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Ksju [112]
2 years ago
7

9. In the figure below, Angle 1 is congruent to Angle 2.

Mathematics
1 answer:
trapecia [35]2 years ago
8 0

Answer:

D

Step-by-step explanation:

When 2 angles are congruent and corresponding, the lines are parallel

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BRAINLIESTT ASAP! PLEASE HELP ME :)<br> thanks!
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Step-by-step explanation:

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3 years ago
At the circus, 3 adult tickets and 4 child tickets cost $47, and 6 adult tickets and 2 child tickets cost $64. Which system of l
Artemon [7]

Answer:

The adult tickets cost $9 each. The child tickets cost $5 each.

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Step-by-step explanation:

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3 years ago
Can you guys help me with this question?
Rasek [7]

Answer:

it represents 10 stars in the galaxies

Step-by-step explanation:

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8 0
2 years ago
Substitution to evaluate the indefinite integral
gregori [183]

Answer:

\displaystyle \int {e^{5x}} \, dx = \boxed{ \frac{e^{5x}}{5} + C }

General Formulas and Concepts:
<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:
\displaystyle (cu)' = cu'
Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals

Integration Rule [Reverse Power Rule]:
\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Property [Multiplied Constant]:
\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

Integration Methods: U-Substitution

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given.</em>

\displaystyle \int {e^{5x}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution</em>.

  1. Set <em>u</em>:
    \displaystyle u = 5x
  2. [<em>u</em>] Differentiate [Derivative Rules and Properties]:
    \displaystyle du = 5 \ dx

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Rewrite [Integration Property - Multiplied Constant]:
    \displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\\end{aligned}
  2. [Integral] Apply Integration Method [U-Substitution]:
    \displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\\end{aligned}
  3. [Integral] Apply Exponential Integration:
    \displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\\end{aligned}
  4. [<em>u</em>] Back-substitute:
    \displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\& = \boxed{ \frac{e^{5x}}{5} + C } \\\end{aligned}

∴ we have used substitution to <em>evaluate</em> the indefinite integral.

---

Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27593180

---

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

Unit: Integration

3 0
2 years ago
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