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3 years ago

Do these 3 side lengths form a right triangle? (Yes or no question): 9 in, 12 in, 15 in

Mathematics

2 answers:

lisabon 2012 [21]3 years ago

8 0

Answer:

the answer is yes

Step-by-step explanation:

Natasha_Volkova [10]3 years ago

3 0

Answer:

No because two of the sides should be the same length!

Step-by-step explanation:

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Determine whether each function has an inverse function. If it does, find the inverse function and state any restrictions on its

Talja [164]

QUESTION 1

The given function is;

$f(x) = |x - 6|$

This is an absolute value function.

For this function to have an inverse it must be a one-to-one function.

This absolute value function is not one-to-one
because

$f( 5)=1$
and

$f(7) = 1$

Since this function has more than one x-value mapping onto one y-value, it is not one-to-one and cannot have an inverse.

You can see from the graph that this function cannot pass the horizontal line test.

QUESTION 2

The given function is

$f(x) = \sqrt{6 - {x}^{2} }$

Let

$y= \sqrt{6 - {x}^{2} }$

This implies that,

${y}^{2} + {x}^{2} = 6$

We see clearly that, this function is a circle that is centered at the origin.

This means that,

$f(x) = \sqrt{6 - {x}^{2} }$

is a semicircle.

This function will not pass the horizontal line test and hence does not have an inverse.

QUESTION 3

The given function is

$h(x) = \frac{x+4}{3x-5}$

If we put

$h(a) = h(b)$

We obtain,

$\frac{a+4}{3a-5} = \frac{b+4}{3b-5}$

$(a + 4)(3b - 5) = (b + 4)(3a - 5)$

$3ab - 5a + 12b - 20 = 3ab - 5b + 12a - 20$

$- 17a = - 17b$

$a = b$

This shows that h(x) has an inverse because it is one-to-one.

Let

$y=\frac{x+4}{3x-5}$

We interchange x and y to get,

$x=\frac{y+4}{3y-5}$

$x(3y - 5) = y + 4$

$3xy - 5x = y + 4$

Group like terms to get,

$3xy - y = 5x + 4$

Factor to get,

$y(3x - 1) = 5x + 4$
Solve for y,

$y = \frac{5x + 4}{3x - 1}$

Hence

${f}^{ - 1}(x) = \frac{5x + 4}{3x - 1}$

where

$x \ne \frac{1}{3}$

6 0

3 years ago

A historic museum charges a rental fee plus $2 per hour for an audio tour guide. The total cost for 4 hours is $12. Find and int

Serhud [2]

We can represent this problem with the following linear equation
y = 2x + 4
where
y: total cost
x: number of hours
the slope of the line is
m = 2
Which means that for every hour of audio tour guide they charge $ 2.
For "zero" hours (x = 0) a rental fee of $ 4 must be paid.

3 0

4 years ago

Consider the function f(x)=−34x+1 .

Stells [14]

(Edit: 34 is meant to be 3/4)

I hope I can help! :)
f(1/2) = -11/8

f(x) basically means y. So, you could translate it as
y= -3/4x + 1

(1/2) would equal (x) so the function would look like this:

f(1/2) = -3/4(1/2)+1

Here are the steps to solve:
1. Multiply -3/4(1/2)
-3/4(1/2) = -3/8

2. Add 1 to -3/8
1 + -3/8 = -1 3/8

3.Reduce -1 3/8
-1 3/8 = -11/8

f(1/2) = -11/8
---------------------------
Have a great day/evening/night! :)
Let me know if you have any additional questions!
-Kappifilms

3 0

4 years ago

What is the quotient of 75.42 and 0.1

Rufina [12.5K]

Answer:

754.2

Step-by-step explanation:

First of all, we cannot solve the question the way it is. We need to make 0.1 into a whole number. If we move the decimal to the right, once, then it will become the number one.

Of course, what we do to one, we have to do to the other. We move the decimal to 75.42 to the right one. Now it is 754.2

That looks like the answer. The reason is because we are now dividing by one. Something divided by one, will always be itself.

Now we have the answer of 754.2.

4 0

4 years ago

Read 2 more answers

What is 1/4th of 52?

Paul [167]

The answer would be 13

3 0

3 years ago

Read 2 more answers