X = short section of rope
4x = longer section of rope
x + 4x = 25
5x = 25
x = 5
…or in other words the shorter piece of rope is 5 feet long
Answer:
Step-by-step explanation:
The diagram of the right angle triangle is shown in the attached photo.
From the given right angle triangle,
AC represents the hypotenuse of the right angle triangle.
With m∠32 as the reference angle,
BC represents the adjacent side of the right angle triangle.
AB represents the opposite side of the right angle triangle.
To determine BC, we would apply
the Sine trigonometric ratio which is expressed as
Sin θ= opposite side/hypotenuse. Therefore, the expression used to find BC is
Sin 32 = BC/9
BC = 9Sin32
It can actually be done many ways. You must match up the corresponding sides.
For example, 24/20 and x/7 would work so would, 24/x and 20/7, and 7/20 and x/24. Most proportions are set up the same way. You just have to make sure to go in the same order for the two triangles. Sorry if it's confusing.
So let's use-20/7 and 24/x.
First, we multiply 7*24 and 20*x and we get 20x=168
Then we divide to get 168/20. X=8.4
The quadratic equation

can be written in the form:

Where p and q are the roots of the equation.
Given p = 4, q = -2, a = 3, the quadratic will look like this:

Finally, distribute and combine like terms to put it in standard form.