So focusing on x^4 + 5x^2 - 36, we will be completing the square. Firstly, what two terms have a product of -36x^4 and a sum of 5x^2? That would be 9x^2 and -4x^2. Replace 5x^2 with 9x^2 - 4x^2: 
Next, factor x^4 + 9x^2 and -4x^2 - 36 separately. Make sure that they have the same quantity inside of the parentheses: 
Now you can rewrite this as 
, however this is not completely factored. With (x^2 - 4), we are using the difference of squares, which is 
. Applying that here, we have 
. x^4 + 5x^2 - 36 is completely factored.
Next, focusing now on 2x^2 + 9x - 5, we will also be completing the square. What two terms have a product of -10x^2 and a sum of 9x? That would be 10x and -x. Replace 9x with 10x - x: 
Next, factor 2x^2 + 10x and -x - 5 separately. Make sure that they have the same quantity on the inside: 
Now you can rewrite the equation as 
. 2x^2 + 9x - 5 is completely factored.
<h3><u>Putting it all together, your factored expression is
</u></h3>
Answer:
a=1.29 approx
Step-by-step explanation:
Answer:
170
Step-by-step explanation:
Equations derived from given info.
Use some substitution now.
- P=2(E+40)
- J=E+40
- P+J+E=300
Substitute first and second equation into third.
- 2(E+40)+E+40+E=300
- 2E+80+E+40+E=300
- 4E+120=300
- 4E=180
- E=45
Emily has 45 stickers. But we want to know what Peter has.
Use P=2(E+40)
Peter has 170 stickers.
Answer:
3x - 14 < 3x - 15
-14 < -15
never true
Step-by-step explanation:
Answer:
16 tricycles
12 bicycles
Step-by-step explanation:
If all were bicycles, there would be 28·2 = 56 wheels. Each additional wheel indicates the presence of a tricycle instead of a bicycle.
There are 72 -56 = 16 tricycles. The remaining 28-16 = 12 are bicycles.
