The  length of a rectangle is 2 less than twice its width. The area is 144 squared centimeters. Which quadratic equation in standard form correctly models the situation, where w represents the width of the rectangle

The quadratic equation which correctly models the situation is,

Let us consider that width is w.

Given that The length of a rectangle is 2 less than twice its width.

 Area of rectangle (A)

The area is 144 squared centimeters.

Hence, the quadratic equation which correctly models the situation is,

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w² - w - 72 = 0

Step-by-step explanation:

l = 2w - 2

A = 144

A = l * w

A = (2w - 2)w

144 = 2w² - 2w

0 = 2w² - 2w - 144

2w² - 2w - 144 = 0 (divide all by 2)

w² - w - 72 = 0

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).