What are all the solutions to the equation 10x4 + 30x3 + 35x2 = 0? 0, StartFraction 3 + i StartRoot 5 EndRoot Over 2 EndFraction, StartFraction 3 minus i StartRoot 5 EndRoot Over 2 EndFraction. 0, StartFraction negative 3 + i StartRoot 5 EndRoot Over 2 EndFraction, StartFraction negative 3 minus i StartRoot 5 EndRoot Over 2 EndFraction. 0, 6 + 2 i StartRoot 5 EndRoot, 6 minus 2 i StartRoot 5 EndRoot. 0, negative 6 + 2 i StartRoot 5 EndRoot, negative 6 minus 2 i StartRoot 5 EndRoot.

Answers

Answer 1

The solutions to the equation 10x⁴ + 30x³ + 35x² as required in the task content are; 0, (-3 + i√5)/2, and (-3 - i√5)/2.

What are all the solutions to the equation 10x⁴ + 30x³ + 35x² = 0 as given in the task content?

It follows from the task content that the given equation is; 10x⁴ + 30x³ + 35x² = 0.

Hence, to find all the solutions of the equation, one must factorise the expression on the left hand side so as to obtain the factors as follows;

10x² (x² + 3x +3.5) = 0

Hence, we have;

10x² = 0; x = 0 OR

x² + 3x +3.5 = 0.

Hence, it follows from the quadratic formula that the roots/zeroes of x in the equation above can be evaluated as follows;

x = {-b±√(b²-4ac)}/2a

hence, by comparison, we have;

x = {-3±√(9-14)}/2

x = (-3 ± √-5)/2

x = (-3 ± i√5)/2

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Related Questions

The telephone company offers two billing plans for local calls. Plan 1 charges $21 per month for unlimited calls and Plan 2 charges $15 per month plus $0.06 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a.
a. Let x represent the number of monthly calls.

Answers

Answer:

Step-by-step explanation:

The number of monthly calls for which Plan 1 is more economical than Plan 2 is 200 calls

If more than 200 calls are made, the plan 1 charge will be more than plan 2.

Let the number of charges per month be x

If plan 2 charges ​$16 per month plus ​$0.04 per call, this is expressed as 0.04x + 16

Price that pan 1 charges = $24

If Plan 1 is more economical than Plan 2, this is expressed as:

0.04x + 16 > 24

Subtract 16 from both sides:

0.04x + 16 - 16 > 24 - 16

0.04x > 8

x = 6/0.04

x = 200

This shows that if more than 200 calls are made, the plan 1 charge will be more than plan 2.

100 points!!! Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Multiply or divide as indicated.
x^10/x^4

Answers

Answer:

[tex]x^{6}[/tex]

Step-by-step explanation:

To simply exponents in a fraction, subtract the exponent for each variable in the denominator from the exponent in the numerator.

Answer:

[tex]x^6[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{x^{10}}{x^4}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{x^{10}}{x^4}=x^{(10-4)}=x^6[/tex]

Urgent (I added 35 points)
The diagram below is drawn on a one-centimetre square grid


Work out the area of the shaded triangle:

Answers

Answer:

rr

Step-by-step explanation:

xd

ddddd

given the data in the table below, determine the value of a and b in the model y = a +bx and hence find the value of y when x = 12

X 2 3 4 5 6 8
Y 5 6 8 9 10 12​

Answers

The equation that models the data will be y = 3 + x and for x = 12, y will be 15.

We are given the equation:

y = a + b x

Also, we have some points of the equation as:

X         2         3         4         5         6           8

Y         5         6         8         9         10         12​

For the point ( 2 , 5 ), we have the equation as:

5 = a + b ( 2 )

5 = a + 2 b

a = 5 - 2 b   …(1)

For the point (3 , 6), we have the equation as:

6 = a + b (3)

6 = a + 3 b

a = 6 - 3 b   …(2)

From (1) and (2), we get that:

5 - 2 b = 6 - 3 b

3 b - 2 b = 6 - 5

b = 1

a = 5 - 2

a = 3

So, the equation will become:

y = 3  +  x

For x = 12, we get the value of y as:

y = 3 + 12

y = 15

Therefore, we get that, the equation that models the data will be y = 3 + x and for x = 12, y will be 15.

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There are 5 one-digit numbers in a set of data. The mean is 3, the mode is 1, and the median is 4. What are the numbers in the set of data?

Answers

11445

Not sure what else it could be

You are to move from A to B, always moving
right or down along the lines. On how many
different paths can you go? [The number of paths
from A to various intersections has been included.

Answers

Answer:

  70

Step-by-step explanation:

You want the number of paths from corner to corner on a 5×5 grid with no backtracking.

Pascal's triangle

The geometry of the problem matches that of Pascal's triangle, attached.

In the attached figure, the value at each node is the sum of the values above and to the left. This matches the counting process for paths that can be used to get to any particular point on the grid: the total number of ways to get there is the sum of the ways it can be approached from above and the ways it can be approached from the left.

The given grid has some numbers filled in. If we continue to assign values to nodes that are the sum of the values above and to the left, we find the node values match the upper left 5×5 array of values in the attachment.

The value at the lower right corner of that array is 70. That is, ...

there are 70 ways to get from A to B.

__

Alternate solution

The path taken will always have 8 steps. Of those, 4 must be to the right, and 4 must be down. The number of ways we can choose 4 of those 8 steps to be steps to the right is "8 choose 4" ...

  C(8,4) = 8!/(4!(8-4)!) = (8·7·6·5)/(4·3·2·1) = 70

Of course, using Pascal's triangle is simply another way to find the value of C(n,k).

Write a one-variable equation or inequality with variables on both sides to describe the problem situation. Complete Steps 1 - 3 in order.

Two drones are descending from the sky in vertical lines. A black drone is currently at an altitude of 1,170 feet and is dropping at a rate of 64 feet per minute. A white drone is at an altitude of 966 feet and is dropping at a rate of 52 feet per minute. How many minutes will it take for the two drones be at the same altitude? Use the variable `n` to represent the unknown quantity.

Answers

The number of minutes that it will take for the two drones be at the same altitude is 17 minutes.

How to illustrate the information?

It should be noted that ablack drone is currently at an altitude of 1,170 feet and is dropping at a rate of 64 feet per minute. The expression will be:

1170 - 64m

The white drone is at an altitude of 966 feet and is dropping at a rate of 52 feet per minute. This will be 966 - 52m where m = number of minute

Therefore, we will equate both equations. This will be:

1170 - 64m = 966 - 52m

Collect like terms

-64m + 52m = 966 - 1170

12m = 204

Divide

m = 204 / 12

m = 17

Therefore, the number of minutes that it will take for the two drones be at the same altitude is 17 minutes.

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If the sum of a number and three is ​tripled the result is one less than twice the number. Find the number.

Answers

The number in the equation is -10.

Given,

The sum of a number and three is ​tripled the result is one less than twice the number.

We can take the number as x.

Then,

3(x + 3) = (2x - 1)

Equate the above equation and find x.

3x + 9 = 2x - 1

Add -2x to both sides:

That is,

3x - 2x + 9 = 2x - 2x - 1

x + 9 = -1

Add -9 to both sides:

We get,

x + 9 - 9 = -1 - 9

x = -10.

That is, the number in the equation is -10.

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The composite bar chart Messages received shows the number of messages Tim received each day for five days.
a) How many texts did Tim receive on Monday?
b) How many emails did Tim receive on Thursday?
c) In total, what fraction of the messages were emails?
Give your answer in its simplest form.

Answers

We need to know about a composite bar chart to solve the question. The answer for (a) is Tim received 8 texts on Monday, (b) Tim received 4 emails on Thursday and (c) 0.52 of the messages were emails.

A composite bar chart is used when there are two sets of data that are connected and their frequencies are combined.In this question there are two sets of data emails and texts but both of them belong to the same category which is messages. For question (a) we can easily say from the diagram that the number of texts Tim received on Monday is 8.

For question (b) we need to find out the number of emails Tim received on Thursday, for this we have to look at the bar for Thursday and subtract the number of texts received from total number of messages to get the number of emails received that means, 15-11=4, so Tim received 4 emails on Thursday.

For question (c) we need to find the total number of messages received by Tim for five days, total number of emails received and then calculate the fraction of emails out of messages.

Total number of messages=14+16+14+15+14=73

Total number of emails=6+10+10+4+8=38

Fraction of emails over messages=[tex]\frac{38}{73}[/tex]=0.52

Thus 0.52 of the messages were emails.

We analysed the composite bar chart to find out the answers of the three questions, Tim received 8 texts on Monday,4 emails on Thursday and 0.52 of the messages were emails.

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Answer:

a= 5

b= 7

c=

Step-by-step explanation:

Use mental math strategies to solve the equation.

3,500 +
Choose...
= 3,500

Part B

Which property of addition does the equation show?

A.
Associative Property of Addition

B.
Commutative Property of Addition

C.
Distributive Property of Addition

D.
Identity Property of Addition

Answers

A the associative property of addition

Answer:

the answer would be A

Graph the following line
X=0

Answers

Answer:

the line runs that aligns with the y-intercept

Step-by-step explanation:

what is eight times the square a number z minus three in mathematical translate?​

Answers

Answer:

8*z^2-3

Step-by-step explanation:

Given m n, find the value of x.

Answers

x=32 because m||n
if two lines are parallel then the corresponding angles are same

The value of x from the given parallel lines, using corresponding angles concept, we get 32°.

Given that, straight line m parallel to straight line n and t is the transversal.

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

Here, x°=32°

Therefore, the value of x from the given parallel lines is 32°.

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Simplify the following expression:
3[(x³ -7x+1)-(x+4)]

Answers


It is most likely 3x^3 - 24x - 9

(^3 is to the third power btw)

Sorry my handwriting is super bad lolll

that’s a vague explanation but it might help just to write it down :)

The governor of state A earns $47,535 more than the governor of state B. If the total of their salaries is $299,115, find the salaries of each.

Answers

$299,115 - $47,535 = $251,580

$251,580/2 = $125,790

State A = $173,325
State B = $125,790

In Exercises 11 and 12, find m/1, m/2, and m/3.
Explain your reasoning.

Answers

Answer:

11

m/1= 100, m/2 = 80, m/3 = 100

12

m/1 = 47, m/2= 133, m/3=47

Step-by-step explanation:

Number 11 uses Cointerior angle rule

Number 12 uses Cointerior angle rule and Corresponding angle rules

Which expression represents 7/21

Answers

Answer:
Simplified is 1/3 but the number is 0.3 recurring

Write an algebraic expression for the verbal description.

The discount d is 40% of the list price L.

Answers

Answer:

D = 0.4(L)

Step-by-step explanation:

D = 0.4(L)

Answer: 0.4L=d  

Step-by-step explanation:

40%=0.4

0.4L=d    ==> 40% of L, the listed price, is d, the discount.

Write a function g whose graph represents the
indicated transformation of the graph of f.
f(x)=2x-9; translation 6 units up
The translated function is g(x) =

Answers

Answer: g(x)=2x-3

Step-by-step explanation:

f(x)=2x-9

g(x)=2x-9+6 ==> Translate 6 units up

g(x)=2x-3

Kelly works four hours a day on tickets and solves on average 38 tickets per day. Brian works five hours per day and solves 45 tickets per hour. Marvin works six hours a day on tickets and solves on average 59 tickets per day. Linda works five and a half hours a day on tickets and solves 53 tickets per day. Who solves the most tickets per hour?

Answers

Answer:

Marvin

Step-by-step explanation:

Kelly works four hours a day on tickets and solves on average 38 tickets per day.

38 tickets / 4 hours = 9.5 tickers per hour

_____________________

Brian works five hours per day and solves 45 tickets per hour.

45 tickets / 5 hours = 9 tickers per hour

_____________________________

Marvin works six hours a day on tickets and solves on average 59 tickets per day.

59 tickets / 6 hours = 9.83333 tickers per hour

______________________

Linda works five and a half hours a day on tickets and solves 53 tickets per day.

53 tickets / 5.5 hours = 9.6363637 tickers per hour

Who solves the most tickets per hour? Marvin at 9.833 tickets an hour

10. f(3)=2x-5 Evaluate the function.
Answer should be written: f(3)=?
Type a response
2/1

Answers

The evaluation of function will give the result f(3) = 1

To find the value of function given in question, we will simply keep the desired value in place of variable x.

Rewriting the equation

f(3) = 2x - 5

Keep the value of x in equation, as given in question

f(3) = 2×3 - 5

Performing multiplication to find the value of x in equation given in question

f(3) = 6 - 5

Performing subtraction to find the value of x in equation given in question

f(3) = 1

Therefore, the result of evaluation of given function is f(3) = 1.

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I don't have many points but I will make brainliest, thank you !!

Answers

Answer: The answer for question 48. is -9, The answer for question 49. is 1/2, the answer for question 50. is -2.25, and for question 51 it's 4/5

Step-by-step explanation:

How to solve question 48

1/2(-12-6)-3(5-3)

-6+3-15+9

-3-6

-9

How to solve question 49

(20/2)+10/(-10+20+30)

10+10/40

20/40

1/2

How to solve question 50.

3/4(-15+4)+(8+7)/(-3)

-45/4+3+15/-3

-11.25+3+15/-3

6.75/-3

-2.25

How to solve question 51

5(7)-(3+4)/-2^2-2^2+3^2

35-7/4+4+27

28/35

4/5

Hope this helped owo

Bryan, Michael, and Han are painting a house. Working together, they can paint the house in 6 hr. Working alone, Bryan can paint a similar sized house in 15 hr and Han can paint a similar sized house in 18 hr. How many hours would it take Michael to paint a similar sized house working alone? Enter the answer to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

11x+90=15x

The computation shows that Michael will take 22.5 hours to paint a similar sized house working

How to compute the value?

Based on the information given, the appropriate equation to use will be:

= 1/15 + 1/18 + 1/Michael = 1/6

Add the two fractions on the left

11/90 + 1/Michael = 1/6

1/Michael = 1/6 - 11/90

Take the reciprocal

Michael = 45/2

Michael= 22.5

Michael will take 22.5 hours.

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You need to make 12 servings of fried fish. Each serving takes 7.5 ounces of flour. How many ounces of flour do you need?

Answers

You need 900 ounces of flour.
7.5 x 12 = 900.
1 serving = 7.5 ounces of flour
7.5x12 is 90
the answer is 90

Date
11. Write the fraction below as a decimal rounded
to the nearest hundredth.
25
7

Answers

Answer:

3.57

Step-by-step explanation:

25/7 is the same as 25÷7 which is 3.57

On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 1, negative 11), and goes through (1, 0).
What is the range of the function f(x) = 3x2 + 6x – 8?

{y|y ≥ –1}
{y|y ≤ –1}
{y|y ≥ –11}
{y|y ≤ –11}
TIME REMAINING
22:14
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 2, negative 16), has a y-intercept at (0, negative 12), and goes through (2, 0).

What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12?

(–6, 0), (2,0)
(–2, –16), (0, –12)
(–6, 0), (–2, –16), (2, 0)
(0, –12), (–6, 0), (2, 0)

Answers

1) (c) The range of the function f(x) = 3x² + 6x - 8 is {y|y ≥ –11}.

2) (d) The x-intercepts of the graph of the function f(x) = x² + 4x - 12 are ( - 6, 0) and ( 2, 0 ).

1). A parabola opens upward and it passes through ( - 3, 0) and ( 1, 0), and has vertex at ( - 1, - 11 ).

We have the function for the parabola f(x) = 3x² + 6x - 8.

Vertex and the coefficient of the quadratic term are two features of a parabola that aid in determining its range.

Therefore, the critique point of the range and a portion of the constraint is the vertex's vertical coordinate. The next step is to determine if the parabola is concave up or down. The parabola is concave up in this issue if the coefficient of the quadratic terms is positive. As a result of the parabola's concave upward shape, all real numbers greater than - 11 fall into the function's permissible range.

Hence, the range of the function is {y|y ≥ –11}.

2). The graph of the function with the equation f(x) = x² + 4x - 12 is a parabola that opens upward, passes between the points ( - 6, 0) and ( 2, 0), and its vertex is at ( - 6, 0). ( - 2, - 16). It is the y-intercept ( 0, - 12).

The x-intercepts are the locations where the graph and x-axis meet. The y-coordinate of these points is always zero. A parabola can only have two x-intercepts at most. As we can see, the parabola passes through the points ( - 6, 0) and ( 2, 0), and have y coordinates 0, hence the x-intercepts are ( - 6, 0) and ( 2, 0).

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The complete question is mentioned below:

1. On a coordinate plane, a parabola opens up. It goes through (negative 3, 0), has a vertex at (negative 1, negative 11), and goes through (1, 0).

What is the range of the function f(x) = 3x² + 6x – 8?

(a) {y|y ≥ –1}

(b) {y|y ≤ –1}

(c) {y|y ≥ –11}

(d) {y|y ≤ –11}

2. On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 2, negative 16), has a y-intercept at (0, negative 12), and goes through (2, 0).

What are the x-intercepts of the graph of the function f(x) = x² + 4x – 12?

(a) (-6, 0), (2,0)

(b) (-2, -16), (0, -12)

(c) (- 6, 0), ( - 2, - 16),

(d) ( 2, 0) (0, -12),

(e) ( - 6, 0), (2, 0)

|4y - 10| = 20 for all values of y in simplest form.

Answers

Answer: -5/2

Step-by-step explanation:

4y−10∣=20

Combine like terms and use the properties of equality to get the variable on one side of the equal sign and the numbers on the other side. ∣4y−10∣=20 Use the definition of absolute value.

4y−10=20

4y−10=−20

Add 10 to both sides of the equation. 4y=30 which then equals  4y=−10

Divide both sides by 4 to get y = 15 over 2 converted to y = negative 5 over 2

(hope this is helpful)

39,004 in expanded form

Answers

30,000 9,000 4 this it the answer to your question

help plsssssssssssssssssssssssssssss

Answers

Answer:

8.3x10^1

Step-by-step explanation:

you don't even need to do any math for this question. just look for the number between 1 and 10

Select all the equations that have the same as 3x - 12 = 24

Answers

The equations that have the same solution as 3x - 12 = 24 include:

a. 15x - 60 = 120C. 3x = 36d. x - 4 = 8

Given data

3x - 12 = 24

How to find the solution of the given expression

3x - 12 = 24

3x = 24 + 12

3x = 36

x = 36 / 3

x = 12

substituting the value of x in the equations to get to check if the value is same for the given question

a. 15x - 60 = 120

15 * 12 - 60 = 120

180 - 60 = 120

120 = 120 correct

b. 3x=12

3 * 12 = 12

36 ≠ 12 incorrect

C. 3x = 36

3 * 12 = 36

36 = 36 correct

d. x - 4=  8

12 - 4 = 8

8 = 8 correct

e. 12x - 12 = 24

12 * 12 - 12 = 24

144 - 12 = 24

132 ≠ 24 incorrect

Hence we can say that the equations that have same solution as the given equation are options A, C, and D

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complete question

The complete question is attached

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