Answer:
1. -12 = 12
2. 34 = -34
3. 0 = -0
4. 7 <u><</u> -8
5. -2 <u>></u> -4
6. 4 <u>></u> 0
7. 1 <u>></u> -1
8. -5 <u><</u> -2
9. -6 < -3 < -2 < 0
10. -5 < -1 < 2 < 8
11. a. Sapporo, Moscow, Bangor, Barrow
Answer:
siblings. Each cupcake costs $2, and each piece of fudge costs $1.
This system of inequalities models the scenario:
2x + y = <8
x + y > 4
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part
Answer:
answer is 3
Step-by-step explanation:
add 5 minus 10
something noteworthy is that the independent and squared variable in this case will be the "x", namely the graph of that quadratic is a vertical parabola.
![\bf f(x) = (x+2)(x-4)\implies 0=(x+2)(x-4)\implies x = \begin{cases} -2\\ 4 \end{cases} \\\\\\ \boxed{-2}\rule[0.35em]{7em}{0.25pt}0\rule[0.35em]{3em}{0.25pt}\stackrel{\downarrow }{1}\rule[0.35em]{10em}{0.25pt}\boxed{4}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%20%3D%20%28x%2B2%29%28x-4%29%5Cimplies%200%3D%28x%2B2%29%28x-4%29%5Cimplies%20x%20%3D%20%5Cbegin%7Bcases%7D%20-2%5C%5C%204%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20%5Cboxed%7B-2%7D%5Crule%5B0.35em%5D%7B7em%7D%7B0.25pt%7D0%5Crule%5B0.35em%5D%7B3em%7D%7B0.25pt%7D%5Cstackrel%7B%5Cdownarrow%20%7D%7B1%7D%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D%5Cboxed%7B4%7D)
so the parabola has solutions at x = -2 and x = 4, and its vertex will be half-way between those two guys, namely at x = 1.
since this is a vertical parabola, its axis of symmetry, the line that splits its into twin sides, will be a vertical line, and it'll be the x-coordinate of the vertex, since the vertex hasa a coordinate of x = 1, then the axis of symmetry is the vertical line of x = 1.