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Troyanec [42]
1 year ago
6

Given that ƒ(x) = 3x, identify the function g(x) shown in the figure.

Mathematics
1 answer:
pogonyaev1 year ago
3 0

We will see that g(x) is a reflection across the y-axis of f(x), then:

   g(x) = f(-x) = 3^{-x\\

<h3>How to identify the function g(x)?</h3>

By looking at the graph, we can see that g(x) is a reflection across the y-axis of f(x).

So we can write:

g(x) = f(-x)

Here we know that:

f(x) = 3^x

Then, replacing f(x) on the formula for g(x), we get:

g(x) = f(-x) = 3^{-x\\

That is the function g(x) shown in the figure.

If you want to learn more about transformations:

brainly.com/question/4289712

#SPJ1

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Marizza181 [45]

With some simple rearrangement, we can rewrite the numerator as

2x^3 - 3x^2 - x + 4 = 2(x^3 - x) - 3x^2 + x + 4 \\\\ ~~~~~~~~ = 2x(x^2-1) - 3(x^2 - 1) + x + 1 \\\\ ~~~~~~~~ = (2x-3)(x^2-1) + x+1

Then factorizing the difference of squares, x^2-1=(x-1)(x+1), we end up with

\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}

3 0
2 years ago
The numbering system we commonly use is called the decimal numbering system because it uses ____ symbols to represent all possib
mafiozo [28]

The numbering system we commonly use is called the decimal numbering system because it uses <u> 10 </u> symbols to represent all possible numbers.

A way of writing numbers is known as a number system.

There are the following number systems:

  1. Decimal number system: "Deci" meaning 10, implies that the number system consists of 10 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
  2. Binary number system: "Bi" meaning 2, implies that the number system consists of 2digits or symbols, namely 0, and 1.
  3. Octal number system: "Oct" meaning 8, implies that the number system consists of 8 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, and 8.
  4. Hexa-Decimal number system: "Hexa-Deci" meaning 16, implies that the number system consists of 16 symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

Hence, we can say that the numbering system we commonly use is called the decimal numbering system because it uses <u> 10 </u> symbols to represent all possible numbers.

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6 0
2 years ago
Can someone answer this I’ll give brainliest
Mrac [35]

Answer:

7/13

Step-by-step explanation:

Arrange the numbers so that the number of girls in year 10 is the numerator, and the total number of girls is the denominator. (140/260) Simplify this by dividing both numbers by 20.

8 0
2 years ago
The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of a bridge is 1270 ft long and
deff fn [24]

Answer:

Step-by-step explanation:

Given

span of bridge L=1270\ ft

height of span h=157\ ft

Equation of Parabola

y=0.00039x^2

|x| i.e.

-635

\frac{dy}{dx}=2\times 0.00039

length of Arc=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}

=\int_{-635}^{635}\sqrt{1+(\frac{dy}{dx})^2}

=\int_{-635}^{635}\sqrt{1+(0.00078x)^2}

=2\times \int_{0}^{635}\sqrt{1+(0.00078x)^2}

=2\times (660.08)

=1320.16\ ft

4 0
3 years ago
(3) Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of 2 ft/sec and t
Gekata [30.6K]

Answer:

The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.

Step-by-step explanation:

Here, we note the following

Let the person walking way fom the elevator be X

Let the other person going up in the elevator be Y

Therefore after 15 seconds, their positions will be;

For X,  2 ft/sec × 15 s = 30 ft away from the elevator

For Y,  7 ft/sec × 15 s = 105 ft up in the elevator

At that instant, the distance between them is given as

d² = x² + y²

= 30² +105² = 11925 ft²

d = √11925 ft²  = 109.202 ft

The rate of change of the distance between the two peopl, X and Y is given as

\frac{dd^2}{dt} = \frac{dx^2}{dt} + \frac{dy^2}{dt}

Therefore,  2d\frac{dd}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt} or d\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}

Since \frac{dx}{dt} is given as 2 ft/sec and \frac{dy}{dt} = 7 ft/sec

Then  d\frac{dd}{dt} = 30 \times 2 + 105 \times 7 = 795\\

\frac{dd}{dt} = \frac{795}{109.202 } =7.28 ft/sec

8 0
3 years ago
Read 2 more answers
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