the graph models the number of active projects a company was working on x months after the end of november 2012, where 0 ≤ x ≤ 6. according to the model, what is the predicted number of active projects the company was working on at the end of november 2012?
a) 0
b) 5
c) 1
d) 9
the relationship between two variables, x and y, is linear. for every increase in the value of x by 1, the value of y increases by 8. when the value of x is 2, the value of y is 18. which equation represents this relationship?
a) y = 2x + 18
b) y = 2x+8
c) y = 8x + 2
d) y = 8x+26
the given n, and c. which equation correctly expresses c in terms of p and n?
a) c=\frac{19 + p}{n}
b) c=\frac{19 - p}{n}
c) c = 19+\frac{p}{n}
d) c = 19-\frac{p}{n}
w^{2}+12w - 40 = 0
which of the following is a solution to the given equation?
a) 6 - 2sqrt{19}
b) 2sqrt{19}
c) sqrt{19}
d) - 6+2sqrt{19}

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Accepted Answer

1. **First problem (graph - number of active projects):**
   - # Explanation:
     - ## Step1: Identify the value of $x$ at the end of November 2012.
       - Since $x$ represents the number of months after the end of November 2012, at the end of November 2012, $x = 0$.
     - ## Step2: Find the value of the function at $x = 0$ from the graph.
       - Looking at the graph, when $x = 0$, the number of active - projects is 5.
   - # Answer:
     - B. 5
2. **Second problem (solving the quadratic equation $w^{2}+12w - 40=0$):**
   - # Explanation:
     - ## Step1: Use the quadratic formula $w=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ for the quadratic equation $aw^{2}+bw + c = 0$.
       - For the equation $w^{2}+12w - 40 = 0$, $a = 1$, $b = 12$, and $c=-40$.
     - ## Step2: Calculate the discriminant $\Delta=b^{2}-4ac$.
       - $\Delta=(12)^{2}-4\times1\times(-40)=144 + 160=304$.
     - ## Step3: Calculate $w$.
       - $w=\frac{-12\pm\sqrt{304}}{2}=\frac{-12\pm2\sqrt{76}}{2}=-6\pm\sqrt{76}=-6\pm2\sqrt{19}$.
   - # Answer:
     - D. $-6 + 2\sqrt{19}$
3. **Third problem (linear - relationship between $x$ and $y$):**
   - # Explanation:
     - ## Step1: Recall the slope - intercept form of a linear equation $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.
       - Given that for every increase in $x$ by 1, $y$ increases by 8, so the slope $m = 8$.
     - ## Step2: Substitute the values of $x = 2$, $y = 18$, and $m = 8$ into $y=mx + b$ to find $b$.
       - $18=8\times2 + b$, which simplifies to $18 = 16 + b$. Solving for $b$, we get $b=2$.
     - ## Step3: Write the linear equation.
       - The equation is $y = 8x+2$.
   - # Answer:
     - C. $y = 8x + 2$

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