<span><span>Solve <span>x5 + 3x4 – 23x3 – 51x2 + 94x + 120 </span></span>><span><span> 0</span>. </span></span><span>First, I factor to find the zeroes:<span><span>x5 + 3x4 – 23x3 – 51x2 + 94x + 120</span><span>= (x + 5)(x + 3)(x + 1)(x – 2)(x – 4) = 0</span></span><span>...so </span><span>x = –5, –3, –1, 2,</span><span> and </span>4<span> are the zeroes of this polynomial. (Review how to </span>solve polynomials, if you're not sure how to get this solution.)<span>To solve by the Test-Point Method, I would pick a sample point in each interval, the intervals being </span>(negative infinity, –5)<span>, </span>(–5, –3)<span>, </span>(–3, –1)<span>, </span>(–1, 2)<span>, </span>(2, 4)<span>, and </span>(4, positive infinity). As you can see, if your polynomial or rational function has many factors, the Test-Point Method can become quite time-consuming.<span>To solve by the Factor Method, I would solve each factor for its positivity: </span><span>x + 5 > 0</span><span> for </span><span>x > –5</span>;<span>x + 3 > 0</span><span> for </span><span>x > –3</span><span>; </span><span>x + 1 > 0</span><span> for </span><span>x > –1</span><span>; </span><span>x – 2 > 0</span><span> for </span><span>x > 2</span><span>; and </span><span>x – 4 > 0</span><span> for </span><span>x > 4</span>. Then I draw the grid:...and fill it in:...and solve:<span>Then the solution (remembering to include the endpoints, because this is an "or equal to" inequality) is the set of </span>x-values in the intervals<span> [–5, –3]<span>, </span>[–1, 2]<span>, and </span>[4, positive infinity]</span>. </span>
As you can see, if your polynomial or rational function has many factors, the Factor Method can be much faster.
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Answer:
36 cans
Step-by-step explanation:
6*6=36
Answer:
15
Step-by-step explanation:
Answer:
The y-intercept is (0, 13).
Step-by-step explanation:
First finf the equation of the line:
The slope = (25- 5) / (3 - -2)
= 20/5
= 4
So its equation is
y - 5 = 4(x + 2)
y = 4x + 13
The y-intercept occurs when x = 0
so y-intercept = 4(0) + 13.
It's (0, 13).
Answer:
I am 100% it's D
Step-by-step explanation:
