Answer:
8
Step-by-step explanation:
Step-1 : Multiply the coefficient of the first term by the constant 1 • -16 = -16
Step-2 : Find two factors of -16 whose sum equals the coefficient of the middle term, which is 6 .
-16 + 1 = -15
-8 + 2 = -6
-4 + 4 = 0
-2 + 8 = 6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 8
p2 - 2p + 8p - 16
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (p-2)
Add up the last 2 terms, pulling out common factors :
8 • (p-2)
Step-5 : Add up the four terms of step 4 :
(p+8) • (p-2)
Which is the desired factorization
<em>Answer:</em>
Complete proof is written below.
Facts and explanation about the segments shown in question :
- As BC = EF is a given statement in the question
- AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
- AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
- AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.
Below is the complete proof of the observation given in the question:
<em />
<em>STATEMENT REASON </em>
___________________________________________________
1. BC = EF 1. Given
2. AB + BC = AC 2. Betweenness
3. AC > BC 3. Def. of segment inequality
4. AC > EF 4. Def. of congruent segments
<em />
<em>Keywords: statement, length, reason, proof</em>
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Answer:
A) R = 1900 -24t
B) 1684 billion barrels
C) 79.17 years
Step-by-step explanation:
<h3>A)</h3>
Reserves start at 1900 billion barrels and decrease by 24 billion barrels each year. The value for t=0 is 1900; the value for t=1 is 24 less.
R = 1900 -24t
__
<h3>B)</h3>
For t=9, the reserves will be ...
R = 1900 -24(9) = 1900 -216 = 1684 . . . . billion barrels
__
<h3>C)</h3>
The reserve will be 0 when ...
0 = 1900 -24t
24t = 1900 . . . . . add 24t
t ≈ 79.17 . . . . divide by 24
Reserves will be gone in about 79.17 years.
Answer:
1) A
2) A
3) B
4) D
5)A
6) D
7) A
8) C
9) D
Step-by-step explanation:
1) -5 (-2) -6= 4
2) 3 coins plus c coins = 3 + c
3) x-2 =16, x = 18
4) 
=-5. Clearing, z = 60
5) x =13,4
6) 14=t-4. Clearing t = 58
7) -30=j+50, clearing j=80
8) 2.8x=-9.24, clearing x=-3-3
9) 5.8= 
. Clearing z=12.76
