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Mazyrski [523]
3 years ago
14

Given the function f(x)=g(x-3)+2, describe transformation of f(x) on a coordinate plane relative to g(x).

Mathematics
1 answer:
Fantom [35]3 years ago
3 0
<h2>Answer:</h2>

The transformation of f(x) on a coordinate plane relative to g(x) is that the graph of g(x) has been shifted three units to the right and two units upward.

<h2>Step-by-step explanation:</h2>

If \ c \ is \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=g(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ f(x)=g(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ f(x)=g(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ f(x)=g(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ f(x)=g(x+c)

By knowing this, we can see that the function f(x) takes the following form:

f(x)=g(x-c)+k

Therefore, we can say that g(x-3) represents shifting the graph three units to the right and ultimately g(x-3)+2 tells us that the graph is shifted two units upward. Finally:

  • The transformation of f(x) on a coordinate plane relative to g(x) is that the graph of g(x) has been shifted three units to the right and two units upward.
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3/4 divide by 5 is equal to 3/20
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The table represents the function 7 = 5x- Output ) Input (3) -2 -18 8 x 1 2 2 12 8 2 2. What is the input when the output is 12
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y_{-2}=5\cdot(-2)-8=-10-8=-18y=5x-812=5x-812+8=5x20=5xx=\frac{20}{5}x=4

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A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 8 feet. Find the radius.
siniylev [52]

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Answer:

  6 feet

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr^2·h

For a sphere, the volume is ...

  V = 4/3πr^3

You want the volumes to be the same when h=8, so we have ...

  πr^2·8 = 4/3πr^3

Dividing by πr^2, we have ...

  8 = 4/3r

  r = 3/4·8 = 6

The radius is 6 feet.

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3 years ago
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monitta

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Step-by-step explanation:

Just subtract bro

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5(x+4)= -2(-4-x)+3 <br> what is the answer?
lianna [129]

Answer:

x = -3

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

Step-by-step explanation:

<u>Step 1: Define equation</u>

5(x + 4) = -2(-4 - x) + 3

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Distribute:                                   5x + 20 = 8 + 2x + 3
  2. Combine like terms:                   5x + 20 = 2x + 11
  3. Subtract 2x on both sides:        3x + 20 = 11
  4. Subtract 20 on both sides:        3x = -9
  5. Divide 3 on both sides:              x = -3

<u>Step 3: Check</u>

<em>Plug in x to verify it's a solution.</em>

  1. Substitute:                    5(-3 + 4) = -2(-4 - -3) + 3
  2. Simplify:                        5(-3 + 4) = -2(-4 + 3) + 3
  3. Add:                              5(1) = -2(-1) + 3
  4. Multiply:                        5 = 2 + 3
  5. Add:                              5 = 5

Here we see that 5 does indeed equal 5. ∴ x = -3 is a solution of the equation.

And we have our final answer!

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