I attached the work/steps for my answer.
Let us try to formulate the expressions one by one.
let the number be x.
Step 1:
six time the number is 6*x = 6x
Step 2:
product of the number and -3 is -3x
Step 3:
now let us make equation for it:
adding 3x on the left side,
dividing right side by 9
x=45/9 = 5
So the number is x=5
Answer:
One plus one is two.
Step-by-step explanation:
Answer: 83.5
Step-by-step explanation:
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
<u>Calculus</u>
Implicit Differentiation
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Product Rule:
Chain Rule:
Quotient Rule:
Step-by-step explanation:
<u>Step 1: Define</u>
-xy - 2y = -4
Rate of change of the tangent line at point (-1, 4)
<u>Step 2: Differentiate Pt. 1</u>
<em>Find 1st Derivative</em>
- Implicit Differentiation [Product Rule/Basic Power Rule]:
- [Algebra] Isolate <em>y'</em> terms:
- [Algebra] Factor <em>y'</em>:
- [Algebra] Isolate <em>y'</em>:
- [Algebra] Rewrite:
<u>Step 3: Find </u><em><u>y</u></em>
- Define equation:
- Factor <em>y</em>:
- Isolate <em>y</em>:
- Simplify:
<u>Step 4: Rewrite 1st Derivative</u>
- [Algebra] Substitute in <em>y</em>:
- [Algebra] Simplify:
<u>Step 5: Differentiate Pt. 2</u>
<em>Find 2nd Derivative</em>
- Differentiate [Quotient Rule/Basic Power Rule]:
- [Derivative] Simplify:
<u>Step 6: Find Slope at Given Point</u>
- [Algebra] Substitute in <em>x</em>:
- [Algebra] Evaluate: