Answer:
x = - 100
Step-by-step explanation:
Given
+ 6 = - 14 ( subtract 6 from both sides )
= - 20
Multiply both sides by 5 to clear the fraction
x = 5 × - 20 = - 100
Answer:
(a)Length =2 feet
(b)Width =2 feet
(c)Height=3 feet
Step-by-step explanation:
Let the dimensions of the box be x, y and z
The rectangular box has a square base.
Therefore, Volume of the box
Volume of the box

The material for the base costs
, the material for the sides costs
, and the material for the top costs
.
Area of the base 
Cost of the Base 
Area of the sides 
Cost of the sides=
Area of the Top 
Cost of the Base 
Total Cost, 
Substituting 

To minimize C(x), we solve for the derivative and obtain its critical point
![C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2](https://tex.z-dn.net/?f=C%27%28x%29%3D%5Cdfrac%7B0.6x%5E3-4.8%7D%7Bx%5E2%7D%5C%5CSetting%20%5C%3AC%27%28x%29%3D0%5C%5C0.6x%5E3-4.8%3D0%5C%5C0.6x%5E3%3D4.8%5C%5Cx%5E3%3D4.8%5Cdiv%200.6%5C%5Cx%5E3%3D8%5C%5Cx%3D%5Csqrt%5B3%5D%7B8%7D%3D2)
Recall: 
Therefore, the dimensions that minimizes the cost of the box are:
(a)Length =2 feet
(b)Width =2 feet
(c)Height=3 feet
The quadrilaterals whose consecutive and opposite angles are always congruent are the square and the rectangle. All of the angles of the square and the rectangle are 90 degrees. The consecutive angles of the parallelogram and the rhombus are not equal.
Answer:
Part A:
The probability that all of the balls selected are white:

Part B:
The conditional probability that the die landed on 3 if all the balls selected are white:

Step-by-step explanation:
A is the event all balls are white.
D_i is the dice outcome.
Sine the die is fair:
for i∈{1,2,3,4,5,6}
In case of 10 black and 5 white balls:






Part A:
The probability that all of the balls selected are white:


Part B:
The conditional probability that the die landed on 3 if all the balls selected are white:
We have to find 
The data required is calculated above:

Answer:
c = 10
Explanation:
Use Pythagoras theorem: a² + b² = c²
where 'a' and 'b' are legs and 'c' is the hypotenuse (the longest side)
Here given: a = 8 cm, b = 6 cm, c = ?
Substituting values:
8² + 6² = c²
c² = 64 + 36
c² = 100
c = √100
c = 10