Which is the answer?

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

kenny6666 [7]

Given:

The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation

$y=-29x^2+1388x-10040$

To find:

The maximum amount of profit the company can make, to the nearest dollar.

Solution:

If a quadratic equation is $f(x)=ax^2+bx+c$ , then the vertex is

$Vertex=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)$

If a>0, then vertex is the minimum point and if a<0, then the vertex is the maximum point.

We have,

$y=-29x^2+1388x-10040$

Here, $a=-29,b=1388, c=-10040$ . Clearly, a<0. So, the vertex is the point of maxima.

$-\dfrac{b}{2a}=-\dfrac{1388}{2(-29)}$

$-\dfrac{b}{2a}=-\dfrac{1388}{-58}$

$-\dfrac{b}{2a}\approx 23.931$

Putting x=23.931 in the given equation, we get

$y=-29(23.931)^2+1388(23.931)-10040$

$y=-16608.09+33216.228-10040$

$y=6568.138$

The vertex is at (23.931,6568.138).

Therefore, the maximum profit is $6568.138 when x=23.931.

5 0

3 years ago

Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per we

Allushta [10]

Part a) Use a system of inequalities to model the scenario

Let

x-------> represent babysitting hours

y-------> represent tutoring hours

we know that

--------> inequality

Part b) Use the model created in part A to create a graph representing Jeanne’s probable income earned and possible number of hours worked this week

we know that

--------> inequality

This inequality represent Jeanne’s possible number of hours worked this week

Using a graph tool

the solution of this inequality is the shaded area

see the attached figure N

--------> inequality

This inequality represent Jeanne’s probable income earned this week

Using a graph tool

the solution of this inequality is the shaded area

see the attached figure N

Part c) Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model

we have the system of inequalities

--------> inequality

the solution of the system of inequalities is the shaded area

using a graph tool

see the attached figure N

Let

------> see the attached figure N

The point belongs to the shaded area, so it is a system solution.

If the point is a solution, it must satisfy both inequalities.

Prove algebraically

substitute the value of x and y in the inequalities

inequality

------> is ok

inequality

-------> is ok

the point A satisfy both inequalities

therefore

the point A is a solution of the system

5 0

3 years ago

Read 2 more answers

Can someone plz help me ty

Ostrovityanka [42]

Answer:

8/15

Step-by-step explanation:

you first want to change your whole number, 4, into a fraction so all you have to do is add a 1 in the denominator so it will be 4/1

then you multiply across

2/15 * 4/1

you first multiply 2 and 4 and your answer will be 8 which is the numerator

then multiply 15 and 1 which is 15, the denominator

then you get

8/15

5 0

3 years ago

Pick 1 pls... im not trynna be mean but pls dont put an answer up here if u dont know

Aneli [31]

Answer:

Cilia

Step-by-step explanation:

5 0

3 years ago

Solve the linear system by using elimination

WINSTONCH [101]

Answer:

dltj he rheeh. eegge

Step-by-step explanation:

3kyth y3vyebveyhh

6 0

3 years ago