what is the non real complex solutions of this equation: x^2-4x+20=0

Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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Answer:

The probability is 0.33

Step-by-step explanation:

Please find the attachment for detail

Answer:

the answer to the problem is -1/4

Answer:

\(-7y\)

Step-by-step explanation:

Our equation is:

\(\left(1x-5y\right)-1\left(x+2y\right)\)

First we dritribute

Now we have, \(x-5y-x-2y\)

\(Combine\) light terms

and we get \(-7y\)

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The true statement, regarding the signal of the graphed function, is given by:

F(x) > 0 over the interval (–∞, –4).

Looking at it's graph, we have that:

Researching this problem on the internet and looking at the graph of the function, the function is negative for all values to the right of x = -4,  and positive to the left, hence the correct statement is given by:

F(x) > 0 over the interval (–∞, –4).

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Answer:

y=1/5x+11/5

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  y-y^1=m(x-x^1) to find line parallel to -x+5y=1

Hope this helps

Answer: y = 1/5x+ 2.2

Step-by-step explanation:

First, change the expression into y-intercept form

-x+5y=1

5y=x+1

y=1/5x+1/5

For a line to be parallel to another line, it must have the same slope.  Thus, the slope must be 1/5x.  Then, to find the y-intercept simply do:

y = 1/5x+b, where x = -1 and y = 2

2=1/5(-1)+b

2 = -1/5+b

b = 2 1/5.

Thus, the equation y = 1/5x+ 2.2

Hope it helps <3

Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

Answer:

The opposite or absolute value is 5.2

Answer:

The length of a 180° arc of a unit circle is π ≈ 3.14 units.

Step-by-step explanation:

Use your knowledge of the circumference of a circle (the length full around) and the fact that there are 360° in the central angle of a full circle. The distance around is proportional to the angle, so an arc of measure 180° will have a length equal to

... (180°/360°) × circumference = (1/2)×circumference

For a unit circle, the circumference is 2π (= π×diameter = 2π×radius). Half that length is π units.

Answer:

I can't give a "smart" explanation but the answer is D) 3.14 units

Answer:

D

Step-by-step explanation:

The cost of each pound of grass seed is $6.

A graph of the solution for the cost of each pound of grass seed is shown below.

In order to determine the cost of each pound of grass seed, we would assign a variable to the cost of each pound of grass seed and then translate the word problem into an algebraic linear equation.

Let the variable x represent the cost of each pound of grass seed.

Since Lori bought 3.6 pounds of grass seed and she was charged $22.90, including a tax of $1.30, an algebraic linear equation that best represent this situation is given by;

3.6x + 1.30 = 22.90

3.6x = 22.90 - 1.30

3.6x = 21.60

x = 21.60/3.6

x = $6.

In conclusion, we would sue an online graphing calculator to plot the solution for the cost of each pound of grass seed as shown in the image attached below.

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The sector areas of the grey and white areas are 159.09 in² and 41.87 in²

From the question, we have the following parameters that can be used in our computation:

The area of shaded sector is calculated as

Area = Central angle/360 * π * Radius^2

Substitute the known values in the above equation, so, we have the following representation

Hence, the area is 159.09

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Answer: The best problem solving strategy to solve this problem with is a formula. Additionally Brandon had $12.50 before going to the store.

Step-by-step explanation: Formula and Solving it

He Spent $2.50 on pencils.

Amount left after buying a pencil = x - 2.50

Next, he spent half of the amount left in his pocket.

He spent (x - 2.50)/2 on notebook and paper.

So the total amount he spent = 2.50 + (x -2.50)/2

Amount left when he got home =$ 5.00

That means, x - Total amount spent = 5

=> x - (2.50 + (x -2.50)/2 ) = 5

=> x - 2.50 -x/2 + 2.50/2 = 5

=> x/2 - 2.50/2 = 5

=> x/2 = 5 + 2.50/2

=> x/2 = 6.25

=>x = $12.5

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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Answer:

4, -4, 36

Step-by-step explanation:

a) a*2 = -2*-2 = 4

b) a^2 = -2^2 = -4

c) a*3^2= 3*-2^2 = -36

The correct option is option C.

T(x) = 2.9(1.05)⁴ˣ ⁺ ⁵

Given the number of cities in a region is represented by the function:

C(x) = 2.9(1.05)ˣ

The approximate number of people per city is represented by the function P(x) = (1.05)³ˣ⁺⁵

we are asked to determine T(x), the approximate population in the region = ?

combine C(x) and P(x)

therefore, T(x) = C(x)P(x)

T(x) = 2.9(1.05)ˣ(1.05)³ˣ⁺⁵

During multiplication, when bases are same then powers are added.

T(x) = 2.9(1.05)³ˣ⁺ˣ⁺⁵

T(x) = 2.9(1.05)⁴ˣ⁺⁵

Hence we get the approximate function of T(x) as T(x) = 2.9(1.05)⁴ˣ⁺⁵

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Answer:

3 hr(s)

Step-by-step explanation:

20 km/1 hour

60km/20km = 3

Answer:

Incomplete question, but I gave a guide to solve using the Empirical Rule.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

It is also important to note that the normal distribution is symmetric. This means of the 68% of the measures are within 1 standard deviation of the mean, for example, 68/2 = 34% are between 1 standard deviation below the mean and the mean, and 34% are between the mean and 1 standard deviation above the mean.

In this question:

You take the mean and the standard deviation. Then you take both bounds that the percentage asks, and see how many standard deviations each are from the mean, and you then use the empirical rule to solve.

Around 0.000125 or 0.0125% of the time, the song will be played exactly six out of seven days.

Every day represents a trial in this binomial probability issue, and there are only two potential results:

either the music is played (a success), or it is not (failure). We're looking for the likelihood that exactly 6 out of 7 trials will be successful.

The likelihood of success (performing the song) is 1/6, while the likelihood of failure (not playing the song) is 1 - 1/6 = 5/6, on any given day.

We can use the binomial probability formula to find the probability of exactly 6 successes in 7 trials:

P(6 successes) = (7 choose 6) * (1/6)⁶ * (5/6)¹

where (7 choose 6) is the number of ways to choose 6 days out of 7 to play the song, and is calculated as:

(7 choose 6) = 7! / (6! * 1!) = 7

Plugging in the values, we get:

P(6 successes) = 7 * (1/6)⁶ * (5/6)¹

P(6 successes) ≈0.00012502

Therefore, the probability that the song will be played on exactly 6 days out of 7 is approximately 0.000125 or 0.0125%.

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Answer:

option no. D

Step-by-step explanation:

i+34j+14k

hope it helps

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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Answer:

Step-by-step explanation:

X=25°

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

You can never achieve break even by selling any number of boxes of candy if it costs them an additional $3 to manufacture each box of candy.

In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even."

Although these opportunity costs have been paid and then capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."

Fixed cost (in manufacturing) = $500

Manufacturing cost of each candy = $3

and selling price of candy = $3

let x be a box of candy sold,

hence for no of box to be sold for a break even,

3x + 500 = 3x

but if you see above equation, that has no solution

Hence by providing each candy at $3 with $500 fixed cost and selling cost again at $3 you cannot achieve a break-even point.

hence there is no solution, and you will never be able to achieve break even.

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Answer: is A

Step-by-step explanation:

Step-by-step explanation:

there is nothing missing. this is a complete proof.

yes, the various steps are correct.