What should be added to (-5 a2b - 9 ab) to get a2b + 3 ab?
1 answer:
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Answer:
y=8(x+1)²-2
Step-by-step explanation:
Completing the square is a method of factorising. x²+bx+c=0 becomes x²+bx+(b)²-(
b)²+c=0. This then gets converted to make an equation of (x+
b)²+(-(
b)²+c)=0.
Vertex form is y=a(x-h)²+k.
8x²+16x+6=0 must first be divided by 8 to 8(x²+2x+)=0 (as there cannot be a coefficient for x²).
This will become 8(x²+2x+²-
²+
)=0.
From there, using the method above, we can convert it to 8[(x+1)²-1+]=0.
Solving this gets 8[(x+1)²-]=0.
With 8 as a, 1 as -h, and 8×- (-2) as k, we can input this into vertex format to get the result of y=8(x+1)²-2.
**This equation involves completing the square and vertex form, which you may wish to revise. I'm always happy to help!
Answer:
a) 0.0002 = 0.02% probability that all are silver.
b) 0.0033 = 0.33% probability that 5 are red and 2 are black
c) 0.0345 = 3.45% probability that 4 are red and the rest are silver
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the cars were selected is not important, so we use the combinations formula.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
(a) all are silver
Desired outcomes:
7 silver cars, from a set of 9. So
Total outcomes:
7 cars from a set of 8 + 9 + 5 = 22. So
Probability:
0.0002 = 0.02% probability that all are silver.
(b) 5 are red and 2 are black
Desired outcomes:
5 red, from a set of 8
2 black, from a set of 5
Total outcomes:
7 cars from a set of 8 + 9 + 5 = 22. So
Probability:
0.0033 = 0.33% probability that 5 are red and 2 are black
c) 4 are red and the rest are silver
Desired outcomes:
4 red, from a set of 8
3 silver, from a set of 9
Total outcomes:
7 cars from a set of 8 + 9 + 5 = 22. So
Probability:
0.0345 = 3.45% probability that 4 are red and the rest are silver