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lisabon 2012 [21]
3 years ago
10

5. & 7. simplify 9. & 11. factor completely

Mathematics
1 answer:
snow_tiger [21]3 years ago
5 0
5)

= - i - 2 - 3i
= - 4i - 2
= - 2 (2i + 1)

7)

= - 4 [(2 -2i - i (8 - 4i)]
= - 4 (2 - 2i - 8i + 4i^2)
= - 4 (4i^2 - 10i + 2)
= (- 4) (2) (2i^2 - 5i + 1)
= - 8 (2i^2 - 5i + 1)

9)

= p^2 - 4p - 4p + 16
= p (p - 4) - 4 (p - 4)
= (p - 4) (p - 4)
= (p - 4) ^2

11)

= p^2 - 8p - 8p + 64
= b (b - 8) - 8 (b - 8)
= (b - 8) (b - 8)
= (b - 8)^2
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2 years ago
Using the digits 1 to 9 at most one time each, fill in the boxes to find the largest (or smallest) possible values for x.
Mice21 [21]

Answer:

smallest: 8x -3 = 4; 1y +9 = 2. total = -49/8

 largest: 1x -9 = 8; 2y +3 = 7. total = 19

Step-by-step explanation:

If we use variables to represent the box contents, we can write ...

ax -b = c

dy +e = f

Then the values of x and y are ...

 x = (c +b)/a

 y = (f -e)/d

For positive integer values of the variables, x will always be positive, and y may or may not be negative.

Smallest sum

For the sum to be the smallest, we must have x be as small as possible and the ratio (f-e)/d be as negative as possible.

x will be small for large 'a' and for (c+b) small. For y to be as negative as possible, we want 'd' and 'f' small and 'e' large. Best results are obtained for

8x -3 = 4   ⇒   x = 7/8

1y +9 = 2   ⇒   y = -7

For these coefficients, the sum is -6 1/8 = -49/8.

(note that the values of 'b' and 'c' can be swapped with no net effect)

Largest sum

For the sum to be the largest, we must have x as large as possible: (b+c) large and 'a' small. At the same time we must have y be positive and as large as possible: (f-e) positive and large, 'd' small. Best results are obtained for

1x -9 = 8  ⇒   x = 17

2y +3 = 7   ⇒   y = 2

For these coefficients, the sum is 19. Again, 'b' and 'c' can be swapped with no effect.

_____

Additional comment

These extreme values are verified by examination of the 60,480 possible permutations of the coefficients.

8 0
3 years ago
1. Supposed that a population consists of the values 1.2.3.4.5.6.7.8, 9, and 10. Construct
irina [24]

Answer:

B

Step-by-step explanation:

Just pick B bro it isn't even that hard lol

8 0
3 years ago
2350 million in standard form
topjm [15]

Answer:

in this problem we have

2,350 million

Remember that

1 million=1,000,000

so

2,350 million=2,350*1,000,000=2,350,000,000

convert to standard form

2,350,000,000=2.35*10^{9}

therefore

the answer is

2.35*10^{9}

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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