The length of a rectangle is 7 yd less than three times the width and the area is 66 us square. what is the length and width

L = 3w - 7
Lw = 66

Lw = 66
(3w - 7)w = 66
3ww - 7w - 66 = 0

the above quadratic equation is in standard form, with a=3, b=-7, and c=-66

to solve the quadratic equation, by using the quadratic formula, copy and paste this:
3 -7 -66
into this solver: https://sooeet.com/math/quadratic-equation-solver.php

the quadratic has two real roots at:

w = 6
w = -3.6666666

The negative root doesn't fit the problems statement, so use the positive root instead:

w = 6

L = 3w - 7
L = 3*6 - 7
L = 11

w = 6 yds
L = 11 yds

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).