1. Vertical angles are congruent: a) we're proving that <em>two angles are congruent </em>(we use ≅), and it just happens that those two angles are <em>vertical </em>(opposite angles on two intersecting lines).
2. SAS congruence: It is one of the last three, since we're trying to prove the <em>triangles' congruence</em>, and it is <em>SAS</em>, because our given gives us <em>two pairs of congruent lines</em>, and we find that the angle <em>between</em> them are congruent.
Answer:
different
Step-by-step explanation:
reflection is basically like a mirror where it reflects you. rotation is when an object spins/rotates.
Create a proportion.
Since it takes 7 minutes to print 63 pages, and half an hour is 30 minutes, you create two ratios(unit per unit) and line up the units(minutes to minutes, pages to pages).
Now you cross multiply, 63 * 30 = 1890 and 7 * x = 7x.
So we have 1890 = 7x.
Then we divide both sides by seven.
270 = x, therefore you can print 270 pages in half an hour :)
Answer:
General Formulas and Concepts:
<u>Symbols</u>
- e (Euler's number) ≈ 2.71828
<u>Algebra I</u>
- Exponential Rule [Multiplying]:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integration
- Integrals
- Definite Integrals
- Integration Constant C
Integration Rule [Reverse Power Rule]:
Integration Rule [Fundamental Theorem of Calculus 1]:
Integration Property [Multiplied Constant]:
U-Substitution
Integration by Parts:
- [IBP] LIPET: Logs, inverses, Polynomials, Exponentials, Trig
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Integrate Pt. 1</u>
- [Integrand] Rewrite [Exponential Rule - Multiplying]:
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
<u>Step 3: Integrate Pt. 2</u>
<em>Identify variables for u-solve.</em>
- Set <em>u</em>:
- [<em>u</em>] Differentiate [Basic Power Rule]:
- [<em>u</em>] Rewrite:
- [<em>du</em>] Rewrite:
<u>Step 4: Integrate Pt. 3</u>
- [Integral] U-Solve:
- [Integral] Rewrite [Integration Property - Multiplied Constant]:
- [Integral] Simplify:
- [Integrand] U-Solve:
<u>Step 5: integrate Pt. 4</u>
<em>Identify variables for integration by parts using LIPET.</em>
- Set <em>u</em>:
- [<em>u</em>] Differentiate [Basic Power Rule]:
- Set <em>dv</em>:
- [<em>dv</em>] Exponential Integration:
<u>Step 6: Integrate Pt. 5</u>
- [Integral] Integration by Parts:
- [Integral] Exponential Integration:
- Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:
- Simplify:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e