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2 answers:
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Answer:
(-2, 6)
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
- Solving systems of equations by graphing
Step-by-step explanation:
<u>Step 1: Define systems</u>
4x - 2y = -20
7x + 2y = -2
<u>Step 2: Rewrite systems</u>
4x - 2y = -20
- Add 2y to both sides: 4x = 2y - 20
- Divide 4 on both sides: x = 1/2y - 5
<u>Step 3: Redefine systems</u>
x = 1/2y - 5
7x + 2y = -2
<u>Step 4: Solve for </u><em><u>y</u></em>
<em>Substitution</em>
- Substitute in <em>x</em>: 7(1/2y - 5) + 2y = =-2
- Distribute 7: 7/2y - 35 + 2y = -2
- Combine like terms: 11/2y - 35 = -2
- Add 35 to both sides: 11/2y = 33
- Isolate <em>y</em>: y = 6
<u>Step 5: Solve for </u><em><u>x</u></em>
- Define original equation: 7x + 2y = -2
- Substitute in <em>y</em>: 7x + 2(6) = -2
- Multiply: 7x + 12 = -2
- Subtract 12 on both sides: 7x = -14
- Divide 7 on both sides: x = -2
<u>Step 6: Graph systems</u>
<em>Check the system.</em>
Answer:
For statement 2, reason is Segment addition postulate.
Statement 3 and reason is
BD=AC+CD using substitution property of equality.
Statement 4 and reason is
AC+CD=BD using symmetric property of equality
Statement 5 is
BD= BC+CD
Statement 6 and reason is
AC+CD=BC+CD using transitive property of equality
Reason for 7 is
Subtraction property of equality.
Step-by-step explanation:
For statement 2, we use segment addition postulate to say AC= AE+EC.
<em>120 yd^3</em>
Step-by-step explanation:
The formula for the volume of a pyramid is...
B is the area of the base and h is the height from the middle of the pyramid to the top. Since we know both of these we can plug them in.
<u>120</u>
The volume for the pyramid is <u>120 yd^3</u>.