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zalisa [80]
3 years ago
11

Jordan is kayaking upstream. The following equation models his speed: f(x) = 2x2 − 4x − 9, where x is Anna's speed relative to l

and. What is the domain of the function? x ≥ 1 x ≤ −4 x ≥ −9 All real numbers
Mathematics
1 answer:
andrew11 [14]3 years ago
5 0

Answer:

All real numbers

Step-by-step explanation:

The given equation is:

f(x) = 2 {x}^{2}   - 4x - 9

where x is Ana's speed.

This is a quadratic function.

A quadratic function is a polynomial function.

All polynomial functions are are continuous and defined for all real values of x.

Therefore the domain of

f(x) = 2 {x}^{2}   - 4x - 9

is all real numbers.

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Help me, please!!!!!!!
navik [9.2K]

9514 1404 393

Answer:

  2

Step-by-step explanation:

Alex has 10 money units. Annie has 5 money units. The ratio of amounts is ...

  Alex : Annie = 10 : 5 = 2 : 1

Alex has 2 times as much money as Annie.

8 0
3 years ago
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in
kozerog [31]

Answer: C.  6

Step-by-step explanation:

Given : Time taken by Machine R to do the job = 36 hours

Time taken by Machine S to do the job = 18 hours

Let x be the number of each type of machine to do the job.

Then , according to the question the required equation will be :-

\dfrac{x}{36}+\dfrac{x}{18}=\dfrac{1}{2}\\\\\Rightarrow\ x(\dfrac{1}{36}+\dfrac{1}{18})=\dfrac{1}{2}\\\\\Rightarrow\ \dfrac{x}{12}=\dfrac{1}{2}\\\\\Rightarrow\ x=\dfrac{12}{2}=6

Hence, the number of machines of type R were used =6

8 0
3 years ago
Exercise 3.5. For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ [x^2 − 25}.
masya89 [10]

a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

b. The inverse image of g(x) is g^{-1}(x) = e^{x}

c. The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

<h3 /><h3>The domain of T</h3>

Since T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

⇒ x ≥ ±5

⇒ -5 ≤ x ≤ 5.

<h3>Inverse image of f(x)</h3>

The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

f : R → R defined by f(x) = 3x³

Let f(x) = y.

So, y = 3x³

Dividing through by 3, we have

y/3 = x³

Taking cube root of both sides, we have

x = ∛(y/3)

Replacing y with x we have

y = ∛(x/3)

Replacing y with f⁻¹(x), we have

So,  the inverse image of f(x) is f⁻¹(x) = ∛(x/3)

<h3>Inverse image of g(x)</h3>

The inverse image of g(x) is g^{-1}(x) = e^{x}

g : R+ → R defined by g(x) = ln(x).

Let g(x) = y

y =  ln(x)

Taking exponents of both sides, we have

e^{y} = e^{lnx} \\e^{y} = x

Replacing x with y, we have

y = e^{x}

Replacing y with g⁻¹(x), we have

So, the inverse image of g(x) is g^{-1}(x) = e^{x}

<h3>Inverse image of h(x)</h3>

The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

h : R → R defined by h(x) = x − 9

Let y = h(x)

y = x - 9

Adding 9 to both sides, we have

y + 9 = x

Replacing x with y, we have

x + 9 = y

Replacing y with h⁻¹(x), we have

So, the inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

Learn more about inverse image of a function here:

brainly.com/question/9028678

5 0
2 years ago
The Martinez family went to play and paid $13 for 1 adult and 4 children. The Hernandez family went to the same place and paid $
andrey2020 [161]

Answer: the price for an adult ticket is $3

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one child ticket.

The Martinez family went to play and paid $13 for 1 adult and 4 children. This means that

x + 4y = 13 - - - - - - - - - - -1

The Hernandez family went to the same place and paid $14 for 3 adults and 2 children. This means that

3x + 2y = 14 - - - -- - - - - - - -2

Multiplying equation 1 by 3 and equation 3 by 1, it becomes

3x + 12y = 39

3x + 2y = 14

Subtracting, it becomes

10y = 25

y = 25/10 = 2.5

Substituting y = 2.5 into equation 1, it becomes

x + 4 × 2.5 = 13

x + 10 = 13

x = 13 - 10

x = 3

6 0
2 years ago
How do u make 3/4 in a mix number as a whole number or decimal?
KengaRu [80]
In decimal form it's .75 and that's all you can make it
7 0
2 years ago
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