Answer:
(3, -2)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = -x + 1
y = 4x - 14
<u>Step 2: Rewrite Systems</u>
y = 4x - 14
- Multiply everything by -1: -y = -4x + 14
<u>Step 3: Redefine Systems</u>
y = -x + 1
-y = -4x + 14
<u>Step 4: Solve for </u><em><u>x</u></em>
<em>Elimination</em>
- Combine equations: 0 = -5x + 15
- Isolate <em>x</em> term: -15 = -5x
- Isolate <em>x</em>: 3 = x
- Rewrite: x = 3
<u>Step 5: Check</u>
- Define equation: y = -x + 1
- Substitute in <em>x</em>: y = -3 + 1
- Add: y = -2
We cannot agree with Danika. Why? Well, The reasoning is given as follows:
Two functions are inverses of each other if and only if it is true that the composition function is given by:
Everything is ok up to this point, right?. But let's prove that this is not fulfilled for these functions, then:
<span>
As you can see we did not obtain the function that matches the definition of </span>inverse functions. For that reason <em>we can't agree with Danika</em>.
<span>product of ten thirds and six
10/3 x 6
</span><span>one-fourth of ....
1/4 (10/3 x 6)
</span><span> four less than ....
</span>1/4 (10/3 x 6) - 4
The standard form for an equation is y=mx+b. You find the slope by using the formula of rise over run. This means that for problem 6 you first look to see if its positive or negative slope. The slope is positive if the line is going uphill and if its going downhill its negative. The slope would be negative for number 6 because it is going downhill. Then for the actualy slope you would start with rise. So you look at the point (0,1) and go up 3 until you hit the line of the other point and run over 2. So your slope would be -3/2.
One of the numbers are negative
Remember this... a negative divided by a positive will result in a negative and a negative divided by a negative will result in a positive, the same goes for multiplication
