What is the least possible degree of a polynomial that has roots -5,1 + 4i, and -4i?
3
2
5
4​

Answers

Answer 1

Without any extra conditions, the answer could be 3, and the simplest polynomial with the given roots would be

(x + 5) (x - (1 + 4i )) (x + 4i )

= x ³ + 4x ² + (11 - 4i ) x + 80 - 2i

If the polynomial is supposed to have only real coefficients, then any complex roots must occur along with their complex conjugates:

(x + 5) (x - (1 + 4i )) (x - (1 - 4i )) (x + 4i ) (x - 4i )

= x ⁵ + 3x ⁴ + 23x ³ + 133x ² + 112x + 1360

and then the degree would be 5.


Related Questions

Find the inequality represented by the graph

I'm using khan academy btw

Answers

Answer:

Step-by-step explanation:

slope of line through (0,0) and (4,3) =(3-0)/(4-0)=3/4

eq. of line is y-0=3/4(x-0)

y=3/4 x

put x=4

y=2

2=3/4×4

2=3

which is true if 2<3

2<3

so y<3/4 x

the height of a tree is 170m the lower and upper bound of it's height is ​

Answers

9514 1404 393

Answer:

  [165, 175) meters

Step-by-step explanation:

The rule with respect to questions like this is that the bounds are ±1/2 of the place value of the least-significant digit. Here, the integer portion of the number has trailing zeros, and there is no decimal point or fractional part. Ordinarily, this combination of characteristics would signal that the trailing zeros are not significant, so the only significant digits are 1 and 7. The place value of the least significant digit is 10, so the bounds on the measurement are this number ±1/2(10) = ±5.

Of course, 175 rounds up to 180, so the upper bound is a limit, rather than an actual value. The height should be interpreted in this context as ...

  165 m ≤ height < 175 m

The lower and upper bounds are 165 m and 175 m, respectively.

_____

Additional comment

The best way to avoid any ambiguity as to whether trailing zeros are significant is to use scientific notation. If a zero in the ones place is significant, that is conventionally indicated by a decimal point: "170.". If scientific notation is used, the number would be reported as 1.70×10² to indicate the trailing zero is significant.

For reference, Earth's tallest tree is a redwood just under 116 meters high.

Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.

Answers

(4t - 8/5) - (3 - 4/3t) —> 16/3t - 23/5
5(2t+1) + (-7t+28) —> 3t + 33
(-9/2t + 3) + (7/4 + 33) —> -11/4t + 36
3(3t - 4) - (2t + 10) —> 7t - 22

What is the smallest three-digit odd numb
that can be made from 2, 8,5, 1, 3?

Answers

Answer: 101

Step-by-step explanation:

.

How many hours will it take to complete a 45-km bike ride if you go 12km per hour the whole time?

Answers

Answer:

3.75 hours

Step-by-step explanation:

d = rt

where d is the distance, r is the rate and t is the time

45 = 12 t

Divide each side by 12

45/12 = t

3.75 hours = t

A car is traveling 40 kilometers per hour. What is the speed of that car in meters per second?

Answers

Speed of car in km/h=40km/h

We have to convert it to m/s

[tex]\boxed{\sf 1km/h=\dfrac{5}{18}m/s}[/tex]

[tex]\\ \sf\longmapsto 40km/h[/tex]

[tex]\\ \sf\longmapsto 40\times \dfrac{5}{18}[/tex]

[tex]\\ \sf\longmapsto \dfrac{200}{18}[/tex]

[tex]\\ \sf\longmapsto 11.1m/s[/tex]

km/h > m/s

when converting km/h to m/s all you need to do is divide by 3.6

and vise versa when converting m/s to km/h multiply by 3.6

so therefore,

40km/h > m/s

= 40 / 3.6

= 11.11 m/s (4sf)

A community swimming pool is a rectangular prism that is 30 feet long, 12 feet wide, and 5 feet deep. The wading pool is half as long, half as deep, and the same width as the larger pool.

How many times greater is the volume of the swimming pool than the volume of the wading pool?

Answers

The correct answer is 1,350

Which of the answer choices has matrix multiplication defined?

Answers

Answer:

AB

Step-by-step explanation:

For the multiplication of two matrices to be defined then the number of columns of the first matrix must be equal to the number of rows of the second matrix. For example, 2*3 and 3*2 matrices can be multiplied since the number of columns of the first matrix must be equal to the number of rows of the second matrix.

Matrix A = 2*2

Matrix B = 2*3

Matrix C = 3*3

Matrix D = 1 * 3

From the matrices given, we can see that the matrices that can be multiplied together are AB and BC since the number of columns of the first matrix must be equal to the number of rows of the second matrix. Hence the correct option is AB

How do I solve |10-5| ?

Answers

Answer:

5

Step-by-step explanation:

Subtract  

5

from  

10

.

|

5

|

The absolute value is the distance between a number and zero. The distance between  

0

and  

5

is  

5

.

5

the answer is 5 you subtract

Which is a direct proportion

y = -4
y = 2x + 1
y = 6
y = 2/3x

Answers

Answer:

y=2x+1

Step-by-step explanation:

y is directly proportional to x if it increases as x increases

. Sipho's dad used 4/11 of the packet of oranges to make juice. The
next day he used another 4/11 of the packet of oranges.
a) How many elevenths has he used?​

Answers

Answer:

8 of the 11

Step-by-step explanation:

4+4=8 of the 11

Part of oranges usef from the orange packet used on 1st day = 4/11

Part of oranges used from the orange packet used on 2nd day = 4/11

Total part of oranges used from the orange packet

= (4/11) + (4/11)

= 8/11

So, Sipho's dad used 8 elevenths of the oranges.

What number should be added to -3/2 to get -5/8​

Answers

Answer: 7 / 8 should be added

Step-by-step explanation:

Let x be the number that should be added

Write the equation

-3/2 + x = -5/8

Add -3/2 on both sides

-3/2 + x + 3/2 = -5/8 + 3/2

x = -5/8 + 3/2

Change the denominator of 3/2 to 8 in order to do addition

x = -5/8 + 12 / 8

x = 7 / 8

Hope this helps!! :)

Please let me know if you have any questions

HELP PLEASE AND BE CORRECT

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Each point moves to 3 times its original distance from P.

  A is 2 up and 1 left of P, so A' will be 6 up and 3 left of P.

  B is 1 down and 2 left of P, so B' will be 3 down and 6 left of P.

  C is 2 right of P, so C' will be 6 right of P.

Please help me


(3 more coming soon so if you want points you can do those too when they come out

Answers

Answer:

The choose D. 15/16

Step-by-step explanation:

[tex] 1\frac{1}{4} \times \frac{3}{4} = \frac{15}{16} [/tex]

I hope I helped you^_^

Given the function f ( x ) = { 6 x − 4 x < 0 6 x − 8 x ≥ 0 Calculate the following values: f ( − 1 ) = f ( 0 ) = f ( 2 ) =

Answers

Answer:

[tex]f(-1) = -10[/tex]

[tex]f(0) =- 8[/tex]

[tex]f(2) = 4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 6x - 4[/tex] --- [tex]x < 0[/tex]

[tex]f(x) = 6x - 8<0[/tex] -- [tex]x \ge 0[/tex]

Solving (a); f(-1)

Here [tex]x= -1[/tex]

[tex]-1 < 0[/tex], so:

[tex]f(x) = 6x - 4[/tex]

[tex]f(-1) = 6 *-1 -4[/tex]

[tex]f(-1) = -10[/tex]

Solving (b); f(0)

Here [tex]x = 0[/tex]

[tex]0 \ge 0[/tex], so:

[tex]f(x) = 6x - 8[/tex]

[tex]f(0) = 6*0 - 8[/tex]

[tex]f(0) =- 8[/tex]

Solving (c) f(2)

Here [tex]x = 2[/tex]

[tex]2 \ge 0[/tex], so:

[tex]f(x) = 6x - 8[/tex]

[tex]f(2) = 6*2 - 8[/tex]

[tex]f(2) = 4[/tex]

200m^4+80m^3+8m^2=0

I got m = 0, -5 but I could be wrong

Answers

Answer:

m= 0, -0.2

Step-by-step explanation:

that's what I got when I did it

Answer:

m = 0m = -1/5m = -1/5

Step-by-step explanation:

200m^4 + 80m^3 + 8m^2 = 0

~Factor

8m²(5m + 1)(5m + 1) = 0

~Set everything to equal 0 and solve

8m² = 0 → m² = 0 → m = 0

5m + 1 = 0 → 5m = -1 → m = -1/5

5m + 1 = 0 → 5m = -1 → m = -1/5

Best of Luck!

1. Use the circle shown to answer each question a. Name the circle b. Identify a radius of the circle c. Identify a diameter of the circle d. Identify a different diameter of the circle. ​

Answers

i think the answe is sixteen

In a regression analysis involving 30 observations, the following estimated regression equation was obtained. If required enter negative values as negative numbers.
In a regression analysis involving 30 observations
Interpret b1, b2, b3, and b4 in this estimated regression equation (to 1 decimal). Assume that for each coefficient statement, the remaining three variables are held constant. Enter negative values as negative numbers.
b1 = estimated change in y per 1 unit change in x1
b2 = estimated change in y per 1 unit change in x2
b3 = estimated change in y per 1 unit change in x3
b4 = estimated change in y per 1 unit change in x4
Predict y when x1 = 10, x2 = 5, x3 = 1, and x4 = 2 (to 1 decimal).

Answers

In this, question the equation is missing that's why in the solution we define the equation and its complete solution:

Let the given equation:

[tex]\bold{\hat{h}=17.6+3.8x_1-2.3x_2+7.6x_3+2.7x_4}[/tex]

[tex]\bold{b1 = 3.8}[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_1}[/tex]

[tex]\bold{b2 = -2.3 }[/tex] units expect changes in the y for each 1 unit change in  [tex]\bold{x_2}[/tex]

[tex]\bold{b3 = 7.6 }[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_3}[/tex]

[tex]\bold{b4 = 2.7}[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_4}[/tex]

Calculating the estimated value of the y when:

[tex]\to \bold{x_1 = 10}\\\\ \to \bold{x_2 = 5}\\\\\to \bold{x_3 = 1}\\\\\to \bold{x_4 = 2}\\\\[/tex]

Put the value into the above-given equation:

[tex]\to \bold{17.6 + 3.8(10) - 2.3(5) + 7.6(1) + 2.7(2)} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{68.6-11.5}\\\\\to \bold{57.1}[/tex]

So, the final answer is "57.1".  

Learn more:

brainly.com/question/14127435

Please help! Identify which of the following is not equivalent to a1/4

Answers (images below)
no links please!

Answers

Answer: B

Step-by-step explanation:

A) [tex]a^\frac{3}{4}[/tex]÷[tex]a^\frac{1}{2}[/tex] cannot be the answer. When a to the power of x is divided by a to the power of y it is a to the power of x-y. Ex: [tex]a^x[/tex]÷[tex]a^y=a^x^-^y[/tex]

So 3/4-1/2 is 1/4 giving us [tex]a^{\frac{1}{4} }[/tex]

B is the answer because taking the square root of a is the same as [tex]a^\frac{1}{2}[/tex] which isn't the same as [tex]a^\frac{1}{4}[/tex]

C is not the answer because when a to the power of x is multiplied by a to the power of y it is a to the power of x+y. Ex:  [tex]a^x[/tex]·[tex]a^y[/tex]=[tex]a^{x+y}[/tex]

1/8+1/8=1/4 so it is [tex]a^\frac{1}{4}[/tex]

D can't be the answer. [tex]a^\frac{1}{8}[/tex] squared is the same as [tex]a^\frac{1}{8}[/tex]·[tex]a^\frac{1}{8}[/tex] so the same explanation of c applies to d

A recipe asks that the following three ingredients be mixed together as follows: add 1/2 of a cup of flour for every 1/2 of a teaspoon of baking soda, and every 1/4 of a teaspoon of salt.
Which of the following rates is a unit rate equivalent to the ratios shown above?

A. 2 teaspoons of salt per 1 cup of flour

B. 1/2 teaspoon of salt per 1 teaspoon of baking soda

C .2 teaspoons of salt per 1 teaspoon of baking soda

D. 1 teaspoon of baking soda per 2 teaspoons of salt

Answers

Answer:

all of the above

Step-by-step explanation:

the ratio between the flour, the baking soda, and the salt would = 1:1:2 (disregarding tsp or cup measurements, since all the units stay the same in the choices)

so really, all the answers are correct

hope this helps!

Answer:

B. 1/2 teaspoon of salt per 1 teaspoon of baking soda.

Step-by-step explanation:

The ratio of cups of flour to tsp. of baking soda to tsp. of salt shown above is:

1/2 : 1/2 : 1/4

An equivalent rate to the ratio of tsp. of salt to tsp. of baking soda is 1/2 : 1 because:

Ratio of tsp. of salt to tsp. of baking soda is:

1/4 : 1/2

If we were to find an equivalent rate to this, it would be 1/2 teaspoon of salt per 1 teaspoon of baking soda for:

Multiply 2 to both terms in the ratio 1/4 : 1/2:

1/4 x 2 = 1/2 (simplified)

1/2 x 2 = 1 (simplified)

The new ratio is 1/2 : 1, which also represents the rate 1/2 teaspoon of salt per 1 teaspoon of baking soda.

Hope this helps!

Please comment back if this was correct.

Please help to solve this.
Find sin5x,if sinx+cosx=1,4

Answers

Answer:

Hello,

Step-by-step explanation:

we must first remember that:

[tex]\boxed{sin(5x)=5sin(x)-20*sin^3(x)+16*sin^5(x)}\\\\[/tex]

Let say t=sin(x)

[tex]sin(x)+cos(x)=1.4\\\\t+\sqrt{1-t^2}=1.4\\\sqrt{1-t^2}=1.4-t\ we\ square\\1-t^2=1.4^2+t^2-2.8*t\\2t^2-2.8*t+0.96=0\\\Delta=2.8^2-4*2*0.96=0.16=0.4^2\\\\t=\dfrac{2.8-0.4}{4} =0.6\ or\ t=\dfrac{2.8+0.4}{4}=0.8\\\\t^3=0,216\ or\ t^3=0,512\\\\t^5=0,07776\ or\ t^5=0,32768\\\\\boxed{sin(5x)=5*0.6-20*0.216+16*0.07776=-0,07584}\\\\or\\\\\boxed{sin(5x)=5*0.8-20*0.512+16*0.32768=-0,99712}[/tex]

Three construction companies have bid for a job. Max knows that the two companies with which he is competing have probabilities 1/3 and 1/9, respectively, of getting the job. What is the probability that Max will get the job?

Answers

Answer:

0.5555 = 55.55% probability that Max will get the job.

Step-by-step explanation:

What is the probability that Max will get the job?

The sum of all probabilities is 100% = 1, so, considering Max's probability as x:

[tex]x + \frac{1}{3} + \frac{1}{9} = 1[/tex]

[tex]\frac{9x + 3 + 1}{9} = 1[/tex]

[tex]9x + 4 = 9[/tex]

[tex]9x = 5[/tex]

[tex]x = \frac{5}{9}[/tex]

[tex]x = 0.5555[/tex]

0.5555 = 55.55% probability that Max will get the job.

The max has probability of getting this job is x= 0.5555 and 55.55%

Suppose that ;

Max has probability of getting this job is = x

and other two companies have probability to get job is [tex]\frac{1}{3} or \frac{1}{9}[/tex].

Sum of the probability have bid a job is 100% which is equal to 1.

The sum of the probabilities in a probability distribution is always 1. A probability distribution is a collection of probabilities that defines the likelihood of observing all of the various outcomes of an event or experiment. Based on this definition, a probability distribution has two important properties that are always true:

According to given question ;

Sum of all the companies having probability to get the job = 1

[tex]x + \frac{1}{3} + \frac{1}{9} = 1[/tex]

[tex]\frac{9.x+1.3+1.1}{9} = 1\\9x+3+1 = 9.1\\9x+4 =9\\9x = 9-4\\9x = 5\\x = \frac{5}{9}[/tex]

x = 0.5555

The Max has probability of getting this job is x= 0.5555 or 55.55%

For the more information about probability click the link given below

https://brainly.com/question/14210034

What is the midpoint between A(-6,1) and B(0,2)?

Answers

Answer:

(-3, 3/2)

Step-by-step explanation:

To find the midpoint between two points you are going to add the X1 and X2, then divide by two. Then you are going to add the Y1 and Y2, and divide by two.

A(-6,1)       B(0,2)

= (-6+0, 1+2)

= (-6, 3)

=(-6/2, 3/2)

=(-3, 3/2)

Find the area of the triangle with the following measurements:

Answers

Answer:

56.25

Step-by-step explanation:

(9x12.5)÷2

just use a c calculator

Can any one solve this.Please

Answers

Answer:

True

Step-by-step explanation:

The first derivative tells you the slope of the graph at a specific point. If f'(c) =0, then that means that at f(c), the slope of the graph is 0. It is neither going up nor down

The second derivative tells you the slope of the slope of the graph. If f''(c) < 0, this means that the slope is decreasing. This means that going from the left to f(c), the slope is greater than the slope at f(c), and going from f(c) to the right, the slope is less than the slope at f(c).

Therefore, since the slope at f(c) is 0, the slope is positive to the left of f(c) and negative to the right of f(c). This means that the graph is going up until it hits f(c) and then goes down. Because f(c) is greater than the values to the left of it (because it is going up until it hits f(c)) and the values to the right of it (because it is going down past f(c)), f(c) is a local maximum

An amount of $700 was invested at 7% for 7 months what is the interest? Round your answer to your nearest cent.

Answers

Answer:

$343

step by step explanation: interest=PRT/100

:I=700×7×7/100

:I=$343.

Given:

Principal, P = $700

Rate of interest, R = 7% = 0.07

Time period, T = 7 months (it is considered as a monthly investment)

∴ Simple Interest, SI = PRT

SI = 700 × 0.07 × 7

SI = $343

What is straightforward interest and model?

Straightforward Simple Interest is the strategy for working out the premium sum for a specific chief measure of cash at some pace of revenue. For instance, when an individual takes credit of Rs. 5000, at a pace of 10 p.a. for a very long time, the individual's advantage for quite some time will be S.I. on the acquired cash.

Straightforward recipes generally start with an equivalent sign (=), trailed by constants that are numeric qualities and computation administrators like in addition to (+), short (- ), asterisk(*), or forward cut (/) signs.

Learn more about Simple Interest here

https://brainly.com/question/2294792

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5 times a certain number plus 2 times that number plus 2 is 16 what is the number​

Answers

let the number be x

ATQ

[tex]\\ \sf\longmapsto 5x+2x+2=16[/tex]

[tex]\\ \sf\longmapsto (5+2)x+2=16[/tex]

[tex]\\ \sf\longmapsto 7x+2=16[/tex]

[tex]\\ \sf\longmapsto 7x=16-2[/tex]

[tex]\\ \sf\longmapsto 7x=14[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{14}{7}[/tex]

[tex]\\ \sf\longmapsto x=2[/tex]

Answer:

The number is

2

Explanation:

Let

n

represent the number.

Translating the given statement into algebraic notation, we have

XXX

5

n

+

2

n

+

2

=

16

Therefore

XXX

7

n

+

2

=

16

XXX

7

n

=

14

XXX

n

=

2

answered by: Alan P.

look at the image for the question

Answers

9514 1404 393

Answer:

  246.6 in²

Step-by-step explanation:

The surface area is the sum of the base area and the areas of the four triangular faces. The relevant area formulas are ...

  A = s² . . . . . . area of a square of side length s

  A = 1/2bh . . . . area of a triangle with base b and height h

Then the surface area of this figure is ...

  A = (9 in)² + 4×(1/2)(9 in)(9.2 in) = 81 in² +165.6 in² = 246.6 in²

please help!! need answer will give brainliest

Answers

Answer:

k(3) is 7 and f(h(15)) is 43

Step-by-step explanation:

(a).

[tex]{ \sf{k(x) = h(x) + g(x)}} \\ { \sf{k(x) = (3 \sqrt{x + 1}) + ( - {x}^{2} + 3x + 1) }} \\ { \sf{k(x) = (3 \sqrt{3 + 1} ) + ( - {3}^{2} + 3(3) + 1) }} \\ { \sf{k(x) = 6 + 1}} \\ { \sf{k(x) = 7}}[/tex]

b).

[tex]{ \sf{f(h(x)) = 4(3 \sqrt{x + 1}) - 5 }} \\ { \sf{f(h(15)) = 4(3 \sqrt{15 + 1}) - 5 }} \\ { \sf{f(h(15)) = 4(3 \sqrt{16} ) - 5}} \\ { \sf{f(h(15)) = 48 - 5}} \\ { \sf{f(h(15)) = 43}}[/tex]

Subtract.
7x2-5x+3
-(2x2 + 7X - 4)

Answers

Answer:

5x^2-12x+7

Step-by-step explanation:

7x^2-5x+3-(2x^2 + 7X - 4)

Distribute the minus sign

7x^2-5x+3 - 2x^2 - 7X + 4

Combine like terms

5x^2-12x+7

Answer:

-12x + 17

Step-by-step explanation:

hope this helps!

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