What is the next number in the sequence? 9….16….24….33…

Answer:

[tex]x=6-\sqrt{ -100}/2=3-5i=3.0000-5.0000i\\x=6+\sqrt{-100} )/2=3+5i=3.0000+5.0000i[/tex]

Step-by-step explanation:

Step 1: Trying to factor by splitting the middle term

The first term is,  x²  its coefficient is  1 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  +34

Step-1 : Multiply the coefficient of the first term by the constant   1 • 34 = 34

Step-2 : Find two factors of  34  whose sum equals the coefficient of the middle term, which is   -6 .

     -34    +    -1    =    -35

     -17    +    -2    =    -19

     -2    +    -17    =    -19

     -1    +    -34    =    -35

     1    +    34    =    35

     2    +    17    =    19

     17    +    2    =    19

     34    +    1    =    35

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 1:

 x² - 6x + 34  = 0

Parabola, Finding the Vertex:

 Find the Vertex of   y = x^2-6x+34

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   3.0000  

Plugging into the parabola formula   3.0000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 34.0

or   y = 25.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-6x+34

Axis of Symmetry (dashed)  {x}={ 3.00}

Vertex at  {x,y} = { 3.00,25.00}

Function has no real roots

Solve Quadratic Equation by Completing The Square

Solving   x2-6x+34 = 0 by Completing The Square .

Subtract  34  from both side of the equation :

  x2-6x = -34

Now the clever bit: Take the coefficient of  x , which is  6 , divide by two, giving  3 , and finally square it giving  9

Add  9  to both sides of the equation :

 On the right hand side we have :

  -34  +  9    or,  (-34/1)+(9/1)

 The common denominator of the two fractions is  1   Adding  (-34/1)+(9/1)  gives  -25/1

 So adding to both sides we finally get :

  x2-6x+9 = -25

Adding  9  has completed the left hand side into a perfect square :

  x2-6x+9  =

  (x-3) • (x-3)  =

 (x-3)2

Things which are equal to the same thing are also equal to one another. Since

  x2-6x+9 = -25 and

  x2-6x+9 = (x-3)2

then, according to the law of transitivity,

  (x-3)2 = -25

We'll refer to this Equation as  Eq. #2.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-3)2   is

  (x-3)2/2 =

 (x-3)1 =

  x-3

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  x-3 = √ -25

Add  3  to both sides to obtain:

  x = 3 + √ -25

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1

Since a square root has two values, one positive and the other negative

  x2 - 6x + 34 = 0

  has two solutions:

 x = 3 + √ 25 •  i

  or

 x = 3 - √ 25 •  i

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-6x+34 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -6

                     C   =   34

Accordingly,  B2  -  4AC   =

                    36 - 136 =

                    -100

Applying the quadratic formula :

x = 6 ± √ -100/2

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -100  =

                   √ 100 • (-1)  =

                   √ 100  • √ -1   =

                   ±  √ 100  • i

Can  √ 100 be simplified ?

Yes!   The prime factorization of  100   is

  2•2•5•5

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 100   =  √ 2•2•5•5   =2•5•√ 1   =

               ±  10 • √ 1   =

               ±  10

So now we are looking at:

          x  =  ( 6 ± 10i ) / 2

Two imaginary solutions :

x =(6+√-100)/2=3+5i= 3.0000+5.0000i

 or:

x =(6-√-100)/2=3-5i= 3.0000-5.0000i

Two solutions were found :

x =(6-√-100)/2=3-5i= 3.0000-5.0000i

x =(6+√-100)/2=3+5i= 3.0000+5.0000i

Answer:

5x(squared)-4x+1

2x(squared)+11xy+14

7x(squared)+7xy+3x-17

Step-by-step explanation:

Step-by-step explanation:

[tex] \frac{19695}{x - 15605} = 100[/tex]

[tex]19695 = 100(x - 15605)[/tex]

[tex]19695 = 100x - 1560500[/tex]

[tex]19695 + 1560500 = 100x[/tex]

[tex]15801 95 = 100x[/tex]

[tex] \frac{1580195}{100} = x[/tex]

[tex]x = 15801.95[/tex]

Answer:

iam thinking the answer is ""-262,5ft""

The height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.

The height is a vertical distance between two points. It is given that A model rocket is launched 25 feet from you. When the rocket is at height h, the distance d between you and the rocket is given by d = 625 + h² where h and d are measured in feet.

The height will be calculated by forming the two equations from the given data in the question.

25  =  625  +  h²

100  =  4  (  625   +  h² )

100  =  ( 2500   +  4h²  )

By solving both the equations:

100  -  25  =  2500  -  625  +  4h²   -   h²

3h²   =  1800

h   =   √600

h   =   24.49 feet

Therefore the height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.

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Answer:

[tex]3z {}^{3} \times 12[/tex]

[tex]36z {}^{3} [/tex]

Answer: Degenerate

Step-by-step explanation:

This conic section (intersecting lines) is a degenerate

The conic section is degenerate.

The correct option is (e).

Any curve produced by the intersection of a plane and a right circular cone.

As, the given figure shows a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve.

Hence, the conic section is degenerate.

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Answer:

1 1/3 cups of milk

Step-by-step explanation:

In our recipe

For every 1 1/2 cups of flour we need  2 cups of milk

then the flour and milk are two proportional quantities

1 1/2 ————-> 2

We know that 1 1/2 = 1/2 + 1/2 + 1/2  then

1/2 + 1/2 + 1/2 ————-> 2

Then (we divide both sides by 3)

1/2 ————-> 2/3

Then (we multiply  both sides by 2)

1 ————-> 4/3

finally , 4/3 = 1 1/3

Step-by-step explanation:

You can find the complete solution

You should use cross multiplication to solve

I hope it helped you

Answer:

Step-by-step explanation:

This is a proportion question which is 2 ratios which are equal to one another. If 3 of the 4 parts are known, the 4th part can be calculated.

36 liters.

36 km/3 Liters = x / 36             multiply both sides by 36

36*36 / 3 =  x

1296/3 = x

x = 432 km

So on 36 L he can go 432 km

3 liters

Given as 36 km

48 liters

36km/3 liters = x / 48 liters         Multiply both sides by 48

48*36/3 = x

576 km = x

So on 48 liters, he can go 576 km

132 liters

36 km/ 3 liters = x/132

x = 1564 km

On 132 liters Pat can go 1564 km

The LSRL is the Least Squares Regression Line of the new engine design performance

This is the equation of the Least Squares Regression Line.

From the calculation summary, we have the following parameters:

So, the LSRL is:

y = 11.6559 + 3.47812x

Where y represents the predicted volume and x represents the weight.

In (a), we have:

y = 11.6559 + 3.47812x

Substitute 100 for x

y = 11.6559 + 3.47812 * 100

Evaluate

y = 359.4679

Hence, the predicted top speed when the weight is 100 tons is 359.4679

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Step-by-step explanation:

so, they want to sell 200,000 tickets (and we assume they can really sell all of these).

they have to pay the prize money afterwards :

1 × $8,000 = $8,000

10 × $300 = $3,000

75 × $50 = $3,750

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

$14,750

and they have to pay for the ticket production at the beginning.

this is not really well defined, but I assume the following :

C(20) = 4500 + 6x

x = units of 10,000 tickets (because of the functional argument of 20, and we have to deal with 200,000 tickets).

that means the cost for these 200,000 tickets is then

4500 + 6×20 = $4,620

$4,500 are fixed costs insurgent of the number of tickets (like for creating the design, configuring the printing machines for the design, ...).

and 6×20 = $120 are the cost of actuality printing the tickets ($6 per 10,000 ticket prints).

so, the total expenses are

$14,750 + $4,620 = $19,370

under the assumption they can sell all 200,000 tickets to just break even, the prize for each ticket must be

19,370 / 200,000 = $ 0.09685 ≈ $0.10

if my assumptions are wrong, please adapt the numbers in the calculations i showed you here.

for example, what if the x in the printing cost is per ticket and not per 10,000 tickets ?

then the printing costs would be

4500 + 6×200000 = $1,204,500

and the total expenses would be

$14,750 + $1,204,500 = $1,219,250

and the prize per ticket would have to be

1,219,250 / 200,000 = $ 6.09625 ≈ $6.10

The total amount of all the prize money is $14,750, and the price of each of the 200,000 raffle tickets in order to break even should be $0.08.

Given that to raise money for malaria research the New York City Rotary Club is going to sell 200,000 raffle tickets, and one ticket will have an 8000 dollar prize attached to it, while ten tickets will have a 300 dollar prize attached to it, and seventy-five tickets will have a 50 dollar prize, to determine what is the total amount of all the prize money and what should be the price of each of the 200,000 raffle tickets in order to break even, the following calculation must be made:

Therefore, the total amount of all the prize money is $14,750, and the price of each of the 200,000 raffle tickets in order to break even should be $0.08.

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100x³²

..................

Answer:

the answer is 56in2

Step-by-step explanation:

[tex]b = 14in \\ h = 8in \\ area \: of \: triangle = \frac{1}{2} b \times h \\ = \frac{1}{2} \times 14 \times 8 \\ = 56inches[/tex]

Answer:

600in³

Step-by-step explanation:

the equation for volume is:

V=s*3

(s is a varible which means LengthxHeightxWidth)

step 1

V= (10")(5")(12")

then it equals your answer

up above is the answer.

Hope it help you out.

Don't forget to label.

Answer:

y=1/4x+3

Step-by-step explanation:

You can find the slope by starting at the point (4,2), then using "rise over run" you can count up(rise) 1, then side(run) 4. So the slope, or "m" would be 1/4x. The B value is the y Intercept, and the y Intercept is (0,3) so you would write it as 3 in the equation.

A graph that shows a function must pass the vertical line test

The true statement is (b) No; the graph fails the vertical line test.

For a graph to show a function, the graph must pass the vertical line test

The given graph do not pass the vertical line test;

This is so because, a line drawn from the x-axis would touch the graph at at least two different points

Hence, the true statement is (b) No; the graph fails the vertical line test.

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Answer:

x=6

Step-by-step explanation:

Rearrange terms:

8+x=14

x+8=14

Subtract 8 from both sides and simplify.

Given :-

To find :-

Solution :-

8+x = 14

x = 14-8 (Signs change when transferred to opposite side)

x = 6

Answer:

1/6

Step-by-step explanation:

it is like a cube just with slightly different numbers on each side. but the probabilty structure is still the same.

we have 6 different possible outcomes, all with the same basic probabilty (as every field on the spinner is seemingly of the same size as the others).

and we desire one of these possible outcomes (6).

so the probabilty to get 6 is still 1/6 (1 desired over 6 possible outcomes).

45-12=33

then divide 33 by 9: 33÷9=3.66666666 repeating forever. you can round up to 3.7.

Answer:

56 Chickens

36 Cows

Step-by-step explanation:

You can set this up as a system of equations:

(x=chickens, y=cows)

[tex]\left \{ {{92 = x+y} \atop {256=2x+4y}} \right. \\[/tex]

To solve this system, first we can solve for x in the top equation:

[tex]x=92-y[/tex]

Next, we can plug in x to the second equation and solve for y:

[tex]256=2(92-y)+4y\\256=184+2y\\2y=72\\y=36[/tex]

And now that we have y, we can plug it into the first equation and solve for x:

[tex]92=x+36\\x=56[/tex]

Answer:

10 x 0.007 = 0.07

Step-by-step explanation:

im not sure if thats what you meant

Answer:

1. 3.33

2. 8.75

3. 4.8

4. 2.5

Step-by-step explanation:

divide the numbers.

Answer:

Angle u is 52

Step-by-step explanation:

I only know this

52 because internal angle of triangle is 180 subtract 90 and 38 from 180 and you will get 52

Answer:

Pls try to send ur questions the right way and ask again attaching the picture of the figure. Otherwise, there is no way to solve

Answer: 4n-7

Step-by-step explanation:

Answer:

B  Angle obtuse Since 126o 32 ' is bigger  90o but  smaller than 180o.

Step-by-step explanation:

Acute: An angle that measures < 90o.

Right: An angle that measures 90o.

Obtuse : An angle that is > 90o but < 180o.

Straight: An angle that measures 180o.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=10297\\ h=21 \end{cases}\implies 10297=\pi r^2(21)\implies \cfrac{10297}{21\pi }=r^2 \\\\\\ \cfrac{1471}{3\pi }=r^2\implies \sqrt{\cfrac{1471}{3\pi }}=r\implies 12\approx r[/tex]

Answer:

$35

Step-by-step explanation:

7 customers - 2 who didn't tip =  5 who did tip

$7 from those who did tip * 5 ppl who tipped = $35 earned

Answer:

^EKF and^HKI

Step-by-step explanation: