<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:
The ratio of juices to ginger ale is 2 to 2
The ratio of orange juice to the cranberry juice is 1 to 1
Step-by-step explanation:
Ginger ale = 2 liters
Orange juice = 1 liter
Cranberry juice = 1 liter
Total ratio = 2 + 1 + 1 = 4
The ratio of ginger ale to the entire punch bowl is 1 to 4.
Ginger ale : entire punch bowl
= 2 : 4
= 1 : 2
Not true
The ratio of orange juice to ginger ale is 2 to 1.
Orange juice : ginger ale = 1 : 2
Not true
The ratio of juices to ginger ale is 2 to 2.
juices : ginger ale = orange juice + cranberry juice : ginger ale
= 1 + 1 : 2
= 2 : 2
True
The ratio of the entire punch bowl to the juices is 2 to 4.
Entire punch bowl : juices 4 : 2
Not true
The ratio of orange juice to the cranberry juice is 1 to 1.
Orange juice : cranberry juice = 1 : 1
True
To determine the total distance traveled by an object in constant speed, just multiply the speed by the time. So, for the car, the total distance traveled is,
distance by car = (20 m/s)(5s) = 100 m
For decelerating object, the distance traveled is,
distance = Vt - (at^2)/2
For the truck,
distance by truck = (20 m/s)(10s) - (2m/s^2)((10s)^2)/2 = 100 m
Relatively, both have traveled the same distance.
-1 C, that's the only logical answer I can think of. Or does it have to be in F?