19 - 1 = 18 and 7 - 6 = 1
Since anything multiplied by 1 is itself, the answer is 18.
Consider the vertex form of the parabola.<span><span>y=a<span><span>(x+h)</span>2</span>+k</span><span>y=a<span><span>(x+h)</span>2</span>+k</span></span>Rewrite the function in terms of <span>xx</span> and <span>yy</span>.<span><span>y=<span>x2</span>+6x−7</span><span>y=<span>x2</span>+6x-7</span></span>Complete the square on the right side of the equation.<span><span><span><span>(x+3)</span>2</span>−16</span><span><span><span>(x+3)</span>2</span>-16</span></span>Reorder the right side of the equation to match the vertex form of a parabola.<span><span>y=<span><span>(x+3)</span>2</span>−16</span><span>y=<span><span>(x+3)</span>2</span>-16</span></span>Since <span>33</span> does not contain the variable to solve for, move it to the right side of the equation by subtracting <span>33</span> from both sides.<span><span>x=−3</span><span>x=-3</span></span>Use the vertex form, <span><span>y=a<span><span>(x−h)</span>2</span>+k</span><span>y=a<span><span>(x-h)</span>2</span>+k</span></span>, to determine the values of <span>aa</span>, <span>hh</span>, and <span>kk</span>.<span><span>a=1</span><span>a=1</span></span><span><span>h=−3</span><span>h=-3</span></span><span><span>k=−16</span><span>k=-16</span></span>Since the value of <span>aa</span> is positive, the parabola opens up.Opens UpFind the vertex <span><span>(h,k)</span><span>(h,k)</span></span>.<span><span>(−3,−16)</span><span>(-3,-16)</span></span>Find <span>pp</span>, the distance from the vertex to the focus.<span><span>14</span><span>14</span></span>Find the focus.<span><span>(−3,−<span>634</span>)</span><span>(-3,-<span>634</span>)</span></span>Find the axis of symmetry by finding the line that passes through the vertex and the focus.<span><span>x=−3</span><span>x=-3</span></span>Find the directrix.<span><span>y=−<span>654</span></span><span>y=-<span>654</span></span></span>Use the properties of the parabola to analyze and graph the parabola.Direction: Opens UpVertex: <span><span>(−3,−16)</span><span>(-3,-16)</span></span>Focus: <span><span>(−3,−<span>634</span>)</span><span>(-3,-<span>634</span>)</span></span>Axis of Symmetry: <span><span>x=−3</span><span>x=-3</span></span>Directrix: <span>y=−<span><span>654
I sorta shortened the steps a bit if you need me to explain any more steps I will just ask.
I am sure you probably went over some of this in your class that is why I skipped a few steps so you would at least learn a little bit hehe.
I really hope this helps you.
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Answer:
be the second player, and always leave a multiple of 3 balloons
Step-by-step explanation:
In order to win, a player must force the other player to leave one or two balloons. To do that, the winning player must leave one more balloon than the maximum number that can be popped. That is, the winner will be the player who leaves 3 balloons,
Working backward, we find that the winner must leave a multiple of 3 after each turn. Since the starting number is a multiple of 3, the first player must lose if the second player plays optimally.
The winning strategy is ...
- be the second player
- always leave a multiple of 3 balloons.
The answer to that is 0.80 which is f because you convert the answer like you would do normal equations