<span> (x + 3) • (x - 12)
</span>
The first term is, <span> <span>x2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> -9x </span> its coefficient is <span> -9 </span>.
The last term, "the constant", is <span> -36 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • -36 = -36</span>
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is <span> -9 </span>.
<span><span> -36 + 1 = -35</span><span> -18 + 2 = -16</span><span> -12 + 3 = -9 That's it</span></span>
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and 3
<span>x2 - 12x</span> + 3x - 36
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-12)
Add up the last 2 terms, pulling out common factors :
3 • (x-12)
Step-5 : Add up the four terms of step 4 :
(x+3) • (x-12)
Which is the desired factorization
Final result :<span> (x + 3) • (x - 12)</span>
<span>v = 45 km/hr
u = 72 km/hr
Can't sketch the graph, but can describe it.
The Y-axis will be the distance. At the origin it will be 0, and at the highest point it will have the value of 120. The X-axis will be time in minutes. At the origin it will be 0 and at the rightmost point, it will be 160. The graph will consist of 3 line segments. They are
1. A segment from (0,0) to (80,60)
2. A segment from (80,60) to (110,60)
3. A segment from (110,60) to (160,120)
The motorist originally intended on driving for 2 2/3 hours to travel 120 km. So divide the distance by the time to get the original intended speed.
120 km / 8/3 = 120 km * 3/8 = 360/8 = 45 km/hr
After traveling for 80 minutes (half of the original time allowed), the motorist should be half of the way to the destination, or 120/2 = 60km. Let's verify that.
45 * 4/3 = 180/3 = 60 km.
So we have a good cross check that our initial speed was correct. v = 45 km/hr
Now having spent 30 minutes fixing the problem, out motorist now has 160-80-30 = 50 minutes available to travel 60 km. So let's divide the distance by time:
60 / 5/6 = 60 * 6/5 = 360/5 = 72 km/hr
So the 2nd leg of the trip was at a speed of 72 km/hr</span>
Answer:
4.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
4t + 11 = 19
Subtract 11 from both sides
4t = 19 - 11
4t = 8
Divide both sides by 4
t = 8/4
t = 2
