3x² - 12x +9=0 using quadratic formula

Answer:

x = 5.

Step-by-step explanation:

x^3 - x = 120

We first guess the value of x and calculate the left side.

Take x = 4:-

4^3 - 4 = 64-4 = 60  

This is < 120 so try x = 5:

5^3 - 5 = 125 - 5 = 120.

So one solution is x = 5.

[tex]\displaystyle|\Omega|=6^3=216\\A=\binom{3}{2}\cdot5=3\cdot5=15\\|A|=\dfrac{15}{216}=\dfrac{5}{72}\approx0.069[/tex]

Answer:

Circle D

Step-by-step explanation:

The circumference of a circle can be calculated by multiplying the diameter by π.  Therefore, the circle with the greatest circumference will be the circle with the greatest diameter.

The only circle for which we have been told the radius is Circle D.  The diameter of a circle is twice the radius, therefore the diameter of Circle D is 50 in × 2 = 100 in

There are 12 inches in 1 ft.

Therefore, the circumferences of the circles in order from smallest to largest is:  B < C < A < D

Proof

Diameters

Answer:

40

Step-by-step explanation:

32÷100= 0.32

0.32×125= 40

convert your percentage into a number first, so that you are working with normal numbers only, and then multiply that by your total.

Answer:

  23.20°, 71.57°, 85.24°

Step-by-step explanation:

The angle between two vectors can be found by making use of the definition of the dot product. The computed angle is the angle between the  vectors when they are placed tail-to-tail.

__

vector definition

The second attachment shows the given points plotted as A, B, C in the order given. In the diagram, the vectors a, b, c are defined as BA, CB, AC, respectively. That is, the vector a is ...

  a = A -B = (-6, -9) -(2, 7) = (-6-2, -9-7) = (-8, -16)

The vectors are defined in counterclockwise order around the triangle, though that makes no difference to the calculation.

dot product definition

The definition of the dot product of vectors A and B is ...

  A·B = |A|×|B|×cos(θ) . . . . . where θ is the angle between the vectors

Solving for the angle, we find it to be ...

  [tex]\theta=\arccos\left(\dfrac{\vec{A}\cdot\vec{B}}{|\vec{A}|\,|\vec{B}|}\right)[/tex]

__

Because of the way the vectors in this solution are defined, the angle between any given pair of vectors will be an exterior angle of the triangle. In order to find the measure of the interior angle, we must reverse one of the vectors. That is, the dot product used in our computation will be the opposite of the dot product of the vectors we have found.

The spreadsheet shown in the first attachment does the necessary computations.

As a check, the spreadsheet shows the sum of the angle values. (The rounded values add up to 180.01°.)

The interior angles of the triangle are 23.20°, 71.57°, 85.24°.

_____

Additional comment

Another way to find the interior angles from coordinates is to consider the slope of each side of the triangle as being the tangent of the angle it makes with the x-axis. The difference of these angles can be used to find the interior angles of the triangle. Less work is involved because there is no dot-product or magnitude computation.

Both the first and second statements are true and therefore Option D is the correct answer .

A function can be defined as the equation that identifies relation between a dependent variable and an independent variable.

A function always has a defined range and domain.

In the following statements

I. If f '(c) = 0, then f has a local maximum or minimum at x = c.

f'(c) = 0

It means that the slope of f(x) = 0 at x = c

If f has a local maximum or minimum at x = c  It is a True statement

II. If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].

If f'(x) = 0 on (a, b),

then f is neither increasing nor decreasing

and therefore is constant on [a, b]

So it is a True statement.

III. The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [−1, 1].

No the theorem cannot be applied as, f is neither continuous nor differentiable at x = 0

It is a False Statement.

Therefore Option D is the correct answer.

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Solution:

[tex] - 18 \sqrt{10} [/tex]

[tex] = - 6 \sqrt{2} \: \: • \: \: 3 \sqrt{5} [/tex]

2. Apply radical rule : [tex] \sqrt{a} \sqrt{b} = \sqrt{ab} [/tex] , [tex]a \geqslant 0[/tex], [tex]b[/tex]

[tex] = 6 \sqrt{2 \: • \: 5} \: • \: 3[/tex]

=[tex]6 \sqrt{10} •3[/tex]

[tex] = - 18 \sqrt{10} [/tex]

200 is the median (50%) of the data represented in the box plot. The fraction of the books has 200 or fewer pages is: 1/2.

In a box plot, the median is indicated as the value marked by the vertical line that divides the rectangular box of the box plot.

The median is the middle of the data and represents the 50th percentile. That is 1/2 the data.

In the box plot given, 200 pages is the median. Therefore, the fraction of the books that have 200 or fewer pages is: 1/2.

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Answer: x=-5, y=20

Step-by-step explanation:

Opposite sides of a parallelogram are congruent, so AB=CD.

[tex]x^{2}-15=-2x\\x^{2}+2x-15=0\\(x+5)(x-3)=0\\x=-5, 3[/tex]

But as distance must be positive, as CD=-2x, x must be negative, so x=-5.

Opposite angles of a parallelogram are congruent, so [tex]m\angle D=m\angle B[/tex].

[tex]4y+26=106\\4y=80\\y=20[/tex]

Answer:

  E.  18.6

Step-by-step explanation:

The diagonals of a rhombus bisect each other at right angles. The means all of the triangles shown are right triangles, and the two marked angles are complementary.

__

Complementary angles total 90°.

  (x°) +(4x -3)° = 90° . . . . . the marked angles are complementary

  5x = 93 . . . . . . . . . . . .  divide by °, add 3

  x = 93/5 = 18.6 . . . . . divide by the coefficient of x

The value of x is 18.6.

The options that are true as a result of doubling the rectangle dimensions are;

p → q represents the original conditional statement.

p → ~q represents the contrapositive of the original conditional statement.

We are told that;

Doubling the dimensions of a rectangle increases the area by a factor of 4.

Now, p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4.

Thus, using conditional statements notation, we can say that;

p → q represents the original conditional statement.

p → ~q represents the contrapositive of the original conditional statement.

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Answer:  Check out the screenshot below for the answers

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

Explanation:

For each column, we divide the values by the sum of each column.

The sum of the first column is 6+8 = 14, and the sum of the second column is 7+3 = 10.

Column 1:

Those values are approximate to two decimal places.

Column 2:

Those values are exact.

The values in bold are then filled in the table as you see below.

A result like 0.43 means that 43% of those who play a sport also play an instrument. The other values are interpreted in a similar fashion.

Answer:

152

Step-by-step explanation:

If you substitute the 6, the expression will look like this-

8( 3(6) + 1 )

You can then times 3 by 6, this makes 18. You then add the one, this equals 19.

19 times 8 = 152.

I hope this helps, have a lovely day.

Answer:

y = - 5 or y = 9

Step-by-step explanation:

using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (- 1, y )

d = [tex]\sqrt{(-1-4)^2+(y-2)^2}[/tex]

   = [tex]\sqrt{(-5)^2+(y-2)^2}[/tex]

   = [tex]\sqrt{25+(y-2)^2}[/tex]

equating to [tex]\sqrt{74}[/tex] , that is

[tex]\sqrt{25+(y-2)^2}[/tex]  = [tex]\sqrt{74}[/tex] ( square both sides )

25 + (y - 2)² = 74 ( subtract 25 from both sides )

(y - 2)² = 49 ( take square root of both sides )

y - 2 = ± [tex]\sqrt{49}[/tex] = ± 7 ( add 2 to both sides )

y = 2 ± 7

Then

y = 2 + 7 = 9 or y = 2 - 7 = - 5

Answer:

mean = 3.5

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{1+2+3+4+5+6}{6}[/tex] = [tex]\frac{21}{6}[/tex] = 3.5

Answer:

The mean of 1 , 2 , 3 , 4 , 5 , 6 is 3.5

Given :

The observations 1 , 2 , 3 , 4 , 5 , 6

To find :

The mean of 1 , 2 , 3 , 4 , 5 , 6

Solution :

Step 1 of 2 :

Calculate sum of the observations

Here the given observations are 1 , 2 , 3 , 4 , 5 , 6

Number of observations = 6

Sum of the observations

= 1 + 2 + 3 + 4 + 5 + 6

= 21

Step 2 of 2 :

Find the mean

The required mean

The critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074

The dataset is given as:

21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1

The sample mean is:

[tex]\bar x = 22.1[/tex]

The significance level is

α = 0.010

Start by calculating the degrees of freedom using:

df = n - 1

Where n represents the sample size (n = 7)

So, we have:

df = 7 - 1

df = 6

Using the table for t critical values for a two-tailed test, we have:

Critical value = ±3.7074

Hence, the critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074

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Answer:

The Sierpinski triangle is also called the Sierpinski gasket.

Step-by-step explanation:

The Sierpinski triangle is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915.

Answer:

[tex]m\angle B = 28^{\circ}[/tex]

Step-by-step explanation:

All angles in a triangle must add up to [tex]180^{\circ}[/tex]

We can solve for [tex]\angle B[/tex] using this knowledge

[tex]\angle B + 40 + 112 = 180\\\angle B + 152 = 180\\\boxed{\angle B = 28}[/tex]

That is the answer

- Kan Academy Advance

Due to length restrictions, we kindly invite to check the explanation of this question to understand the derivation of the polynomic expressions.

Cubic functions are polynomials of grade 3. In this case, we have pairs of cubic functions of the following form:

y = (x - h)³ + k       (1)

y = - (x - h)³ + k     (2)

a) Where (h, k) are the coordinates of the vertex of each cubic function. There is a translation of (x, y) = (3, 1) between each two consecutive pairs of cubic functions. Hence, we have the following fourteen cubic functions:

b) Another family of functions with a similar pattern is shown below:

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The new dimension of the rectangle are as follows;

The new dimension of the rectangle can be found as follows;

The sides of a square are equal.

Therefore,

let the side of the square = x

Hence,

length = x + 3

width = x + 1

area of rectangle = lw

where

Therefore,

24 = (x + 3)(x + 1)

24 = x² + x + 3x + 3

24 = x² + 4x + 3

x² + 4x + 3 - 24

x² + 4x - 21 = 0

(x - 3)(x + 7)

Therefore,

x = 3 or -7

It can't be negative. Hence, x = 3 ft

Therefore, the new dimension of the rectangle are as follows;

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Answer:

is that the ixl

website ????????????????????????????????

Based on the interest rate and continuous compounding, the investment would double in value after 18.5 years.

We have given that,

investment to double at a 3 3/4% interest rate,

The future value using continuous compounding is:

= Amount x e ^ (rate x time)

Interest is

= 3.75%

2 = e ^ (0.0375 x time)

In2 = 0.0375 x time

t = In2 / 0.0375

t= 18.5 years

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That statistic is based on a pinterest quote, the actual statistic is closer to 8-10%

Answer:

6.36 years (the .36 repeats), so rounded is 6.4.

Step-by-step explanation:

First, I'm going to convert all measurements to meters.

Since 1000 mm = 1 m, divide 44 by 1000.

44/1000 = 0.044 m

Since 100 cm = 1 m, divide 72 by 100.

72/100 = 0.72 m

Next, I'm going to setup an equation using y = mx + b.

b is the beginning amount which is 0.72.

m in the equation represents the rate which is 0.044.

y represents the total which is 1.

Plugin the numbers and solve for x.

1 = 0.044x + 0.72

1 - 0.72 = 0.044x + 0.72 - 0.72

0.28 = 0.044x

0.28/0.044 = 0.044x/0.044

6.36 = x

The given equation is equivalent to Option D .

The mission option is

A. x+10= x+10

B. x+9 =x² + 20x + 100

C. x² +81 = x² + 100

D. x² + 81 = x² +20x + 100

An equation is a mathematical statement formed when two algebraic expression is equated by an equal sign .

An equation is given in the question

[tex]\rm \sqrt{x^2 + 81} = x +10[/tex]

[tex]\rm {x^2 + 9^2} = (x +10)^2[/tex]

[tex]\rm {x^2 + 81} = x^2 +20x + 100[/tex]

Therefore the given equation is equivalent to Option D .

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The predicted number of plants with aphids is 109.

The predicted number of plants with aphids is the ratio of the random plants with aphids to total number of random plants selected multiplied by the number of plants in the nursery.

Predicted number = (7/50) x 780 = 109.

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A viable argument showing how it is reflected by the Cost Function for Wichita’s factory is; The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.

From the given options, the best statement is;

The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.

A cost function is a formula used to predict the cost that will be experienced at a certain activity level. Thus, the cost function for the best option is;

The cost of production per unit of item produced is 1$ as long as total units produced is less than 2500. If more than 2500 units are produced than the cost per unit actually comes down to 0.8$per unit.

The missing options are;

___ The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.

___ The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.

___ Overtime wages were required to produce at levels above 25,000 units.

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The area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.

A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.

We have given a rhombus with diagonals.

The length of the long diagonal p = 2×52 = 104 m

The length of the short diagonal q = 2×8 = 16 m

Area = pq/2 = (104×16)/2 = 832 square m

Thus, the area of the rhombus is 832 square m if the length of the diagonals are 104 m and 16 m.

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Answer:

SORRY I DONOT KNOW THE ANSWER

Step-by-step explanation:

i am sorry i do not know the amswer

Answer:

F(x) = (x+2)(-x+3)(x-2)^2. I think answer should be like this