Linear-Quadratic Systems — Quiz

Question 1

A boutique owner sells handcrafted scarves. The fixed monthly costs are $⁢500 , and the variable cost per scarf is $⁢10 The boutique's revenue is $⁢0 when 0 scarves are sold and $⁢0 when 100 scarves are sold due to market saturation. The maximum revenue occurs when 50 scarves are sold. Which system of equations represents the linear cost function C⁡(x) and the quadratic revenue function R⁡(x) , where x represents the number of scarves sold?

Revolt · Accepted Answer

cap c times x is equal to 10 x plus 500 cap r times x is equal to negative x times open paren x minus 100 close paren

Question 2

A software company has fixed monthly expenses of $⁢10,000 and a variable cost of $⁢100 per software license sold. Due to market capacity, revenue is $⁢0 when 0 licenses are sold and $⁢0 when 200 licenses are sold. The maximum revenue occurs when 100 licenses are sold. Which system of equations represents the linear cost function C⁡(x) and the quadratic revenue function R⁡(x) , where x represents the number of software licenses sold?

Revolt · Accepted Answer

cap c times x is equal to 100 x plus 10 comma 000 cap r times x is equal to negative x times open paren x minus 200 close paren

Question 3

Part of the system of equations has been graphed. Graph the linear equation. y=x^2−2⁢x y=−x+6

Revolt · Accepted Answer

parabola; 1; -1; 0; line; 6; 4; 2

Question 4

Part of the system of equations has been graphed. Graph the linear equation. y=x^2+2⁢x−3 y=−x−3

Revolt · Accepted Answer

parabola; -1; -4; 0; -3; line; 4; -7

Question 5

Which graph represents the system of equations? y=x^2−2⁢x+1 y=x+5

Revolt · Accepted Answer

Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 3 to 5 and the y-axis is labeled from 0 to 50. Points on the line are (negative 1, 5), (4, 9), (5, 10). Points on the curved line are (negative 1, 5), (1, 0), (4, 9).

Question 6

A company's revenue, R⁡(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R⁡(x)=−x^2+9⁢x−10 Its cost, C⁡(x) , in thousands of dollars, is modeled by the linear function C⁡(x)=2⁢x How many units must the company sell to break even?

Revolt · Accepted Answer

2 comma 000 or 5 comma 000 units

Question 7

A farmer sells organic apples at a local market. The fixed costs are $⁢800 per season, and the variable cost is $⁢1 per kilogram of apples sold. The revenue is $⁢0 when 0 kg or 160 kg of apples are sold due to market limitations. The maximum revenue occurs when 80 kg of apples are sold. Which system of equations represents the linear cost function C⁡(x) and the quadratic revenue function R⁡(x) , where x represents the kilograms of apples sold?

Revolt · Accepted Answer

cap c times x is equal to x plus 800 cap r times x is equal to negative x times open paren x minus 160 close paren

Question 8

Part of the system of equations has been graphed. Graph the linear equation. y=x^2−6⁢x+8 y=x−4

Revolt · Accepted Answer

parabola; 3; -1; 0; 8; line; -4; 4

Question 9

Part of the system of equations has been graphed. Graph the linear equation. y=x^2−4 y=x−2

Revolt · Accepted Answer

parabola; 0; -4; 2; line; -2

Question 10

Jamar owns a clothing store. His fixed costs are $⁢800 per month, and it costs $⁢10 to produce each item. Your revenue is $⁢0 when 0 items are sold and $⁢0 when 150 items are sold due to market saturation. The maximum revenue occurs when 75 items are sold. Write a system of equations for the linear cost function, C⁡(x) , and a quadratic revenue function, R⁡(x) , where x represents the number of items sold.

Revolt · Accepted Answer

C(x)=10x+800|R(x)=-x^2+150x

Linear-Quadratic Systems — Quiz Answers

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