Answer:
(0,-1)
(1,-5)
(2,-9)
Step-by-step explanation:
y = −4x −1
Let x=0
y = 0-1 = -1 (0,-1)
Let x = 1
y = -4(1) -1 = -4-1 =-5 (1,-5)
Let x = 2
y = -4(2) -1 = -8-1 =-9 (2,-9)
A = hb/2
A = (15)(11) / 2
A = 165/2
A = 82.5 <===
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:
The minimum cost is $9,105
Step-by-step explanation:
<em>To find the minimum cost differentiate the equation of the cost and equate the answer by 0 to find the value of x which gives the minimum cost, then substitute the value of x in the equation of the cost to find it</em>
∵ C(x) = 0.5x² - 130x + 17,555
- Differentiate it with respect to x
∴ C'(x) = (0.5)(2)x - 130(1) + 0
∴ C'(x) = x - 130
Equate C' by 0 to find x
∵ x - 130 = 0
- Add 130 to both sides
∴ x = 130
∴ The minimum cost is at x = 130
Substitute the value of x in C(x) to find the minimum unit cost
∵ C(130) = 0.5(130)² - 130(130) + 17,555
∴ C(130) = 9,105
∵ C(130) is the minimum cost
∴ The minimum cost is $9,105
4.6x^2+3.2-4x+2.7x^2-x=4.6x^2+3.2x+-4x+2.7x^2+-xCombine like terms:4.6x^2+3.2x+-4x+2.7x^2+-x=(4.6x^2+2.7x^2)+(3.2x+-4x+-x)=7.3x^2+-1.8xAnswer:7.3x^2-1.8x
