Answer:
B. {16, 19, 20}
Step-by-step explanation:
The <em>triangle inequality</em> requires for any sides a, b, c you must have ...
a + b > c
b + c > a
c + a > b
The net result of those requirements are ...
- the sum of the two shortest sides must be greater than the longest side
- the length of the third side lies between the difference and sum of the other two sides
__
If we look at the offered side length choices, we see ...
A: 8+11 = 19 . . . not > 19; not a triangle
B: 16+19 = 35 > 20; could be a triangle
C: 3+4 = 7 . . . not > 8; not a triangle
D: 5+5 = 10 . . . not > 11; not a triangle
The side lengths {16, 19, 20} could represent the sides of a triangle.
_____
<em>Additional comment</em>
The version of triangle inequality shown above ensures that a triangle will have non-zero area.
The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")
Answer:
120 degrees
Step-by-step explanation:
360/3=120
Answer:
7
Step-by-step explanation:
5( x - 3)/2 - 1 = 9
5/2(x-3)-1=9
5/2x-15/2-1=9
5x-15-2=18
5x-17=18
5x=35
x=7
Answer:
t = -14
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
- Subtract Property of Equality
Step-by-step explanation:
<u>Step 1: Define</u>
-98 = 7t
<u>Step 2: Solve for </u><em><u>t</u></em>
- Divide 7 on both sides: -14 = t
- Rewrite: t = -14
<u>Step 3: Check</u>
<em>Plug in t into the original equation to verify it's a solution.</em>
- Substitute in <em>t</em>: -98 = 7(-14)
- Multiply: -98 = -98
Here we see that -98 is equal to -98.
∴ t = -14 is the solution to the equation.
The time when the maximum serum concentration is reached is obtained by equating the derivative of C(t) to 0.
i.e. dC(t)/dt = 0.06 - 2(0.0002t) = 0.06 - 0.0004t = 0
0.0004t = 0.06
t = 0.06/0.0004 = 150
Therefore, the maximum serum concentration is reached at t = 150 mins
The maximum concentration = 0.06(150) - 0.0002(150)^2 = 9 - 0.0002(22,500) = 9 - 4.5 = 4.5
Therefore, the maximum concentration is 4.5mg/L
