5 times a number increased by 4 is at least nineteen

18 is 32% of what number w? what is w?

tatyana61 [14]

18 = 32/100 x ?
? = 18 x 100/32 = 50

7 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

3 years ago

What is the slope and y-intercept of y= 2x - 7 ???

OLEGan [10]

The slope-intercept formula is y=mx+b
where m represents the slope and b represents the y-intercept
In this problem, 2 is the slope and -7 is the y-intercept.

6 0

4 years ago

Two Customers took out car loans from a bank.

padilas [110]

10,000(1+(0.047*5))=12350
Marcus-12350

10,000(1+(0.045*6))=12,700
Gianna-12,700

12,700-12,350=$350 difference

6 0

3 years ago

Item 1 Find the dimensions of the square. Area = 441 cm²

mafiozo [28]

Answer:

21 cm by 21 cm

Step-by-step explanation:

The formula for the area of a square is A = x^2, where x is the length of any one side of the square. Here,

441 cm² = x²

This actually has two roots: {√441, -√441), but since x must be positive here, to be a dimension of the square, we choose +√441, or +21.

The dimensions of the square are 21 cm by 21 cm.

3 0

3 years ago