Cos (A-B) - cos (A+B)
= (cosAcosB +sinAsinB) - (cosAcosB - sinAsinB)
=2sinAsinB
Ans: 4
The average speed is given by:
average speed=(total distance)/(total time)
total time for the first 30 miles was:
time=distance/speed
=30/30
=1 hr
total time for the remaining 30 miles
=30/60
=0.5
hence the average speed will be:
speed=(30+30)/(1+0.5)=60/1.5=40 miles per hour
Answer: 11 party bags with 1 sticker leftover
Each bag contains 4 bubbles, 8 stickers, and 5 pencils.
<u>Step-by-step explanation:</u>
Find the GCF of 44 (bubbles), 89 (stickers), and 55 (pencils)
44: 2 x 2 x <u>11</u>
89: prime so choose 88 with 1 leftover
88: 2 x 2 x 2 x <u>11</u>
55: 5 x <u>11</u>
GCF = 11
Disregard the GCF to see how many of that item should go in each bag.
Bubbles: 2 x 2
Stickers: 2 x 2 x 2
Pencils: 5
You may notice that all of the terms have a common factor: 
. So, let's take the out of all the terms. This gives us:
Using the Zero Product Property, we can say that both 
and 
.
Let's solve both. is obvious, but we still need to solve our other term:
- Apply the Zero Product Property
Our answer is x = -6, 0, 4.
X=3 and y=-5/2. Here is why, when we do 7x+5x that gives us 12x. -2y+2y=0 and then we have 16 plus 20 which gives us 36. Now we gotta isolate x which right now we have 12x=36. Therefore divide by 12 to get x alone, which 36 divided by 12 is equal to 3. X=3. Plug it back into the equation, 7(3)=21 plus 2y=16. Subtract 21 from both sides 16-21 is equal to -5. Then 2y=-5 divide by 2 on both sides you will have -5/2=y or y=-5/2. Hope this helps!
