Answer:
She should cut each diagonal piece 10 ft long.
Step-by-step explanation:
The bottom face of the box is a rectangle 8 ft by 6 ft.
A diagonal of a rectangle divides the rectangle into two congruent right triangles. With a right triangle you can use the Pythagorean theorem.
a = length of rectangle = leg of right triangle
b = width of rectangle = other leg of right triangle
c = diagonal of rectangle = hypotenuse of right triangle
a^2 + b^2 = c^2
(8 ft)^2 + (6 ft)^2 = c^2
64 ft^2 + 36 ft^2 = c^2
c^2 = 100 ft^2
Take the square root of each side.
c = 10 ft
Answer: She should cut each diagonal piece 10 ft long.
Answer: ![6\ units^2](https://tex.z-dn.net/?f=6%5C%20units%5E2)
Step-by-step explanation:
Plot the vertices of the rectangle on a coordinate plane (Observe the figure attached where the rectangle is identified as ABCD).
The area of a rectangle can be calculated with this formula:
![A=lw](https://tex.z-dn.net/?f=A%3Dlw)
Where "l" is the lenght and "w" is the width.
In order to find the lenght and the width, you can use the formula for calculate the distance between two points:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Knowing the coordinates of the vertices, you get:
![w=d_{AB}=\sqrt{(-4-(-3))^2+(0-1)^2}=\sqrt{2}\ units\\\\l=d_{BC}=\sqrt{(0-(-3))^2+(-2-1)^2}=3\sqrt{2}\ units](https://tex.z-dn.net/?f=w%3Dd_%7BAB%7D%3D%5Csqrt%7B%28-4-%28-3%29%29%5E2%2B%280-1%29%5E2%7D%3D%5Csqrt%7B2%7D%5C%20units%5C%5C%5C%5Cl%3Dd_%7BBC%7D%3D%5Csqrt%7B%280-%28-3%29%29%5E2%2B%28-2-1%29%5E2%7D%3D3%5Csqrt%7B2%7D%5C%20units)
Therefore, substituting values into the formula
, you get that the area of the rectangle is:
![A=(3\sqrt{2}\ units)(\sqrt{2}\ units)=6\ units^2](https://tex.z-dn.net/?f=A%3D%283%5Csqrt%7B2%7D%5C%20units%29%28%5Csqrt%7B2%7D%5C%20units%29%3D6%5C%20units%5E2)
Answer:
"2.25" is the right answer.
Step-by-step explanation:
According to the question,
The expected value will be:
= ![\sum_{i=1}^{n} x_i P(X = x_i)](https://tex.z-dn.net/?f=%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20x_i%20P%28X%20%3D%20x_i%29)
= ![0\times \frac{1}{8}+1\times \frac{1}{4}+2\times \frac{3}{16}+3\times \frac{1}{4}+4\times \frac{1}{6}+5\times \frac{1}{8}](https://tex.z-dn.net/?f=0%5Ctimes%20%5Cfrac%7B1%7D%7B8%7D%2B1%5Ctimes%20%5Cfrac%7B1%7D%7B4%7D%2B2%5Ctimes%20%5Cfrac%7B3%7D%7B16%7D%2B3%5Ctimes%20%5Cfrac%7B1%7D%7B4%7D%2B4%5Ctimes%20%5Cfrac%7B1%7D%7B6%7D%2B5%5Ctimes%20%5Cfrac%7B1%7D%7B8%7D)
= ![0+\frac{1}{4}+\frac{3}{8} +\frac{3}{4}+\frac{1}{4} +\frac{5}{8}](https://tex.z-dn.net/?f=0%2B%5Cfrac%7B1%7D%7B4%7D%2B%5Cfrac%7B3%7D%7B8%7D%20%2B%5Cfrac%7B3%7D%7B4%7D%2B%5Cfrac%7B1%7D%7B4%7D%20%2B%5Cfrac%7B5%7D%7B8%7D)
= ![\frac{1}{4} +\frac{8}{8} +\frac{4}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%2B%5Cfrac%7B8%7D%7B8%7D%20%2B%5Cfrac%7B4%7D%7B4%7D)
= ![\frac{1}{4} +1+1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%2B1%2B1)
= ![0.25+2](https://tex.z-dn.net/?f=0.25%2B2)
= ![2.25](https://tex.z-dn.net/?f=2.25)
Thus the above is the right approach.
Answer:
an infinite number
Step-by-step explanation:
This equation has a graph that is a line. Every point on the line is a solution.
There are an infinite number of solutions.