Answer:
Step 3.
m∠ AEB = m∠ CED .........By Vertical Angles Theorem.
Step-by-step explanation:
Vertical Angles Theorem:
Vertical angle theorem states that vertical angles, angles that are opposite each other and formed by two intersecting lines,are congruent.
If two lines intersect each other we have two pair of vertical opposite angles. As shown in the figure.
Here,
∠ 1 and ∠ 2 are vertical opposite angles and also they are equal.
∠ 3 and ∠ 4 are also vertical opposite angles and also they are equal.
For,
step 3. m∠ AEB = m∠ CED
Therefore, the reason for step 3 of this proof is Vertical Angles Theorem.
Answer:
20%
Step-by-step explanation:
To find the percent decrease, we do old number subtracted from the new numbers over old.
We do
40 - 32 = 8
Then we put the 8 over the old and get
8/40
In percentage form it would be 20%
Let h = height of the box,
x = side length of the base.
Volume of the box is
.
So
Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.
![4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86](https://tex.z-dn.net/?f=%204x%20%3D%20%5Cfrac%7B460%7D%7B%20x%5E%7B2%7D%20%7D%20%20%5C%5C%20%204x%5E%7B3%7D%20%3D%20460%20%20%5C%5C%20x%5E%7B3%7D%20%3D%20115%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B115%7D%20%3D%204.86%20)
Then
So the box is 4.86 in. wide and 4.87 in. high.
Yes both rates are equivalent
