Answer:
5x and -4x
Step-by-step explanation:
Paul wants M₁ and M₂ to have a total that is +x, and a product that is -20x². The values of M₁ and M₂ that will do that are ...
5x and -4x
Answer:
C. 17.6
General Formulas and Concepts:
<u>Math</u>
<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>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] tanθ = opposite over adjacent
Step-by-step explanation:
<u>Step 1: Identify Variables</u>
Angle θ = 40°
Opposite Leg = <em>x</em>
Adjacent Leg = 21
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [tangent]:
- [Multiplication Property of Equality] Isolate <em>x</em>:
- Rewrite:
- Evaluate:
- Round:
Find where the two curves intersect:
<em>y</em> = 6<em>x</em> - 2<em>x</em> ²
<em>y</em> = <em>x</em> ²
6<em>x</em> - 2<em>x</em> ² = <em>x</em> ² → 3<em>x</em> ² - 6<em>x</em> = 3<em>x</em> (<em>x</em> - 2) = 0 → <em>x</em> = 0 and <em>x</em> = 2
Now, for a shell of radius <em>x</em> units away from the axis of revolution, the height of the shell would be the vertical distance between the upper curve and the lower curve. For 0 ≤ <em>x</em> ≤ 2, we have 6<em>x</em> - <em>x</em> ² ≥ <em>x</em> ², so the height of any given shell is (6<em>x</em> - <em>x</em> ²) - <em>x</em> ² = 6<em>x</em> - 2<em>x</em> ².
Then volume of the solid is
Answer:
15 pairwise comparisons; 30 pairwise rankings.
Step-by-step explanation:
Each of the 6 candidates can be ranked #1 in relation to the other 5, for a total of 30 pairwise rankings.
Of course, two of those are comparisons of the same pair of candidates. The same is true of all pairs of candiates, so the number of pairwise comparisons is half the possible number of rankings: 30/2 = 15.
_____
For example, for the pair of candidates A and B, you can have the two rankings ...
These cases are possible outcomes of the the one pairwise comparison ...