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1 year ago

Question 2 of 25

Mathematics

1 answer:

notsponge [240]1 year ago

6 0

The inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6

<h3>How to determine the inverse function?</h3>

The function is given as:

f(x) = 6x + 4

Rewrite as:

y = 6x + 4

Swap x and y

x = 6y + 4

Subtract 4 from both sides

6y = x - 4

Divide through by 6

y = (x - 4)/6

Rewrite as:

f^-1(x) = (x - 4)/6

Hence, the inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6

Read more about inverse functions at:

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A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

------------------------------

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

5 0

2 years ago

Number 9 please. I need help

Sloan [31]

(1/12)X = 6800

6800/ (1/12) = X

X = 81600 (hours)

6800 (6.8 * 10^3) divided by 1/12 (12^-1) equals 81600. It will take 81600 hours for the pool to completely empty at a rate of 0.833333333 or 12^-1 gallons per second.

8 0

3 years ago

Which polyhedron has more faces than a hexahedron, but fewer faces than an dodecahedron?

timurjin [86]

The best and most correct answer among the choices provided by your question is the fourth choice or letter D.

Octahedron (8) is a <span>polyhedron has more faces than a hexahedron, but fewer faces than an dodecahedron.</span>

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

5 0

2 years ago

Read 2 more answers

Persons who work as sales managers, therapists, and teachers may be high in ____ intelligence.

Basile [38]

These are all service professions and ones in which the individual does well if they are in tune with how their clients, patients and students are feeling/understanding. Therefore, it is likely that people who excel in these fields are high in "emotional intelligence."

7 0

2 years ago

What is the perimeter of the triangle?<br>units=<br>

Luba_88 [7]

Answer:

Step-by-step explanation:

Use pythagorean theorem

side 1 = 9

side 2 = 12

9^2 + 12^2 = third side ^2

third side = 15

9+12+15 = 36

Hope this helpful!!!!! :)

8 0

2 years ago