A kinara is a candle holder used during Kwanzaa celebrations. The graph shows the
number of kinaras, rounded to the nearest 500, an online store sold each year for 15
years. A line of fit is drawn to show the trend of the data. What does the slope of the line
represent?

The required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 +  i√3,  -2 -  i√3

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

4x^3 + 16x^2 + 28x = 0

Taking x common we get,

x(4x^2 + 16x + 28) = 0

So, we get

x = 0

And 4x^2 + 16x + 28 = 0

or, x^2 + 4x + 7 = 0

Thus from the above equation is of the form

ax^2 + bx + c = 0

where, a = 1, b = 4 and c = 7

Therefore solution of the above equation is given as,

x = [-b ± √(b^2 - 4ac)] / 2a

Putting the values we get,

x = [-4 ± √(4^2 - 4*1*7)] / 2*1

so, x = [-4 ± √(16 - 28)] / 2

x = [-4 ± √(- 12)] / 2

x = [-4 ± 2√(- 3)] / 2

or, x = [-2 ± √(- 3)]

Since √-1 = i

∴ √(- 3) = i√3

Thus,

x = -2 ±  i√3

So, the required values of x are 0,  -2 +  i√3,  -2 -  i√3.

Thus, the required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 +  i√3,  -2 -  i√3.

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Answer:

Mathematics shaping the modern world.

Answer:

here is the answers

Step-by-step explanation:

sample:

1. 4x = 68

x = 68/4

x = 17

Solution :

1) x + 2x + x = 68

>> 4x = 68

>> x = 68 / 4

>> x = 17

2) x + y + 3y = 45

>> x + 4y = 45

>> 17 + 4y = 45

>> 4y = 45 - 17

>> 4y = 28

>> y = 28 / 4

>> y = 7

3) x + y - 4z = -32

>> 17 + 7 - 4z = -32

>> 24 - 4z = -32

>> -4z = -32 - 24

>> -4z = -56

>> z = 56 / 4

>> z = 14

4) x + y + z = ?

>> 17 + 7 + 14

>> 24 + 14

>> 38

5) -x + 8x = 63

>> 7x = 63

>> x = 63 / 7

>> x = 9

6) 4x + 3x - x = 42

>> 7x - x = 42

>> 6x = 42

>> x = 42 / 6

>> x = 7

The amount used in decimal is 1.50

The given parameters are

Cans = 2

Amount used = 6/4

The amount used in decimal is calculated as:

Amount used = 6/4

Divide 6 by 4

So, we have

Amount used = 1.50

Hence, the amount used in decimal is 1.50

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Answer:

x=19

Step-by-step explanation:

All of the angles add up to 180 degrees since it is a straight angle. So, the equation is:

3x+7+90+x+7=180

You combine like terms:

4x+104=180

Then you subtract on both sides:

4x=76

Then you divide by 4 on both sides:

x=19

The initial total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x will be 17371.

It should be noted that from the information, the total attendance at a science museum is modeled by the function

In this case, the total attendance when x=0 will be:

f(x) = 17,371(1.041)x.

f(x) = 17,371(1.041^0)

= 17371 × 1

= 17371

Therefore, the total attendance when x = 0 will be 17371.

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The value of the angle 16°43'27"is approximately 16.724167 degrees.

A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees.

To convert a degree from minutes and seconds to decimal we must know the relation between degree and minutes and seconds.

1 degree=60 minutes.

1 minute = 60 seconds.

The given angle is 16°43'27"

27 seconds = 27 ÷ 60 minutes = 0.45 minutes = 0.45 ÷ 60 degree =0.0075 degree

43 minutes= 43 ÷ 60 degree = 0.71666666..

Total angle in decimal = 16+0.71666666+0.0075 =16.7241666...

Therefore required angle ≈ 16.7241667 degrees.

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There is a real number whose product with every real number equals zero

a. Some real number has the property that its product with every real number equals 0.

b. There is a real number a such that the product of á and any real equals zero.

c. There is a real number á with the property that for every real number b, the product of a and b equals zero.

The value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4

In this question,

we have been given a function f(n) = f(n - 1) - 2

Also, we have been given the value of function f(n) for n = 1

i.e., f(1) = 6

We need to find the value of f(6).

For n = 2,

f(2) = f(2 - 1) - 2

f(2) = f(1) - 2

f(2) = 6 - 2

f(2) = 4

For n = 3,

f(3) = f(3 - 1) - 2

f(3) = f(2) - 2

f(3) = 4 - 2

f(3) = 2

For n = 4,

f(4) = f(4 - 1) - 2

f(4) = f(3) - 2

f(4) = 2 - 2

f(4) = 0

For n = 5,

f(5) = f(5 - 1) - 2

f(5) = f(4) - 2

f(5) = 0 - 2

f(5) = -2

For n = 6,

f(6) = f(6 - 1) - 2

f(6) = f(5) - 2

f(6) = -2 - 2

f(6) = -4

Therefore, the value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4

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Answer:

At 65mph the car traveled 195 miles in 3hrs.

So divide 195 miles by 80mph to get 2.4375 hrs

Answer: 2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3

Step-by-step explanation:

f(x)=2x^2-2

g(x)=x^2-3x

(f/g)(x)=

[tex]\frac{2x^2-2}{x^2-3x}[/tex]=

[tex]\frac{2x^2-6x+6x-2}{x^2-3x}[/tex]=

[tex]\frac{2x^2-6x+6x-2}{x^2-3x}[/tex]=

2+[tex]\frac{6x-2}{x^2-3x}[/tex]=2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3

The value of the function f(3) is 1

The graph represents the given parameter

The value of f(3) implies that we calculate the value of the function when x = 3

From the graph, we have

f(x) = 1, when x = 3

This means that

f(3) = 1

The above is calculated by substituting 3 for x in the equation f(x) = 1

Hence,  the value of f(3) is 1

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Answer:

Step-by-step explanation:

more taking a shower you use almost 3 gallons per a shower

Answer:

f(x) = [tex]{\displaystyle {\sqrt[8]{x}}}[/tex]

Step-by-step explanation:

If we let
[tex]g(x) = x^2 - 3\\\\\rm Then \;f(g(x) \;also \;written\; as\; (f\;\circ \rm \;g) \;is\; f(x^2 - 3)\\\\For\; this \;to \;be\; \sqrt[8]{x^2-3} , \\\\\rm f(x) \;has\;to\;be\;\sqrt[8]{x}[/tex]

Answer:

(r+21 ) / 4

Step-by-step explanation:

as we can see DF = FM
and DF = 4R ,  FM =r+21

so,
4R = r+21
=> R= (r+21)/4

The required simplification of the given expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex] is 1.

Given that,
To determine the simplified value of the expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
[tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex]
[tex]=\lim_{x \to \infty} \frac{x^2(1-4/x +4/x^2)}{x^2(1-4/x^2)}[/tex]
Now put limits, so 1 / x², 1 / x becomes zero so,
= 1

Thus, the required simplification of the given expression is 1.

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For the function f(x) =(4 sin x)/(1+cosx) , then f'(x) = 4/(1+cosx) using quotient rule of differentiation and f'(2) = 2.00

Quotient rule for differentiation states that the differentiation the division of two functions u, v is given as

(u/v)' = (u' v  - u v')/v² , where '  represents first derivative  with respect to independent variable

Given f(x) = (4sinx)/(1+cosx)

let u =4 sin x , v = 1+cos x , u'=4cos x , v' = -sin x

Then f(x) =u / v

Using quotient rule of differentiation:

f'(x) = ( u' v -u v' )/v² = (4cosx(1+cosx) +4sin²x )/(1+cos x)²

f'(x) = = 4(cos x +cos² x +sin² x)/(1+ cos x)² = 4(cos x +1)/(1+ cos x)²  

f'(x) = 4/(1+ cos x)

To find value of f'(x) at x= 2

f'(5) = 4/(1+cos2) = 2.000609= 2.00(rounding off )

Therefore if f(x) = (4x² tan x)/sec x  then f'(x) = 4/(1+cos x) and f'(2) =2.00

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The unit price of the pairs of padded will be $1.23 per pair. The error is the price of the pairs of pads should have been divided by 12.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

For $44.28 a contractor buys 3 dozen pairs of cushioned work gloves.

The unit price of the pairs of padded will be given as,

⇒ $44.28 / (12 x 3)

⇒ $1.23 per pair

The unit price of the pairs of padded will be $1.23 per pair.

The error is the price of the pairs of pads should have been divided by 12.

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The answer is (2) 2f-5=86; I hope- :\

Answer:

Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =85 \end{cases}\implies \begin{array}{llll} A=\cfrac{(85)\pi (10)^2}{360} \\\\\\ A=\cfrac{425\pi }{18}\implies A\approx 74.18~cm^2 \end{array}[/tex]

Answer: Answer choice 'B'

Step-by-step explanation:

4.00 + 0.75 + 0.40 + 0.03 = $5.18. This is Jill's amount.

3.00 + 0.40 + 0.02 = $3.42. This is Mark's amount.

To find out how much more money Jill has in comparison to how much mark has, we need to subtract Jill's money by Mark's money ($5.18 - $3.42)

if done correctly, your answer should be $1.76 (answer 'B')

The median is a better measure of center for the male's data, while the mean is a better for the female's data.

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

(a) The IQR of the male's data

From the given male's boxplot, we have the following data elements;

Upper quartile (Q3) = 14

Lower quartile (Q1) = 2

Then the IQR is calculated as:

IQR = Q3 - Q1

So, we have:

IQR = 14 - 2

IQR = 12

Hence, the IQR for the given males' data is 12

(b) The difference between the median values can be calculated as;

Median of male's data = 14

Median of female's data = 9

The difference (d) between the median values is;

d = 14 - 9

d = 5

Hence, the difference between the median values of each data set is 5

(c) The distribution of data

It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.

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The median is a better measure of center for the male's data, while the mean is a better for the female's data.

What are quartiles?

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

(a) The IQR of the male's data

From the given male's boxplot, we have the following data elements;

Upper quartile (Q3) = 14

Lower quartile (Q1) = 2

Then the IQR is calculated as:

IQR = Q3 - Q1

So, we have:

IQR = 14 - 2

IQR = 12

Hence, the IQR for the given males' data is 12

(b) The difference between the median values can be calculated as;

Median of male's data = 14

Median of female's data = 9

The difference (d) between the median values is;

d = 14 - 9

d = 5

Hence, the difference between the median values of each data set is 5

(c) The distribution of data

It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.

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The slope of  P=(-4,-1) Q=(-3,-3) is -2.

Given,

 P=(-4,-1)

Q=(-3,-3)

The  slope  between two points   P=(x₁, y₁)

Q=(x₂ ,y₂)

slope = (y₂-y₁)/(x₂-x₁)

So slope between  P=(-4,-1)   Q=(-3,-3) is

 [(-3)-(-1) ]/ [(-3)-(-4)]

=-2/1

=-2

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

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Month  Cost at Stack n’ Store   Cost at Smart Storage

1               $325                              $185

2              $475                                 $370

3               $625                                  $555

4               $775                                   $740

5                $925                                 $925

6                $1075                                $1100

The company that offers the better deal is Smart Storage.

After 5 months the cost would be the same at both storage companies.

The equation that represent the total cost of renting at Stack n’ Store is:

Total cost = non refundable deposit + charge per month

Total cost in the first month : $175 x ($150 x 1 ) = $325

Total cost in the second month : $175 x ($150 x 2 ) = $475

Total cost in the third month : $175 x ($150 x 3 ) = $625

Total cost in the fourth month : $175 x ($150 x 4) = $775

Total cost in the fifth month : $175 x ($150 x 5) = $925

Total cost in the sixth month : $175 x ($150 x 6) = $1075

The equation that represent the total cost of renting at Smart Storage is:

Total cost = cost per month x number of months

Total cost in the first month : $185 x 1 = $185

Total cost in the second month : $185 x 2 = $370

Total cost in the third month : $185 x 3 = $555

Total cost in the fourth month : $185 x 4 = $740

Total cost in the fifth month : $185 x 5 = $925

Total cost in the sixth month : $185 x 6 = $1,110

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Answer:

X= 1/y

Step-by-step explanation:

[tex]y = 1 - \frac{1}{ \sqrt{1} - \frac{1}{1 - x} } \\ y = 1 - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{ \frac{1 - x - 1}{1 - x} } \\ y - 1 = - \frac{1 - x}{ - x} \\ y - 1 = \frac{1 - x}{x} \\ yx - x = 1 - x \\ yx = 1 \\ x = \frac{1}{y} [/tex]

The vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).

Herein we find the expression of a quadratic equation in vertex form, whose definition is shown below:

4 · p · (y - k) = (x - h)²      (1)

Where:

h, k - Coordinates of the vertex.

p - Distance from the vertex to the focus.

Then, the vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).

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