Answer:
(3, -9)
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>
-5x - 3y = 12
y = x - 12
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: -5x - 3(x - 12) = 12
- Distribute -3: -5x - 3x + 36 = 12
- Combine like terms: -8x + 36 = 12
- Isolate <em>x</em> term: -8x = -24
- Isolate <em>x</em>: x = 3
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: y = x - 12
- Substitute in <em>x</em>: y = 3 - 12
- Subtract: y = -9
<u>Step 4: Graph systems</u>
<em>Check the solution set.</em>
Answer:
The sine and cosine functions have a period of 2π radians and the tangent function has a period of π radians. Domain and range: From the graphs above we see that for both the sine and cosine functions the domain is all real numbers and the range is all reals from −1 to +1 inclusive.
Step-by-step explanation:

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Tags: <em>set theory divibilility divisible integers union intersection</em>
9514 1404 393
Answer:
x ≠ 3
Step-by-step explanation:
In any case, the domain is restricted to values of the variable for which the function is defined. The value 1/0 is not defined, so the variable cannot allow the denominator to be zero. The denominator x-3 will be zero for x=3, so that value of the variable cannot be in the domain.
The domain is all real numbers except x=3.
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<em>Additional comments</em>
It is useful to become familiar with the domains of different functions. As we saw above, the reciprocal of 0 is undefined. The square root of a negative number is undefined. The log of a non-positive number is undefined. Trig functions are defined everywhere, but their inverse functions are not. Polynomial functions are defined everywhere, but ratios of polynomials have the same restriction on denominators that we see above.