All categories

2 years ago

If a polynomial function f(x) has roots -8,1, and -6i , what must also be a root of f(x) ?

1 answer:

6 0

Heya !

In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.

Here , one complex root is given -6i hence , the other must be 6i.

Hope it helps you ! :)

You might be interested in

The volume v of a gas kept at constant temperature varies inversely with the pressure p. If the pressure is 24 pounds per square

daser333 [38]

Answer:

$V=12\ ft^{3}$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form $y*x=k$ or $y=k/x$

In this problem

$P*V=k$

step 1

Find the value of K

For $P=24\ psi ,V=15\ ft^{3}$

substitute

$24*15=k$

$k=360$

the equation is $P*V=360$

step 2

For $P=30\ psi ,V=\ ft^{3}$

substitute in the equation

$(30)*V=360$

$V=360/30=12\ ft^{3}$

5 0

3 years ago

High School Geometry!

astraxan [27]

Answer:

19.5

Step-by-step explanation:

I'm presuming the scale factor's 1.75/1

14*1.75=21.5

21.5-2=19.5

3 0

3 years ago

Suppose that you are asked if there would be a strong or weak correlation between the number of people shopping in malls and the

solong [7]

There could be a strong correlation between the proximity of the holiday season and the number of people who buy in the shopping centers.

It is known that when there are vacations people tend to frequent shopping centers more often than when they are busy with work or school.

Therefore, the proximity in the holiday season is related to the increase in the number of people who buy in the shopping centers.

This means that there is a strong correlation between both variables, since when one increases the other also does. This type of correlation is called positive. When, on the contrary, the increase of one variable causes the decrease of another variable, it is said that there is a negative correlation.

There are several coefficients that measure the degree of correlation (strong or weak), adapted to the nature of the data. The best known is the 'r' coefficient of Pearson correlation

A correlation is strong when the change in a variable x produces a significant change in a variable 'y'. In this case, the correlation coefficient r approaches | 1 |.

When the correlation between two variables is weak, the change of one causes a very slight and difficult to perceive change in the other variable. In this case, the correlation coefficient approaches zero

6 0

2 years ago

Read 2 more answers

For the school play,adult tickets cost $4 and children tickets cost $2. Natalie is working at the tickets counter just sold $20

Lisa [10]

Adult tickets = A
Children tickets = C

A×4. C×2

A×3. C×4

A×2. C×6

A×1. C×8

5 0

2 years ago

the graph shows the speed of a vehicle during the final 50 seconds of a journey at the start of the 50 seconds the speed is k me

Simora [160]

Answer:

a) 27 m/s

b) 30 m/s

c) i) 3

ii) Deceleration

Step-by-step explanation:

The question is not complete, the correct question is given as:

The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per second. The distance travelled during the 50 seconds is 1.35 kilometres.

(a) Work out the average speed of the vehicle during the 50 seconds

(b) Work out the value of k.

(ii) Describe what this gradient represents

Answer:

The graph is attached. The total time = 50 seconds, total distance = 1.35 km = 1350 m

a) The average speed is the ratio of the total distance traveled to the total time taken to cover this distance. The average speed is given by the formula:

$Average \ speed=\frac{total\ distance}{total\ time}\\ Substituting: \\ Average \ speed=\frac{1350\ m}{50\ s} = 27\ m/s$

b) From the graph, the total distance covered is the area of the graph. The graph is made up of a rectangle and triangle, the area of the graph is equal to the sum of area of rectangle and area of triangle.

$Total \ distance=Total\ area=Area\ of \ rectangle+Area\ of \ triangle\\Total \ distance=(length *breadth)+\frac{1}{2}base*height\\1350 \ m=(40*k)+0.5*10*k\\1350=40k+5k\\45k=1350\\k=1350/45\\k=30\ m/s$ c) i) The gradient in the last 10 seconds is the ratio of change in speed to change in time

$Gradient=\frac{change\ in\ speed }{change\ in\ time}=\frac{0-k}{50-40} \\ bt \ k=30\\Gradient=\frac{0-30}{50-40}= \frac{-30}{10} =-3$

ii) Since the gradient is negative it means it is deceleration. That is in the in the last 10 seconds the vehicle decelerates at a rate of 3 m/s²

6 0

3 years ago