Answer:
(-1, 4)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define systems</u>
10x + 6y = 14
-x - 6y = -23
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Elimination</em>
- Add 2 equations together: 9x = -9
- Divide 9 on both sides: x = -1
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: -x - 6y = -23
- Substitute in <em>x</em>: -(-1) - 6y = -23
- Multiply: 1 - 6y = -23
- Subtract 1 on both sides: -6y = -24
- Divide -6 on both sides: y = 4
Answer:
1.) Alex and Jemma decided that they will separate the dozen doughnuts that they bought. Since Jemma loved doughnuts she got 7, and Alex got 5.
2.) 35:49
Divide 35 and 5.
35/5=7
Multiply 7 by 7.
7 x 7=49.
The missing side will be 35:49
The steps to determine whether the pillars have the same volume are;
First, we must know that the volume of an object of uniform surface area is the product of its Area and height.
The uniform area of each pillar is then evaluated and if equal;
Both pillars can be concluded to have the same volume.
We must first recall that for various shapes, the volume of the shape is a function of its height.
For example: a A cylinderical pillar and a rectangular prism pillar;
Volume of a cylinder = πr²h
Volume of a Cuboid = l × w × h
Since h = h.
Therefore, for both pillars to have the same volume; their Areas must be equal.
πr² = l × w
Learn more about Area and volume here
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Answer:
4 units
Step-by-step explanation:
The volume of a square pyramid is (a²)*h/3
256=a²*12/3
256=a²*4
256/4=a²
64=a²
a=8
Now we know that the square is 8 by 8.
The volume of a square prism is a²h
256=64h
256/64=h
h=4
Also, a square pyramid is 1/3 the volume of a square prism.
12÷3=4