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3 years ago

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A triangle has vertices A(-6,3), B(1,5), and C(4,-4). this triangle is dilated with the origin at its center by a scale factor o

f 3. Write the ordered pair of the new vertices of the new image

1 answer:

IceJOKER [234]3 years ago

7 0

Answer:

2

Step-by-step explanation:

2

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Step-by-step explanation:

The -3 under the radical is the result of combining the terms

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16 is factored out. It is done this way because 16 is a perfect square factor, so wants to maintain that identity while you figure out the rest of the radical.

$=\dfrac{-4\pm\sqrt{16-4(16)}}{2}=\dfrac{-4\pm\sqrt{16(1-4)}}{2}=\dfrac{-4\pm\sqrt{-3(16)}}{2}\\\\=\dfrac{-4\pm\sqrt{-3(4^2)}}{2}=\dfrac{-4\pm 4\sqrt{-3}}{2}=-2\pm2\sqrt{-3}=-2\pm2i\sqrt{3}$

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Answer:

Step-by-step explanation:

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4 years ago

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Anna71 [15]

Answer:

$\displaystyle J'(3) = -1$

General Formulas and Concepts:

<u>Algebra I</u>

Functions
Function Notation

<u>Calculus</u>

Derivatives

Derivative Notation

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative: $\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'$

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em /> $\displaystyle J(x) = e^{f(x)}$ <em />

<em />

<u>Step 2: Differentiate</u>

eˣ Derivative [Derivative Rule - Chain Rule]: $\displaystyle J'(x) = \frac{d}{dx}[e^{f(x)}] \cdot \frac{d}{dx}[f(x)]$
Simplify: $\displaystyle J'(x) = f'(x)e^{f(x)}$

<u>Step 3: Evaluate</u>

Substitute in <em>x</em> [Derivative]: $\displaystyle J'(3) = f'(3)e^{f(3)}$
Substitute in function values: $\displaystyle J'(3) = -e^{0}$
Simplify: $\displaystyle J'(3) = -1$

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

Unit: Derivatives

Book: College Calculus 10e

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