Answer:
1) 27/128 ft³
2) 40cm³
Step-by-step explanation:
1) The diagram is a cuboid not a prism.
Volume of the shape = Length × Breadth × Height
Given the following dimension
Length = 3/8 ft
Breadth = 3/4 ft
Height = 3/4 ft
Volume = 3/8 × 3/4 × 3/4
Volume of the shape = 27/128 ft³
2) Volume of a rectangular prism = Base Area × Height
Given base area = 12cm²
Height of the prism = 3 1/3 cm
Volume = 12 × 3 1/3
Volume = 12 × 10/3
Volume = 4 × 10
Volume of the prism = 40cm³
Answer:
![\left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.](https://tex.z-dn.net/?f=%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dy%5Cge%20-x-6%5C%5C%20%5C%5C%20y%5Cle%202x%2B4%5Cend%7Barray%7D%5Cright.)
Step-by-step explanation:
The diagram shows shaded region which boundary is bounded with two lines.
<u>Equation of the 1st line:</u>
This line passes through the points (-6,0) and (0,-6), so its equation is
![\dfrac{x-(-6)}{0-(-6)}=\dfrac{y-0}{-6-0}\\ \\\dfrac{x+6}{6}=\dfrac{y}{-6}\\ \\y=-x-6](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-%28-6%29%7D%7B0-%28-6%29%7D%3D%5Cdfrac%7By-0%7D%7B-6-0%7D%5C%5C%20%5C%5C%5Cdfrac%7Bx%2B6%7D%7B6%7D%3D%5Cdfrac%7By%7D%7B-6%7D%5C%5C%20%5C%5Cy%3D-x-6)
<u>Equation of the 2nd line:</u>
This line passes through the points (-2,0) and (0,4), so its equation is
![\dfrac{x-(-2)}{0-(-2)}=\dfrac{y-0}{4-0}\\ \\\dfrac{x+2}{2}=\dfrac{y}{4}\\ \\y=2x+4](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-%28-2%29%7D%7B0-%28-2%29%7D%3D%5Cdfrac%7By-0%7D%7B4-0%7D%5C%5C%20%5C%5C%5Cdfrac%7Bx%2B2%7D%7B2%7D%3D%5Cdfrac%7By%7D%7B4%7D%5C%5C%20%5C%5Cy%3D2x%2B4)
The origin belongs to the shaded region, so it must satisfy both inequalities, so
correct inequality is ![-x-6\le y](https://tex.z-dn.net/?f=-x-6%5Cle%20y)
correct inequality is ![2x+4\ge y](https://tex.z-dn.net/?f=2x%2B4%5Cge%20y)
Note that signsare with notion "or equal to" because lines are solid.
Answer:
![\left\{\begin{array}{l}-x-6\le y\\ \\2x+4\ge y\end{array}\right.\Rightarrow \left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D-x-6%5Cle%20y%5C%5C%20%5C%5C2x%2B4%5Cge%20y%5Cend%7Barray%7D%5Cright.%5CRightarrow%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dy%5Cge%20-x-6%5C%5C%20%5C%5C%20y%5Cle%202x%2B4%5Cend%7Barray%7D%5Cright.)
How many liters do Ima need to make one scone? ... when u have that , place 1 over (the number of liters to make one scone) ... then place 80 over x ... (yes they are fractions) now just multiply across ... so 80 times (the number of liters to make one scone) ... then divide that by one ... now u know how many liters u need to make 80 scones ... so , is 3 liters enough?
37.68 Anything in the hundredths column that is five or higher, would raise the tenths column by one number. <span>37.7 In your example the 8 is higher than 5, so the 6 is raised to a 7 for rounding.</span>