + ac</em>
4(x + 2y) and 8y + 4x - EQUIVALENT because
4(x + 2y) = (4)(x) + (4)(2y) = 4x + 8y = 8y + 4x
<em>used distributive property a(b + c) = ab + ac</em>
<em>and commutative property a + b = b + a</em>
Answer:

General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]: ![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- Logarithmic Differentiation [Derivative Rule - Chain Rule]:

- Trigonometric Differentiation [Derivative Rule - Chain Rule]:

- Basic Power Rule:

- Rewrite [Trigonometric Identities]:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation