Which expression is equivalent to (x Superscript 27 Baseline y) Superscript one-third?
x cubed (RootIndex 3 StartRoot y EndRoot)
x Superscript 9 Baseline (RootIndex 3 StartRoot y EndRoot)
x Superscript 27 Baseline (RootIndex 3 StartRoot y EndRoot)
x Superscript 24 Baseline (RootIndex 3 StartRoot y EndRoot)

Answer:

x2-16x+100=0  

Two solutions were found :

x =(16-√-144)/2=8-6i= 8.0000-6.0000i

x =(16+√-144)/2=8+6i= 8.0000+6.0000i

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  x2-16x+100  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -16x  its coefficient is  -16 .

The last term, "the constant", is  +100  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 100 = 100  

Step-2 : Find two factors of  100  whose sum equals the coefficient of the middle term, which is   -16 .

     -100    +    -1    =    -101  

     -50    +    -2    =    -52  

     -25    +    -4    =    -29  

     -20    +    -5    =    -25  

     -10    +    -10    =    -20  

     -5    +    -20    =    -25  

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  1  :

 x2 - 16x + 100  = 0  

Step  2  :

Parabola, Finding the Vertex :

2.1      Find the Vertex of   y = x2-16x+100

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   8.0000  

Plugging into the parabola formula   8.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 8.00 * 8.00 - 16.0 * 8.00 + 100.0

or   y = 36.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-16x+100

Axis of Symmetry (dashed)  {x}={ 8.00}  

Vertex at  {x,y} = { 8.00,36.00}  

Function has no real roots

Solve Quadratic Equation by Completing The Square

2.2     Solving   x2-16x+100 = 0 by Completing The Square .

Subtract  100  from both side of the equation :

  x2-16x = -100

Now the clever bit: Take the coefficient of  x , which is  16 , divide by two, giving  8 , and finally square it giving  64  

Add  64  to both sides of the equation :

 On the right hand side we have :

  -100  +  64    or,  (-100/1)+(64/1)  

 The common denominator of the two fractions is  1   Adding  (-100/1)+(64/1)  gives  -36/1  

 So adding to both sides we finally get :

  x2-16x+64 = -36

Adding  64  has completed the left hand side into a perfect square :

  x2-16x+64  =

  (x-8) • (x-8)  =

 (x-8)2

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

  x2-16x+64 = -36 and

  x2-16x+64 = (x-8)2

then, according to the law of transitivity,

  (x-8)2 = -36

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-8)2   is

  (x-8)2/2 =

 (x-8)1 =

  x-8

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

  x-8 = √ -36

Add  8  to both sides to obtain:

  x = 8 + √ -36

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 - 16x + 100 = 0

  has two solutions:

 x = 8 + √ 36 •  i  

  or

 x = 8 - √ 36 •  i  

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-16x+100 = 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   =   -16

                     C   =  100

Accordingly,  B2  -  4AC   =

                    256 - 400 =

                    -144

Applying the quadratic formula :

              16 ± √ -144

  x  =    ——————

                     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,√ -144  =  

                   √ 144 • (-1)  =

                   √ 144  • √ -1   =

                   ±  √ 144  • i

Can  √ 144 be simplified ?

Yes!   The prime factorization of  144   is

  2•2•2•2•3•3  

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).

√ 144   =  √ 2•2•2•2•3•3   =2•2•3•√ 1   =

               ±  12 • √ 1   =

               ±  12

So now we are looking at:

          x  =  ( 16 ± 12i ) / 2

Two imaginary solutions :

x =(16+√-144)/2=8+6i= 8.0000+6.0000i

 or:  

x =(16-√-144)/2=8-6i= 8.0000-6.0000i

Two solutions were found :

x =(16-√-144)/2=8-6i= 8.0000-6.0000i

x =(16+√-144)/2=8+6i= 8.0000+6.0000i

Step-by-step explanation:

Answer:

18,736.80

Step-by-step explanation:

Final answer:

To determine the original purchase price of the van, we apply the formula for exponential decay and find that Ethan paid approximately $10,100.45 for the van two years ago, taking into account a depreciation rate of 11% per year.

Explanation:

To find how much Ethan paid for the van, we need to work backwards from the current value and consider the annual depreciation rate.

To do this, we can use the formula for exponential decay which is final value = initial value × (1 - rate of depreciation)number of years. Given the final value ($8000) and the depreciation rate (11% or 0.11), we need to solve for the initial value, which represents the price Ethan paid for the van.

Let's set up the equation:

8000 = initial value × (1 - 0.11)2

8000 = initial value × (0.89)2

8000 = initial value × 0.7921

Initial value = 8000 / 0.7921

Initial value ≈ $10,100.45

Therefore, Ethan paid approximately $10,100.45 for the van.

Answer:

V = 77 m^3

Step-by-step explanation:

We want the volume of the cylinder

V = pi r^2 h

We know the diameter not the radius

r = d/2 = 7/2 = 3.5

V = 3.14 * (3.5)^2 (2)

V = 76.93 m^3

To the nearest cubic meter

V = 77 m^3

The answer is 77 m^3

Quick question though... Why say "easy" and ask for an answer?

D. Graph D. A graph that shows a quadratic function with a discriminant value of 0 is graph D.

In Mathemeatics, the number of zeros for any quadratic function by using the discriminant formula as follows;

Discriminant, D = b² - 4ac

where:

a, b, and c are constants.

Note:

If D equals 0, the quadratic equation has only one real solution.

If D is greater than 0, the quadratic equation has two real solutions.

If D is less than 0, the quadratic equation has two complex solutions

In this context, we can logically deduce that only graph D shows a quadratic function with a discriminant value of 0 because it has only one real solution (x = 1).

Answer:

adbbcbaca

Step-by-step explanation:

Answer:

24/25

Step-by-step explanation:

3/5×8/5

24/25

Step-by-step explanation:

The following match

* a² + 2ab + b² and (a + b)²

* a² - b² and (a - b)(a + b)

* a² - 2ab + b² and (a - b)²

* a³ - b³ and (a - b)(a² + ab + b²)

* a³ + b³ and (a + b)(a² - ab + b²)

* y = 10x Direct variation

* xy = 18 Algorithm

* y = 4xz Joint variation

* y = 4x/z Inverse variation

Answer:

[tex]10\pi[/tex]

Step-by-step explanation:

The penguin swam around half of the perimeter, or circumference, of the pool. The first step is to calculate that. You can find the circumference of a circle by multiplying the diameter by pi. Therefore, the circumference of this island is 20pi. Half of that is [tex]10\pi[/tex] meters. Hope this helps!

Answer:

10 meters

Step-by-step explanation:

20 / 2 = 10

Answer:

15

Step-by-step explanation:

Answer:

x=8

A = 192

Step-by-step explanation:

The perimeter is the sum of the outer lengths

17.9 + 22.6 + 3x = 64.5

Combine like terms

40.5 +3x = 64.5

Subtract 40.5 from each side

40.5 +3x -40.5 = 64.5 - 40.5

3x =24

Divide each side by 3

3x/3 = 24/3

x = 8

The area of a triangle is given by

A = 1/2 bh

The base is 3x = 3(8) =24

and the height is 2x = 2(8) =16

A = 1/2 (24) * 16

A =192

Answer:

47

Step-by-step explanation:

add all the numbers and divide them by however many numbers there are.

Answer: The mean is 47.

There are 5 numbers.

To find the mean of them we add them and divide the sum by 5.

Mean = [tex]\frac{\left(40+40+52+41+62\right)}{5}=\frac{235}{5}=47[/tex]

Learn more: https://brainly.com/question/12049968

Answer:

This means that there is no solution

Step-by-step explanation:

When solving for a system of linear equations, we are solving for the intersection point. If we cannot algebraically solve for a system, it automatically means you made a mistake or the lines are parallel.  Since the two lines are parallel, there is no intersection point, so there is no solution

Answer:

1099.6 m³

Step-by-step explanation:

The formula for the volume of a cylinder of radius r and height h is

V = πr²h.  In this case, the radius, r, is half the diameter, 10 m:  r = 5 m, and the height is 14 m.  

Thus, the volume of this cylinder is

V = π(5 m)²(14 m) = 1099.6 m³ (to the nearest tenths place).

The volume of the cylinder is approximately 1099.6 cubic meters to the nearest tenth place.

A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.

The formula for the volume of a cylinder is:

V = πr²h

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14159).

To find the radius of the cylinder, we need to divide the diameter by 2:

r = d/2 = 10m / 2 = 5m

Now we can plug in the values:

V = πr²h = π(5m)²(14m) = 350π m³

To approximate the value to the nearest tenths place, we can substitute the value of π as 3.14159 and use a calculator to evaluate the expression:

V ≈ 350 × 3.14159 ≈ 1099.56 ≈ 1099.6

Therefore, the volume is 1099.6 cubic meters.

To learn more about the cylinder;

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Answer:

B. 7 inches

Step-by-step explanation:

The area of a rectangle is given by

A = l*w  where l is the length and w is the width

56 = 8*w

Divide each side by 8

56/8 = 8w/8

7 =w

Answer: 7 inches

Step-by-step-Explanation: The formula for the area of a rectangle is below shown below.

Area = length · width

Since we know that the area of the rectangle is 56 in² and the length of the rectangle is 8 inches, we have 56 = 8 · w.

Now to find w or the width of the rectangle, we divide

both sides of the equation by 8 to get 7 = w.

So the width of the rectangle is 7 inches.

Notice that we include inches in our final answer because we were given inches as units in the original problem.

Also notice that we don't ever have to draw a picture of the rectangle in this problem. We can find our answer by simply using the formula for the area of a rectangle.

Answer:

[tex] df = n-1= 16-1 =15[/tex]

And the significance level is [tex]\alpha=0.05[/tex] and since we are conducting a bilateral test then the critical values are founded with the t distribution with 15 degrees of freedom and we got:

[tex] t_{\alpha/2}= \pm 2.131[/tex]

Step-by-step explanation:

Information given

[tex]\bar X=45[/tex] represent the sample mean

[tex]s=3.65[/tex] represent the sample standard deviation

[tex]n=16[/tex] sample size  

[tex]\mu_o =41[/tex] represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to determine the true mean is 41 per day, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 41[/tex]  

Alternative hypothesis:[tex]\mu \neq 41[/tex]  

We need to find the degrees of freedom first:

[tex] df = n-1= 16-1 =15[/tex]

And the significance level is [tex]\alpha=0.05[/tex] and since we are conducting a bilateral test then the critical values are founded with the t distribution with 15 degrees of freedom and we got:

[tex] t_{\alpha/2}= \pm 2.131[/tex]

Answer: 72

72/8 will get you 9. To see if the answer is correct Multiply 9*8.

Answer:

72

Step-by-step explanation:

c/8 = 9

Multiply each side by 8

c/8 * 8 =9*8

c = 72

Answer:

438.86

Step-by-step explanation:

1. 457 x 0.99 = 452.43 - Decreased by 1%

2. We need to decrease 452.43 again but this time by 3% - 452.43 x 0.97

3. This gives us an answer of 438.8571

4. Finally we need to round this to 2DP, the 7 (438.8571) rounds up so the number to the left increases. This leaves an answer of 438.86

Hope this helps :D

Answer:

The inverse of the function is ±sqrt( (x+4)/2

Step-by-step explanation:

Set the function equal to y

y = 2x^2 -4

Exchange x and y

x = 2y^2 -4

Solve for y

Add 4 to each side

x+4 = 2y^2 -4+4

x+4 = 2y^2

Divide each side by 2

(x+4)/2 = 2/2y^2

(x+4)/2 = y^2

Take the square root of each side

±sqrt( (x+4)/2 )= sqrt(y^2)

±sqrt( (x+4)/2 )= y

The inverse of the function is ±sqrt( (x+4)/2

Answer:

10 cm

Step-by-step explanation:

We want to find TS = ST

ST = CD  from the second statement of congruence

CD = IJ  from the first statement of congruence

We know IJ = 10

That means ST = 10

Answer:

5 dollars

Step-by-step explanation:

Answer:

5 dollars

Step-by-step explanation:

Answer:

90

Solution:

The 1st choice is 1 of 10.

The 2nd is one of 9.

Therefore, 10 times 9= 90

After a series of movements starting on the 10th floor, the elevator stopped on the 13th floor.

To determine which floor the elevator was on when it stopped, we need to perform a series of additions and subtractions based on the elevator's movements, as described:

The elevator started on the 10th floor.

It traveled up 4 floors: 10 + 4 = 14th floor.

Then down 6 floors: 14 - 6 = 8th floor.

Then down 2 more floors: 8 - 2 = 6th floor.

Finally, it went back up 7 floors: 6 + 7 = 13th floor.

After completing all these movements, the elevator stopped on the 13th floor.

Answer:

4 = x

Step-by-step explanation:

x³ - 5 = 59     Add five to both sides of the equation.

x³ = 64          Now find the cubed root of 64

∛64 = 4

x = 4

Answer: B. 105

Step-by-step explanation:

      180 - 75 = 105

Hope this helps!

Answer:

3.75 in.

Step-by-step explanation:

Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regular hexagon with a perimeter of 7.5 in.

3 regular hexagons are connected at their sides. A dotted line is drawn through the middle of the 3 hexagons. The top image is a reflection of the bottom image. The dotted line is the length of one side and the distance from one point of the hexagon to the opposite point.

What is the length of the dotted line? Round to the nearest hundredth.

2.50 in.

3.75 in.

5.00 in.

6.25 in.

The length of the dotted line in the hexagon is 3.75 cm.

A polygon with 6 sides is called a hexagon.

Finding the length across one entire hexagon :-

We can draw 6 small triangles from the center of the hexagon. The top vertex of this triangle will be 60°; this is because there are 6 angles, and 360.

The sum of the measures of the angles in a triangle is 180°; taking out the top angle, we have 180-60 = 120°.  

Since the triangle is isosceles, the base angles will be equal to 120/2 = 60

The bottom two angles will also be 60°.  

This makes the triangle equiangular, which also makes it equilateral; all 3 sides will be 1.25.

Hence,

This means across the dotted line we have 1.25+1.25+1.25 = 3.75.

Learn more about hexagon on:

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Answer: Mike started with 75 cards

Step-by-step explanation:

Hi, to answer this question we have to write an equation:

The number of cards mike started with (x) plus the new cards added (7) must be divided by 2 (since his dog ate half of his collection).

That expression must be equal to the number of cards left (41)

Mathematically speaking:

(x + 7) /2 = 41

Solving for x:

x+7 = 41x2

x+7 = 82

x = 82-7

x = 75 cards

Feel free to ask for more if needed or if you did not understand something.  

Answer:

23 1/3   or 70/3 =p

Step-by-step explanation:

7/p = 3/10

Using cross products

7*10 = 3p

70 = 3p

Divide each side by 3

70/3 = 3p/3

70/3 =p

or as a mixed number

23 1/3 =p

Answer:

55 words per minute

Step-by-step explanation:

165/3

Final answer:

The ratio of words typed per minute for Kale who typed 165 words in 3 minutes is calculated by dividing the number of words by the number of minutes, resulting in 55 words per minute.

Explanation:

To calculate the number of words typed per minute, you take the total number of words typed and divide it by the number of minutes it took to type them. In this case, Kale typed 165 words in 3 minutes, so the ratio of words to minutes is:

165 words / 3 minutes = 55 words per minute

This ratio indicates the typing speed, measured in words per minute (wpm), which is a common way to express typing efficiency.