Answer:
(-3, 4)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
- Terms/Coefficients
- Coordinates (x, y)
- Solving systems of equation using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
3y = -5x - 3
y = -x + 1
<u>Step 2: Rewrite Systems</u>
Equation y = -x + 1
- [Multiplication Property of Equality] Multiply everything by -3: -3y = 3x - 3
<u>Step 3: Redefine Systems</u>
3y = -5x - 3
-3y = 3x - 3
<u>Step 4: Solve for </u><em><u>x</u></em>
<em>Elimination</em>
- Combine 2 equations: 0 = -2x - 6
- [Addition Property of Equality] Add 6 on both sides: 6 = -2x
- [Division Property of Equality] Divide -2 on both sides: -3 = x
<u>Step 5: Solve for </u><em><u>y</u></em>
- Define original equation: y = -x + 1
- Substitute in <em>x</em>: y = -(-3) + 1
- Simplify: y = 3 + 1
- Add: y = 4
Answer:
The answer is <em>C</em>
Explanation: Given:A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.
there is only 2 numbers which are greater than 7 i.e. 8 and 9. ∴ there is 2 possibility for first place.
For the remaining 3 digits there is 9 possibilities (including 1 which would left after choosing 1 from first place )
No of ways for the alarm code beginning with a number greater than 7= 2 P 1 x 9 P 3
<em>Total ways of code with 4 digits= 10 P 4.</em> Hope this helps :)
n=# of nickels
q=# of quarters
$12 is 1200 cents
5n+25q=1200
n=q
substitute q for n or n for q
5q+25q=1200
30q=1200
q=1200/30
q=40 quarters and therefore n=40 nickels
40 quarters is $10 and 40 nickels is $2, therefore you have $12
Hope this helps.
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