3.1x^3-2.4x² +6x – 3 = 4x² + 3x +2


solving problem​

Answers

Answer 1

Answer:

The roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Step-by-step explanation:

The given equation is 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2

Which gives;

3.1·x³ - 2.4·x²+ 6·x - 3 - 4·x² - 3·x - 2 = 0

3.1·x³ - 6.4·x²+ 3·x  - 5 = 0

Factorizing online, we get;

3.1·x³ - 6.4·x²+ 6·x + 3·x - 5 = 3.1·(x - 1.986)·(x² - 0.0784·x + 0.812) = 0

Therefore, the possible solutions are;

x - 1.986= 0 or x² - 0.0784·x + 0.812 = 0

The roots of the equation are x² - 0.0784·x + 0.812 = 0 are;

x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Therefore, the roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2,  are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i.


Related Questions

how many are 4 raised to 4 ???​

Answers

Answer:

256

Step-by-step explanation:

The expression 4 raised to 4 can be written in mathematical term as [tex]4^4[/tex] and this means the value of 4 in four places as shown;

[tex]4^4\\\\= 4 * 4* 4* 4\\\\= (4 * 4)* (4* 4)\\\\= 16*16\\\\= 256\\\\[/tex]

Hence the expression 4 raised to 4 is equivalent to 256

please help me solve

Answers

Answer:

18 square centimeters

Step-by-step explanation:

Notice that if e is the midpoint of the side CB, and angle [tex]\angle x = 45^o[/tex], then this rectangle is in fact two squares of side 3 cm put together. therefore, side CD has a length of 6 cm, and as a result, the area of the figure is given by the product base times height = 6 x 3 = 18 [tex]cm^2[/tex]

Answer:

(B)  18

Step-by-step explanation:

The angle x is 45 degrees.  Since it is bisecting a 90 degree angle, the angle on the other side is 45 degrees.

90 - 45 = 45

Since AB is 3, DC is 3.  Since the right triangle DC is 45-90-45, the other side, CE, will also be 3.  Since CE is half of the side of the rectangle, multiply it by 2 to get 6.  The sides of the rectangle are 3 and 6.  Use the formula for area of a rectangle to solve.

A = lw

A = (6)(3)

A = 18

The answer is B.

Two fractions equivalent to 1/3

Answers

Answer:

2/6 or 3/9

Step-by-step explanation:

1/3 x 2 = 2/6

1/3 x 3 = 3/9

Answer:

2/6 3/9

Step-by-step explanation:

to find equivalent fractions you can just multiply, or count by the denominator for example, 3 , 6 , 9 and so on and then with the numerator you count how much you went like, if you went to sixths than it was 2 because you skip counted.

Can someone PLEASE help with this question? thank you

Answers

Answer:

C) 1

Step-by-step explanation:

First half:

Invert and multiply

x²/y²*y³/x²=x²y³/y²x³=y/x

Second half:

Invert and multiply

1/y*x/1=x/y

Combine

y/x*x/y=xy/xy=1

Part C Now try this one. Write a description of the partitioned function using known function types, including transformations.

Answers

Answer:

Following are the function description to the given question:

Step-by-step explanation:

In the given-question, three functions are used, that can be defined as follows:  

In function 1:

This function is also known as the modulus on the absolute value function, for example:

[tex]f(x)=| x| \left \{ {{x , \ \ \ x>0} \atop {-x, \ \ \ \x<0 }} \right.[/tex]

In the given in the above graph, that is [tex]f(x) = -x , \ \ x<0[/tex]

In function 2:

In this function, It is an algebraic function that is [tex]y=x^2[/tex]

It is also a part of the quadratic polynomial function, and its value is [tex]y=x^2 , \ \ \ x> 0[/tex]  

In function 3:

In this function, it is the cubic polynomial equation that's value is [tex]y=x^3[/tex]

In the graph its value is:

[tex]y=-x^3\\\\and \\ \\\to y= f(x) \\\\ \to y=-f(x)\\[/tex]

Can someone help me find the amount on year 11

Answers

Answer:

525 dollars

Step-by-step explanation:

simple interest yearly ( year 11 does not count because the question asking at the amount at the  beginning of year 11)

interest=300*0.075*10= 225

the amount in the account : 300+225=525 dollars

Possible Points: 100 One January day, the low temperature in Fargo, ND was -8 degrees. Over a period of six hours, the temperature rose 4 degrees per hour. After si hours, what was the temperature?

Answers

29 personal briefing on my p

Find the surface area and volume of cone. A = rs + r2 V = 1/3r2 h A cone's slant height (s) is 15 cm and its radius is 8 cm. Surface area (to the nearest tenth) = cm2 Volume (to the nearest tenth) = cm3

Answers

Answer:

a) 483.6cm²b) 850.1 cm³

Step-by-step explanation:

Given the slant height 's' and its radius 'r' to be 15cm and 8cm respectively.

the total surface of the cone A = πrs+πr² and the volume is expressed as

V = 1/3πr²h

For the surface area of the cone;

Given parameters

radius = 8 cm and slant height s = 15 cm

Total surface area A = π(8)(15) + π(8)²

A = 90π+64π

A = 154π

If π = 3.14

A = 154(3.14)

A = 483.56cm²

A = 483.6cm²

Hence the total surface area of the cone to the nearest tenth is 483.6cm²

For the volume of the cone;

V = 1/3πr²h

Using pythagoras theorem to get the height of the cone;

l² = h²+r²

h² = l²-r²

h² = 15²-8²

h² = 225-64

h² = 161

h = √161

h = 12.69cm

V = 1/3π* (8)² * 12.69

V =  1/3π* 64 * 12.69

V =  1/3*3.14* 64 * 12.69

V = 2550.1824/3

V = 850.06 cm³

V = 850.1 cm³

Hence, the volume of the cone is  850.1 cm³ to the nearest tenth.

A can do a piece of work in 10 days and B in 12 days.
With the help of C they can finish the work in 4 days. How
long will C take to do it alone?
a) 12 days b) 15 days c) 18 days d) 20 days​

Answers

Answer:

B. 15 days

Step-by-step explanation:

A=10=1/10 of the job

B=12=1/12 of the job

A+B+C=4=1/4 of the job

A+B

=1/10 + 1/12

=10+12/120

=22/120

=11/60

(A+B+C) - (A+B)

=1/4 - 11/60

=5 - 11/60

=4/60

=1/15

It would take C alone 15 days to finish the job

The graph of y=3x^2-3x-1 is shown. Use the graph to find estimates for the solutions of i)3x^2-3x+2=2 ii) 3x^2-3x-1=x+1

Answers

Intersection point of graph of function is known as solution of the function.

Graph is attached below, in which solution is shown.

1. Here, given that  [tex]3x^2-3x+2=2[/tex]

It can be written as,   [tex]y=3x^2-3x+2\\\\y=2[/tex]

Intersection point of graph of above two equation will be the solution of given function,

Solutions are (1, 2) and (0, 2)

2. Given that , [tex]3x^2-3x-1=x+1[/tex]

It can be written as

                [tex]y=3x^2-3x-1\\\\y=x+1[/tex]

Intersection of graph of above two equation will be the solution of given equation.

Solutions are  (1.721, 2.721) and (- 0.387, 0.613)

Both graph attached below,

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[tex]\frac{63,756×60}{70×5,280}[/tex]

Answers

Answer:

[tex]1035[/tex]

Step-by-step explanation:

(63756×60)/(70×5280)

=1035

For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.

Answers

Answer:

Ok, our function is:

f(x) = 3*(x - 1)^2 + 2.

First, domain:

We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.

In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)

Then the domain is the set of all real numers.

Vertex:

Let's expand our function:

f(x) = 3*x^2 - 3*2*x + 1 + 2

f(x) = 3*x^2 -6*x + 2

The vertex of a quadratic function:

a*x^2 + b*x + c is at:

x = -b/2a

here we have:

a = 3 and b = -6

x = 6/2*3 = 6/6 = 1.

And the value of y at that point is:

f(1) = 3*(1 - 1)^2 + 2 = 2

Then the vertex is at: (1, 2)

Range:

The range is the set of all the possible values of y.

Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.

Then the minimal value of our quadratic function is the value at the vertex, y = 2.

This means that the range can be written as:

R = y ≥ 2

So the range is the set of all real numbers that are larger or equal than 2.

What is 33⁄5 as an improper fractions

Answers

Answer:

6 3/5

Step-by-step explanation:

33/5 = 6 R3

Answer:

6.6

Step-by-step explanation:

33÷5=6.6

33 divided by 5equal

When the factors of a trinomial are (x-p) and (x+q) then the constant teen of the trinomial is

Answers

(x-p)(x-q)

y(x-q) .... let y = x-p

yx - yq ... distribute

x(y) - q(y)

x(x-p) - q(x-p) ... replace y with x-p

x^2 - px - qx + pq .... distribute

x^2 + (-p-q)x + pq

The last expression is in the form ax^2+bx+c with a = 1, b = -p-q and c = pq

The constant term is the term without any variable x attached to it (either x or x^2), so the constant term is pq

How many solutions does this system of inequalities have graphed below

Answers

Answer:

There is only one solution set.

Step-by-step explanation:

The set can contain any number of solutions or none.

This is all I know, hope it helps.

The sales tax for an item was $15.60 and it cost $390 before tax. Find the sales tax rate. Write your answer as a percentage.

Answers

Answer:

15.60 times 100 divided by 390=4%

Step-by-step explanation:

The required sales tax rate percentage is 4%.

The sales tax for an item was $15.60 and it cost $390 before tax. To find the sales tax rate. Write your answer as a percentage.

What is the percentage?

the percentage is defined as, the composition of something out of whole inbounds of 100.example 10% of 150 = 10 * 150/100
                                                                = 15
It shows that 10 percent of 150 is 15.

sales tax = $15.60
cost = $390
To get the sales tax percentage we have to find out the tax composition of tax to the cost. So,
Sale tax percent = sale tax/cost  * 100
                            = 15.60/390   * 100
                            = 0.04 * 100
                            = 4 %

Thus, the required sales tax rate percentage is 4%.

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Points A, B, and C are collinear. Point B is between A and C. Find the length indicated. Find BC if AB=2x-12, AC=14, and BC=x+2

Answers

Answer:  BC = 10

======================================================

Work Shown:

The term "collinear" means all points fall on the same straight line.

Point B is on segment AC.

Through the segment addition postulate, we can say

AB+BC = AC

This is the idea where we glue together smaller segments to form a larger segment, and we keep everything to be a straight line.

Apply substitution and solve for x

AB+BC = AC

2x-12+x+2 = 14

3x-10 = 14

3x = 14+10

3x = 24

x = 24/3

x = 8

Then we can find the length of BC

BC = x+2

BC = 8+2

BC = 10

--------

Note that AB = 2x-12 = 2*8-12 = 16-12 = 4

and how AB+BC = 4+10 = 14 which matches with AC = 14

Therefore we have shown AB+BC = AC is true to confirm the answer.

Collinear points are points on the same line.

The value of BC is 10

Since points A, B and C are on the same line, where B is between points A and C.

So, we have:

[tex]AC = AB + BC[/tex]

Substitute values for AC, AB and BC

[tex]14 = 2x - 12 + x + 2[/tex]

Collect like terms

[tex]2x +x =14 + 12 - 2[/tex]

[tex]3x =24[/tex]

Divide both sides of the equation by 3

[tex]x =8[/tex]

Substitute 8 for x in BC = x + 2

[tex]BC =8 + 2[/tex]

[tex]BC =10[/tex]

Hence, the value of BC is 10

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(48. PERSEVERE Wha

PERSEVERE What is the greatest number of planes determined using any three of

the points A, B, C, and D if no three points are collinear?

Answers

Answer: 4

Step-by-step explanation:

We know that a plane is 2 dimensional surface that extends infinitely far.

The number of points required to define a plane = 3

Here , we have 4 points A, B, C, and D.

So, the number of possible combinations of 3 points to make a plane from 4 points = [tex]C(4,3)[/tex]

[tex]=4[/tex]            [ [tex]C(n,n-1)=n[/tex] ]

Hence, the greatest number of planes determined using any three of the points A, B, C, and D if no three points are collinear = 4.

A 2-column table with 8 rows. The first column is labeled x with entries negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 34, 3, negative 10, negative 11, negative 6, negative 1, negative 2, negative 15. Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing? (–6, –3) (–3, –1) (–3, 0) (–6, –5)

Answers

Answer:

Step-by-step explanation:

The only place that the function is increasing is [-3, -1] (learn your interval notation). At x = -3, y = -11; at x = -2, y = -6 (-6 is greater than -11); and at x = -1, y = -1 (-1 is greater than -6). The next x value, 0, returns a y value of -2. But -2 is less than -1, the value before it, so it begins deceasing again at x = 0.

Based on the values given in the table for f(x), the interval of x-values that show the function increasing is (-3, -1).

Which interval shows the function increasing?

The value of f(x) was decreasing from 34 until it got to -11 where it then started to rise again. The relevant value of x here is -3.

The value then began to rise until it reached -1 where it then fell to -2. The x value here is -1.

The interval of x-values where the function is increasing is therefore (-3, -1).

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a jar had 6 red marbles and 4 blue marbles. you randomly choose two marbles. find the probability that both marbles are red.

Answers

Hey there! I'm happy to help!

If we have 6 red marbles and 4 blue marbles, we have 10 total marbles.

First, we have the probability that a marble we draw is red, which is 6/10. This simplifies to 3/5.

If this happens, there are only 5 red marbles left and 9 total ones. So, the probability of drawing a red one again is 5/9.

We multiply these two probabilities together to see the probability of them both happening.

[tex]\frac{3}{5} *\frac {5}{9}= \frac{1}{3}[/tex]

The probability that both marbles are red is 1/3.

Have a wonderful day! :D

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

The two inequalities that show the solution to these equations are n ≥ 55 and y ≥ 6

Step-by-step explanation:

We are given two inequalities that we have to solve. We can solve these inequalities as if we are solving for the variable.

n/5 ≥ 11

Multiply by 5 on both sides.

n ≥ 55

Now, let's do the second one.

-3y ≤ -18

Divide by -3 on both sides. When we divide by a negative in inequalities, then the sign is going to flip to its other side. So, this sign (≤) becomes this sign (≥)

y ≥ 6

The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.

Answers

7/3 is the average rate of change.

Average rate of change of a function f(x) between any x values a and b = slope of the secant line connecting f(a) and f(b). This means (f(b)-f(a))/ (b-a). If a=0 and b=3, the average rate of change equals (f(3)-f(0))/(3-0).
f(3)=8+1=9, and f(0)= 1+1=2. So the average rate of change is (9-2)/3= 7/3.

f(x)=x^2 what is g(x)?

pls help me

Answers

g(x) = ax^2
y = ax^2
5 = a(1)^2
a = 5
Therefore, g(x) = 5x^2

(-3)+(-5)

What are the signs and places

Answers

What do the places mean? I’d say the signs are negative since both values are (-3) and (-5), but i don’t know what you mean by placed - if they were placed in a number line, it would go 3 and 5 values left or down.

A golf ball is hit off a tee toward the green. The height of the ball is modeled by the function h(t) = −16t2 + 96t, where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground. t = 3; It takes the ball 3 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Answers

Answer:

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Step-by-step explanation:

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

The time will be t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

What is Function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable the dependent variable.

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum.

We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground.

The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

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Aug 19,7:01:38 PM
Kylie is moving and must rent a truck. There is an initial charge of $50 for the rental
plus a fee of $3 per mile driven. Make a table of values and then write an equation for
C, in terms of m, representing the total cost of renting the truck if Kylie were to
drive m miles.
Number of Miles Driven Total Cost to Rent Truck

Answers

Answer:

0 miles- $50

1 mile- $53

2 miles- $56

3 miles-$59

Step-by-step explanation:

you add $3 to the original 50 as you go each mile.

Does someone know how to solve this?

Answers

Answer:

6 quarts

Step-by-step explanation:

8 bags

--------

2 quarts

Multiply top and bottom by 3

8*3 bags

--------

2*3 quarts

24 bags

--------------

6 quarts

Answer:

6

Step-by-step explanation:

2 quarts of iced tea = 8 tea bags.

x quarts of Iced tea = 24 tea bags

=> 2/8 = x/24

=> Multiply the extremes and means

=> 8x = 48

=> 8x / 8 = 48 / 8

=> x = 6

6 quarts of iced tea can be made with 24 tea bags.

How can I find how many 13 are in 33?

Answers

Answer:

therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)  

Step-by-step explanation:

Long division:

13  33

13*2 = 26

33 - 26 = 7

we have: 33/13 = 2 r7

we know that we can rewrite the remainder as 7/13

therefore, 33 divided by 13 equals 2 and 7 thirteenths (can be rewritten as 2 7/13)  

. Find two polynomial expressions whose quotient, when simplified, is 1/x . Use that division problem to determine whether polynomials are closed under division.

Answers

Answer:

The two polynomials are:

(x + 1) and (x² + x)

Step-by-step explanation:

A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.

Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.

Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.

So,

Let's multiply both numerator and denominator by (x + 1) to get;

(x + 1)/(x(x + 1))

This gives; (x + 1)/(x² + x)

Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.

Help c/8+5 = 24 a) 192 b) 3 c) 7 d) 152

Answers

Answer:

c = 152

Step-by-step explanation:

c/8+5 = 24

Subtract 5 from each side

c/8+5-5 = 24-5

c/8 = 19

Multiply each side by 8

c/8*8 = 19*8

c =152

Answer:

D. 152

Step-by-step explanation:

First, subtract 5 from both sides:

c/8 + 5 = 24

c/8 = 19

Multiply both sides by 8:

c = 152

So, the correct answer is D, 152

Other Questions
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