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1 year ago

F(x)=1/3x-2 g(x)=3(x+2)-2what is the transformation that occurs between f(x) and G(x)

Mathematics

1 answer:

Stels [109]1 year ago

4 0

$f(x)=\frac{1}{3}x-2,g(x)=3(x+2)-2$

Furthermore,

$\begin{gathered} \Rightarrow g(x)=3x+6-2=3x+4 \\ \Rightarrow g(x)=3x+4 \end{gathered}$

Notice that

$\begin{gathered} 9f(x)=3x-18 \\ \Rightarrow9f(x)+22=3x+4=g(x) \\ \Rightarrow9f(x)+22=g(x) \end{gathered}$

Therefore, function g(x) is equal to function f(x) if we dilate f(x) by a factor of 9 and shift it 22 units upwards.

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A beam of light from a monochromatic laser shines into a piece of glass. The glass has thickness L and index of refraction n=1.5

boyakko [2]

Additional information to complete the question:

How long does it take for a short pulse of light to travel from one end of the glass to the other?

Express your answer in terms of some or all of the variables f and L. Use the numeric value given for n in the introduction.

T = ___________ s

Answer:

$T = \frac{15}{f}$

Step-by-step explanation:

Given:

Thickness og glass = L

Index of refraction n=1.5

Frequency = f

$Wavelength = \frac{L}{10}$

λ(air) $= \frac{L}{10}$

λ(glass) = λ(air) / n

= $\frac{\frac{L}{10}}{1.5}$

= $\frac{L}{10} * \frac{1}{1.5}$

= $\frac{L}{15}$

V(glass) = fλ(glass)

$= f * \frac{L}{15}$

$T = \frac{L}{V_{glass}} = \frac{15}{f}$

7 0

3 years ago

4. Phil bought a block of cheese in the shape of a triangular prism measuring 8 inches by 4 inches by 2 inches. What is the volu

makkiz [27]

Answer:

32 inches^3

Step-by-step explanation:

Volume = 1/2 ( base x height x length)

0.5 ( 4 x 2 x 8) = 32 inches^3

6 0

2 years ago

−5.2 + y = 7.5

klio [65]

Answer:

your answer is

d. y = 12.7

5 0

3 years ago

Read 2 more answers

A grocery store had 38 employees, but then they hired 4 more people. What is the percent change in their staff?

gizmo_the_mogwai [7]

The percentage change in the staff strength of the grocery store is 10.53%.

<h3>How to find the percentage change?</h3>

We are given;

Number of employees in store = 38 employees

Number of additional people hired = 4 employees

Thus, percentage change in their staff is;

4/38 * 100% = 10.53%

Thus, the percentage change in the staff strength of the grocery store is 10.53%.

Read more about Percentage change at; brainly.com/question/2085058

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7 0

2 years ago

If x+1 and x-1 are the factors of the polynomial ax^3 + x^2 - 2x +b,find the values of a and b

Nadusha1986 [10]

The polynomial remainder theorem says that dividing a polynomial $p(x)$ by $x-c$ leaves a remainder of $p(c)=0$ if $x-c$ is a factor of $p(x)$ . In this case, check $c=-1$ and $c=1$ .

$a(-1)^3+(-1)^2-2(-1)+b=-a+b+3=0$

$a(1)^3+(1)^2-2(1)+b=a+b-1=0$

From the first equation,

$-a+b+3=0\implies a=b+3$

and substituting into the second gives

$(b+3)+b-1=0\implies2b+2=0\implies b=-1\implies a=2$

3 0

3 years ago