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Pavlova-9 [17]
3 years ago
12

Type the correct answer in each box. Functions h and K are inverse functions, and both are defined for all real numbers Using th

is relationship, what is the value of each function composition?
(h o k) (3)=
(k o h)(-4b) =​
Mathematics
1 answer:
kompoz [17]3 years ago
7 0

Answer:

(h o k) (3) = 3

(k o h) (-4b) = -4b

Step-by-step explanation:

An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.

This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.

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The managers of franks snack shack buys hamburgers in packages of 30 and hamburger buns in packages of 24. He cannot buy part of
Andreas93 [3]

Answer:

He has to buy 4 packages of hamburgers in packages of 30 and 5 packages of hamburgers in packages of 24

Step-by-step explanation:

First we have to calculate the least common multiple (LCM) of 24 and 30

We will calculate the LCM of 24 and 30 by prime factorization method

24 = 2*2*2*3 = 2^{3} * 3^{1}

30 = 2*3*5 = 2^{1} *3^{1}* 5^{1}

LCM = 2^{3}* 3^{1}*5^{1}

LCM = 120

So number of hamburger buns = 120

Therefore, he must buy 120/24 = 5 packages of hamburgers in packages of 24 and he must also buy 120/30 = 4 packages of hamburgers in packages of 30

4 0
3 years ago
Consider the equation y = 4.2x and the table below that represents this relationship. X= 0, 2, 4, 6, Y= 0, 8.4, 16.8, 25.2
enyata [817]
Please present the relationship in a table arranged vertically:

<span>this relationship. X= 0, 2, 4, 6, Y= 0, 8.4, 16.8, 25.2   becomes:

</span><span> x        y
---    -----
 0       0
 2      8.4
 4     16.8
 6     25.2

Notice that as x increases by 2 units from 2 to 4, y increases by 8.4 units to 16.8.  Thus, the slope of this line is 
        16.8
m = -------- = 8.4
          4-2

Your problem statement sounds incomplete; what were you asked to do here?

You could compare the equations of the 2 functions:

y = 4.2x and
y = 8.4x 

The slope of the 2nd function is twice that of the first function.  Both graphs go through the origin, (0,0).</span>
7 0
3 years ago
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Annette [7]

Answer:

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Step-by-step explanation:

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6 0
2 years ago
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Select all options that represents the side lengths of a 30 60 90 triangle.
DerKrebs [107]

Answer:

Options (B) and (D)

Step-by-step explanation:

If a triangle is a 30° - 60° - 90° triangle, measure of the angle between the leg and hypotenuse will be either 60° or 90°.

Therefore, by applying Cosine rule in the given options.

c² = a² + b² - 2abCosC

All the given options are the right triangles.

[Since they follow the Pythagoras theorem]

Option (A),

Angle between the sides having measures 3 and 5 units,

4² = 3² + 5² - 2(3)(5)CosC

16 = 9 + 25 - 30.CosC

30.CosC = 18

C=\text{Cos}^{-1}(\frac{5}{6} )

C = 33.56°

Therefore, this triangle is not a 30-60-90 triangle.

Option (B),

Angle between the sides measuring 5 and 10 units,

(5\sqrt{3})^2=5^2+10^2-2(5)(10)\text{CosC}

75 = 125 - 100(CosC)

Cos(C) = 0.5

C = 60°

Therefore, other angles of the triangle will be 30° and 90°.

And it's a 30°-60°-90° triangle.

Option (C),

10, 10, 10√2

It's a right triangle and the measure of legs are equal.

Since legs of this sides are equal, angles opposite to these equal sides will be equal.

Sum of all interior angles = 180°

m∠A + m∠B + m∠C = 180°

If m∠B = 90°

m∠A + 90° + m∠C = 180°

2(m∠A) = 90°

m∠A = 45°

Therefore, the given sides make a 45°- 45°- 90° triangle.

Option (D).

Angle between the sides 3 and 6,

(3√3)² = 3² + 6² -2(3)(6)CosC

27 = 9 + 36 - 36.(CosC)

CosC = \frac{18}{36}

C = \text{Cos}^{-1}(\frac{1}{2})

C = 60°

Therefore,

These sides make a 30°- 60°- 90° triangle.

Options (B) and (D) are the 30°- 60°- 90° triangle.  

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B because 50 divided by 5 is 10
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