Find the area of the following figure and choose the appropriate result.

Find all the zeros of the function <br> g(x)=x^3-4x^2-x+22

vagabundo [1.1K]

Answer:

x = -2, x = 3 − i√8, and x = 3 + i√8

Step-by-step explanation:

g(x) = x³ − 4x² − x + 22

This is a cubic equation, so it must have either 1 or 3 real roots.

Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.

g(-1) = 18

g(1) = 18

g(-2) = 0

g(2) = 12

g(-11) = 1782

g(11) = 858

g(-22) = -12540

g(22) = 8712

We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.

g(x) = x³ − 4x² − 12x + 11x + 22

g(x) = x (x² − 4x − 12) + 11 (x + 2)

g(x) = x (x − 6) (x + 2) + 11 (x + 2)

g(x) = (x (x − 6) + 11) (x + 2)

g(x) = (x² − 6x + 11) (x + 2)

x² − 6x + 11 = 0

Quadratic formula:

x = [ 6 ± √(36 − 4(1)(11)) ] / 2

x = (6 ± 2i√8) / 2

x = 3 ± i√8

The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.

5 0

3 years ago

the distance around tims rectangulr book is 48 centimeters the length of each longer side is 14 cm what is the length of each sh

yanalaym [24]

let the length of each shorter side be x

length of longer side= x+14

2(x+14) + 2x = 48

2x + 28 + 2x = 48

4x + 28 = 48

4x = 48-28

4x = 20

x = 5

shorter side = 5cm

3 0

3 years ago

A simplified model of the human blood-type system has four blood types: A, B, AB, and O. There are two antigens, anti-A and anti

dexar [7]

Answer: Blood type will be A when event "A" happened and event "B" did not happen. Blood type will be B when event "A" did not happened and event "B" happened. Blood type will be AB when both events happened and blood type will be O when both events did not happen.

Step-by-step explanation:

S={AntiA reacts; AntiA does not react; AntiB reacts; AntiB does not react}

If AntiA reacts and AntiB reacts = AB (A∩B)

If AntiA does not react and AntiB does not react= O (A'∩B')

If AntiA reacts and AntiB does not react= A (A∩B')

If AntiA does not react and AntiB reacts= B (A'∩B)

4 0

3 years ago

Circle the value that is not equivalent to the other values<br> 4.07 4.070 4.70 4.0700

cricket20 [7]

Answer:

4.70

Step-by-step explanation:

it is bigger then the other numbers

6 0

3 years ago

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the popu

vitfil [10]

Answer:

a) The minimum head breadth that will fit the clientele = 4.105 inches to 3d.p = 4.1 inches to 1 d.p

b) The maximum head breadth that will fit the clientele = 8.905 inches to 3 d.p = 8.9 inches to 1 d.p

Step-by-step explanation:

This is normal distribution problem.

A normal distribution has all the data points symmetrically distributed around the mean in a bell shape.

For this question, mean = xbar = 6.1 inches

Standard deviation = σ = 1 inch

And we want to find the lowermost 2.3% and uppermost 2.3% of the data distribution.

The minimum head breadth that will fit the clientele has a z-score with probability of 2.3% = 0.023

Let that z-score be z'

That is, P(z ≤ z') = 0.023

Using the table to obtain the value of z'

z' = - 1.995

P(z ≤ - 1.995) = 0.023

But z-score is for any value, x, is that value minus the mean then divided by the standard deviation.

z' = (x - xbar)/σ

- 1.995 = (x - 6.1)/1

x = -1.995 + 6.1 = 4.105 inches

The maximum head breadth that will fit the clientele has a z-score with probability of 2.3% also = 0.023

Let that z-score be z''

That is, P(z ≥ z'') = 0.023

Using the table to obtain the value of z''

P(z ≥ z") = P(z ≤ -z")

- z'' = - 1.995

z" = 1.995

P(z ≥ 1.995) = 0.023

But z-score is for any value, x, is that value minus the mean then divided by the standard deviation.

z'' = (x - xbar)/σ

1.995 = (x - 6.1)/1

x = 1.995 + 6.1 = 8.905 inches

6 0

3 years ago