How do I do this because I don't understand how to do the ratio

Please solve these questions on the topic of exponents

galina1969 [7]

Answer/Step-by-step explanation:

Recall: $x^{-a} = \frac{1}{x^a}$

a. $4^{-3} = \frac{1}{4^3} = \frac{1}{64}$

b. $13^{-2} = \frac{1}{13^2} = \frac{1}{169}$

c. $(-3)^{-2} = \frac{1}{-3^2} = \frac{1}{9}$

6 0

3 years ago

House of Mohammed sells packaged lunches, where their finance department has established a

blagie [28]

The revenue function is a quadratic equation and the graph of the function

has the shape of a parabola that is concave downwards.

The correct responses are;

(a) R = -x² + 82·x

(b) $1,645

(c) The graph of R has a maximum because the leading coefficient of the quadratic function for R is negative.

(d) R = -1·(x - 41)² + 1,681

(e) 41

(f) $1,681

Reasons:

The given function that gives the weekly revenue is; R = x·(82 - x)

Where;

R = The revenue in dollars

x = The number of lunches

(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;

R = x·(82 - x) = 82·x - x²

Which gives;

R = -x² + 82·x

Where, the constant term, c = 0

(b) When 35 launches are sold, we have;

x = 35

Which by plugging in the value of x = 35, gives;

R = 35 × (82 - 35) = 1,645

The revenue when 35 lunches are sold, R = $1,645

(c) The given function for R is R = x·(82 - x) = -x² + 82·x

Given that the leading coefficient is negative, the shape of graph of the

function R is concave downward, and therefore, the graph has only a

maximum point.

(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;

(h, k) = The vertex of the equation

a = The leading coefficient

The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;

R = x·(82 - x) = -x² + 82·x

At the vertex, of the equation; f(x) = a·x² + b·x + c, we have;

$\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}$

Therefore, for the revenue function, the x-value of the vertex, is; $\displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}$

The revenue at the vertex is; $R_{max}$ = 41×(82 - 41) = 1,681

Which gives;

(h, k) = (41, 1,681)

a = -1 (The coefficient of x² in -x² + 82·x)

The revenue equation in the form, a·(x - h)² + k is; R = -1·(x - 41)² + 1,681

(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41

Therefore;

The number of lunches that must be sold for the maximum revenue to be achieved is 41 lunches

(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681

The maximum revenue of the company is $1,681

Learn more about the quadratic function here:

brainly.com/question/2814100

6 0

2 years ago

"calculate the number of permutations possible when using the first five letters of the alphabet to create 3-letter words.

Hitman42 [59]

That is 5! / (5-3)! = 120 / 2 = 60 answer

5 0

3 years ago

Find the missing length in the right triangle.

Sholpan [36]

10 ft because when you add the sides when squared 36+64 = 100 and the square root of that is 10

5 0

3 years ago

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The equation h(t)=−16t2+19t+110 gives the height of a rock, in feet, t seconds after it is thrown from a cliff. What is the init

Butoxors [25]

The initial velocity is 19 ft/s.

This is in the form f(t) = -16t²+v₀t+h₀, where v₀ is the initial velocity. 19 is in the place of v₀, so it is the initial velocity.

3 0

3 years ago

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