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swat32
2 years ago
8

The graph of g(x) is a transformation of the graph of f(x)=3x. Enter the equation for g(x) in the box. G(x) =.

Mathematics
1 answer:
dalvyx [7]2 years ago
8 0

Function transformation involves changing the form of a function

The function g(x) is \mathbf{g(x) = 8(2)^x}

The function is given as:

\mathbf{f(x) = 3^x}

g(x) is an exponential function that passes through points (-2,2) and (-1,4).

An exponential function is represented as:

\mathbf{y = ab^x}

At point (-2,2), we have:

\mathbf{2 = ab^{-2}}

At point (-1,4), we have:

\mathbf{4 = ab^{-1}}

Divide both equations

\mathbf{\frac 42=\frac{ab^{-1}}{ab^{-2}}}

Simplify

\mathbf{2=\frac{b^{-1}}{b^{-2}}}

Apply law of indices

\mathbf{2=b^{-1+2}}

\mathbf{2=b}

Rewrite as:

\mathbf{b =2}

Substitute 2 for b in \mathbf{2 = ab^{-2}}

\mathbf{2 =a(2^{-2})}

This gives

\mathbf{2 =a(\frac 14)}

Multiply both sides by 4

\mathbf{a = 8}

Substitute 8 for (a) and 2 for (b) in \mathbf{y = ab^x}

\mathbf{y = 8(2)^x}

Express as a function

\mathbf{g(x) = 8(2)^x}

Hence, the function g(x) is \mathbf{g(x) = 8(2)^x}

Read more about exponential functions at:

brainly.com/question/11487261

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X²- 6x = 7 FInd the soultion to the equation by completing the square
atroni [7]

Answer:

x = - 1, x = 7

Step-by-step explanation:

Given

x² - 6x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3) x + 9 = 7 + 9

(x - 3)² = 16 ( take the square root of both sides )

x - 3 = ± \sqrt{16} = ± 4

Add 3 to both sides

x = 3 ± 4, that is

x = 3 + 4 = 7 or x = 3 - 4 = - 1

6 0
3 years ago
Read 2 more answers
Plz help me thank you
MA_775_DIABLO [31]

Answer:

2 cups:16 fluid ounces

96 ounzes: 6 pints

12 pints: 24 cups

4 quarts: 1 gallon

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3 years ago
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Graph the hyperbola using the transverse axis, vertices, and co-vertices:
Reptile [31]

See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0

<h3>How to graph the hyperbola?</h3>

The equation of the hyperbola is given as:

12x^2 - 3y^2 - 108 = 0

Start by calculating the transverse axis

So, we have:

<u>Transverse axis</u>

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

Where

a = 3 and b = 6

The transverse axis is calculated as:

y = ±b/a(x - h) + k

So, we have:

y = ±6/3(x - 0) + 0

Evaluate the difference and sum

y = ±6/3x

Evaluate the quotient

y = ±2x

This means that the transverse axes are y = 2x and y =-2x

<u>The vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

<u>The co-vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

And

a = 3 and b = 6

The co-vertices are

(h - a, k) and (h + a, k)

So, we have:

(0 - 3, 0) and (0 + 3, 0)

Evaluate

(-3,0) and (3, 0)

See attachment for the graph of the hyperbola

Read more about hyperbola at:

brainly.com/question/26250569

#SPJ1

4 0
1 year ago
A and b are positive integers and a–b = 3. Evaluate the following: 27^ (1/3 b)/9^ (1/2 a)
maxonik [38]

Answer:

1/27

Step-by-step explanation:

27^(b/3)/9^(a/2) = (27^(1/3))^b/(9^(1/2))^a = (3^b)/(3^a) = 3^(b-a)

= 3^(-(a-b)) = 3^-3 = 1/3^3 = 1/27

5 0
3 years ago
A scale model of a human heart is 190 Inches long. The scale is 34 to 1. How many Inches long is the actual
Alika [10]

Answer:

6 inches long

Step-by-step explanation:

190/x = 34/1

34x = 190

x= 5.588235294

rounded to the nearest whole number is 6

6 0
2 years ago
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