Answer:
Width = 16(√5) - 1
Step-by-step explanation:
We are told that the golden rectangle is 32 cm long.
Thus, length = 32 cm
We are also told that the ratio of the length to the width is; (1 + √5):2
Thus;
If a length of (1 + √5) yields a width of 2
Then, a length of 32 cm would yield a width of; (32 x 2)/(1 + √5)
So corresponding width = 64/(1 + √5)
We want to reduce this width to it's simplest radical form which means the denominator should have no square root.
Thus, let's multiply top and bottom by (1 - √5);
Width = 64 x (1 - √5)/[(1 + √5) x (1 - √5)]
Width = 64(1 - √5)/(1 - 5)
Width = 64(1 - √5)/(-4)
Width = -16(1 - √5)
Width = 16(√5 - 1)
Width = 16√5 - 1
Answer:
The side length of the original square was 6 inches
Step-by-step explanation:
we know that
The area of a square is

where
b is the length side of the square
Let
x ---> the length of the original square
The area of the original square is

The length of the smaller square is

The area of the smaller square is

The area of the smaller square is 1/4 the area of the original square
so

solve for x

Multiply by 4 both sides


Solve the quadratic equation by graphing
using a graphing tool
x=2, x=6
see the attached figure
The solution is x=6 in
Remember that the solution must be greater than 3 inches (because Stacey cuts 3 inches off of the length of the square and 3 inches off of the width)
therefore
The side length of the original square was 6 inches
Answer: 
Step-by-step explanation:
<h3>
The complete exercise is attached.</h3>
You can observe in the picture attached that the box is a rectangular prism.
The volume of a rectangular prism can be found with this formula:

Where "l" is the length, "w" is the width and "h" is the height.
You know that the lenght of each side of those cubes is 1 centimeter. Therefore, you can multiply the number of cubes on each side of the box by 1 centimeter in order to find the lenght, the width and the height of the box:
Now you can substitute the lenght, the width and the height of the box into the formula shown at the beginning of the explanation:

Finally, evaluating, you get that the volume of the box is:

Answer: 15.7 minutes
Step-by-step explanation:
Let x be the time in the beginning (in minutes).
Given: The track team is trying to reduce their time for a relay race.
First they reduce their time by
2.1 minutes.
Then they are able to reduce that time by
10
If their final time is 3.96 minutes, then
Hence, their beginning time was 15.7 minutes.