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The mathematician Girolamo Cardano is credited with the first use of negative square roots in solving the now-famous problem, "Find two numbers whose sum is 10 and whose product is 40. Show that the complex numbers 5 + iv15 and
5 - i~15 satisfy the conditions of the problem.

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the equation of the required line is 3xâ2y+1=3x1â2y1+1.

(i) We are given the parallel line of the given equation, that is yâ2x=0.

So, the equation of the required line will be yâ2x=c, where c is a constant.

Let the point of intersection of the two lines be (x1, y1).

Then, substituting the values of x1 and y1 in the equation yâ2x=c, we get

y1â2x1=c

or, c=y1â2x1

Hence, the equation of the required line is yâ2x=y1â2x1.

(ii) We are given the perpendicular line of the given equation, that is 2x+yâ5=0.

So, the equation of the required line will be 3xâ2y+1=c, where c is a constant.

Let the point of intersection of the two lines be (x1, y1).

Then, substituting the values of x1 and y1 in the equation 3xâ2y+1=c, we get

3x1â2y1+1=c

or, c=3x1â2y1+1

Hence, the equation of the required line is 3xâ2y+1=3x1â2y1+1.

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The position of the value is shown on the number line attached to this answer.

A number line is a ray which extends from -∞ to +∞ as its two extreme ends. Thus all number fall within this range such that all directed numbers can be located on the number line.

A directed number is a any number which has either a positive or negative sign. This implies that the position of all numbers can be shown on the line.

Thus, from the question to show 2/3 of 4 on the number line;

2/3 of 4 = 2/3 x 4

             = 8/ 3

             = 2 2/3

The position of 2 2/3 is shown on the number line attached to this answer.

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After divide, the value of quotient is 0.133.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ 10 divided by 75.10.

Now, We get;

⇒ 10 divided by 75.10

⇒ 10 ÷ 75.10

⇒ 0.133

Thus, The value of quotient after divide = 0.133

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Answer:

A

Step-by-step explanation:

this is a college level question ? oh my ...

to get the total area we need to add the area of the rectangle and the area of the half-circle.

the area of the rectangle is

length × width = 15 × 5 = 75 ft²

the area of the half-circle is

pi×r² / 2

how do we get r (radius) ?

we know, both lengths of the rectangle must be equally long. so, 15 ft.

we see that the remaining length after the half-circle is 9 ft.

so, the diameter of the half-circle is 15 - 9 = 6 ft.

the radius is half the diameter, so r = 6/2 = 3 ft.

the area is therefore

pi×3² / 2 = 9pi /2 = 14.13716694... ft²

in total that makes

75 + 14.13716694... = 89.13716694... ft²

the closest of your answer options is A : 88 ft²

There is a need for infection control risk assessment is correct statements.

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The standard deviation of the data is  2.41 smartphones.

Data refers to the elements that make up persons, things, events, and ideas. It could be an integer, a title, or anycast. Data must be tabulated after collection in order to study their prominent characteristics. The presentation of data is the name given to such a configuration.

Bar Chart, Histogram, Line Graph, Pie Chart, Frequency Distribution Table.

Given, The number of smartphones sold at an electronic store each day

is represented by the table with two columns and 5 rows.

The mean of the data set is,

= (8 + 13 + 12 + 10 + 15)/5.

= 11.6.

We know the formula for the standard deviation of a data set is,

= [tex]\frac{1}{\sqrt{n}}\sqrt{\sum_{i =1}^{n} (x_i - \overline{x}{}})^2[/tex].

= (1/√5)×√[(-3.6)² + (-1.4)² + (-0.4)² + (-1.6)² +(-3.4)²].

= (1/√5)×[√29.2].

= 2.41.

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Answer:

2.7 Smartphones

Step-by-step explanation: Just did it

The mean birthweight of the obstetrician's own patients is higher than the national mean.

In the first description, 84% is a parameter, since it describes the population as a whole. The survey of 100 residents in Pleasant Valley yields a statistic of 75%, since it is a sample of the population.

In the second description, the mean birthweight of infants in the United States in 2006 of 3.3 kg and the standard deviation of 0.57 kg are both parameters. The mean birthweight of the obstetrician's own patients of 3.6 kg is a statistic. To calculate the difference between the two means, we can subtract the two values: 3.6 kg - 3.3 kg = 0.3 kg. This 0.3 kg difference indicates that the mean birthweight of the obstetrician's own patients is higher than the national mean.

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Answer:

Step-by-step explanation:

Quarter implies 4. If there were 20 items, and you broke them into quarters, each quarter would have 5 items.

The comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.

Suppose that [tex]$\sum_{n=1}^{\infty} a_{n}$ and $\sum_{n=1}^{\infty} b_{n}$[/tex] are series with positive terms. We assume that does not exist and that [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex]diverges.

To prove that [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] also diverges, we will use the comparison test. Since [tex]$\sum_{n=1}^{\infty} b_{n}$[/tex] diverges, we can find a number M such that [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges. Since [tex]$\lim_{n\rightarrow \infty} \frac{a_{n}}{b_{n}}$[/tex] does not exist, we can find a number N such that for all [tex]$n \geq N$, $\frac{a_{n}}{b_{n}} > 1$[/tex].

Now, for any [tex]$n \geq \max \{M,N\}$[/tex], we have [tex]$\frac{a_{n}}{b_{n}} > 1$[/tex]. Thus, [tex]$a_{n} > b_{n}$[/tex]. By the comparison test, [tex]$\sum_{n=1}^{\infty} a_{n}$[/tex] diverges since [tex]$\sum_{n=M}^{\infty} b_{n}$[/tex] diverges.If the ratio of two series with positive terms,[tex]$\sum_{n=1}^{\infty}a_n$[/tex]  and [tex]$\sum_{n=1}^{\infty}b_n$[/tex], does not converge to a limit as n approaches infinity and [tex]$\sum_{n=1}^{\infty}b_n$[/tex] diverges, then [tex]$\sum_{n=1}^{\infty}a_n$[/tex] must also diverge.

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Answer:

87 degrees

ADE ~ ACB (AB is twice the length of AE, AC is twice of AD, CAB and DAE common angle)

So AED and ABC should be equal

11x-2=6x+13

5x=15

x=3

Angle ABC will equal:

6(3)+13= 31 degrees

ACB = 180-31-62

ACB = 87 degrees

An equivalent boolean algebra expression for a circuit with 2 inputs a and b is q = (a XOR b)

One way to represent this circuit using Boolean algebra is to use the logical operators AND, OR, and NOT.

The output of the circuit, q, is true when less than two inputs, a, and b, are true. This can be represented as:

q = (NOT(a) AND NOT(b)) OR (NOT(a) AND b) OR (a AND NOT(b))

This can also be represented using the XOR operator (Exclusive OR) which output is true if one and only one input is true:

q = (a XOR b)

Another equivalent representation can be achieved by using the NOR operator which gives true only when none of the inputs is true:

q = NOT( a NOR b)

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The measures of central tendency are Mean: 22.14, Median: 22.00, Mode: 22.00, and dispersion are Range: 32, Variance: 183.14, Standard deviation: 13.53 Interquartile range: 12.00

According to the question

The mean, median, and mode values for this collection of data are 22, 14, and 22, respectively. The median is the midway value when the data are arranged, while the mode is the value that occurs the most frequently. The mean is the average of the data set. Range = 32, Variance = 183.14, Standard deviation = 13.53, and Interquartile Range = 12.00 are the metrics of dispersion for this data set. The variance measures the spread of the data, the standard deviation is the square root of the variance, and the interquartile range is the difference between the median of the upper half and the median of the lower half of the dataset. The range is the difference between the highest and lowest values.

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The value of x in the angles is 10.

The sum of the measures of angle S and angle T is 120 degrees. Therefore, the measure of the angles are as follows:

Therefore, the value of a can be found as follows;

∠S + ∠T = 120

∠S = 8x + 5  degrees

∠T = 35 degrees

Therefore,

8x + 5 + 35 = 120

8x + 40 = 120

8x  = 120 - 40

8x = 80

divide both sides by 8

x = 80 / 8

x = 10

Therefore,

x = 10

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Answer:

40

Step-by-step explanation:

c= 5*(104-32)/9 =40

The magnitude of the electric flux through the sheet will be 6.1 N.m²/C.

What is Electric flux?

The amount of electric lines of force (or electric field lines), which cross a specific area, is referred to as electric flux, a feature of an electric field. According to this theory, electric field lines begin with positive electric charges and end with negative charges.

The following formula can be used to get the electric flux:

∅ = EAcosФ

where,

∅ = Electric flux

E is the Electric field which is 73.9 N/C.

A is Area of the plate which is =  (0.4 m)(0.6 m) = 0.24 m²

θ is the angle between normal to the area and electric field lines = 90° - 20° = 70°.

Putting these values in our formula, we get:

∅ = (73.9)(0.24)cos(70°)

∅ = 6.1 N.[tex]m^{2}[/tex]/c.

Therefore the Magnitude of the electric flux through the sheet is 6.1 N.m²/C.

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Answer:

18.

3.25

19.

3.125

20.

-26.36

Step-by-step explanation:

Answer: 35/4 or 8.75 or 8 3/4

Step-by-step explanation:

First, you start by multiplying the minus sign by the parenthesis.

you multiply a negative sign by a negative sign so it cancels out into a positive one.

Then it will be -3 1/2 + 12 1/4. Change the denominator to do both 4, so we can solve the equation.

-3 2/4 + 12 1/4. That will equal 8 3/4 or 35/4.

The answer is 8 3/4 or 35/4.

The period that it would take the Dog to finish the remaining food would be a period of 12.5 weeks

The amount that the dog eats weekly is given as 1 / 20 of the food.

The amount that Lian has left in the bag is given as 5 / 8

To get the number of weeks that it would take to finish the food, we would divide 1 / 20  by 5 / 8

1 / 20 ÷ 5 / 8

20 / 1 * 5 / 8

= 100 / 8

= 12.5

Hence it would take 12.5 weeks for the dog to finish the remaining food here.

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'Lian's dog eats 1/20 of a bag of dog food each week. Lian currently has 5/8 of a bag remaining.How many weeks will it take Lian's dog to finish this remaining food?weeksStuck?

Answer:

the third one.

Step-by-step explanation:

clockwise rotation of 90*

Answer:

clockwise rotation of 90 degrees

Step-by-step explanation:

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The percentage change from 20 to 14 is 30% decrease

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

20 to 14

The final value (14) is less than the initial value (20)

So, the change is a percentage decrease

The change is then calculated as

Change = (Final value - Initial value)/Initial value * 100%

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

Change = (14 - 20)/20 * 100%

Evaluate

Change = -30%

Hence, the percentage decrease is 30%

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The solution matrix x is [-15 15].

Without any additional information, matrix representations of linear mappings allow for explicit computations in linear algebra.

We can use the properties of matrices and vectors to simplify the equation.

First, we know that Au = a and Av = b, so we can substitute these equations into our original equation:

Ax = -5Au + 5Av

Now we can substitute in the values of u and v that we know:

Ax = -5[3 -3] + 5[-5 3]

Which simplifies to:

Ax = [-15 15]

So x = [-15 15] is a solution to the equation Ax = -5a + 5b.

Correct question :

Let A be a 3x2 matrix. Suppose we know that u = [3 -3] and v = [-5 3] satisfy the equations Au = a and Av = b. Find a solution matrix x to Ax = -5 a + 5 b.

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The charge of each company will be the same at 40 miles.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let us suppose the miles travelled as x.

Given that:

Cassandra's Car Rentals charges $.10 per mile with a service fee of $40.00, this is represented as:

C = 0.10(x) + 40

Carnuba's Car rental charges $.15 per mile and has a service of $20.

D = 0.15(x) + 20

The charge of both the companies would be equal when C = D:

0.10(x) + 40 = 0.15(x) + 20

40 -20 = 0.15x = 0.10x

20 = 0.5x

x = 20/ 0.5

x = 40

Hence, the charge of each company will be the same at 40 miles.

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1)Therefore the wing area is determined as 5511 ft2 2) The elliptic chord length is 35.87 f t 3) The Reynolds number for the given elliptical wing is 1.672 X 10^8 4) So, the speed of the plane is 733.33 f t/s.

1) Wing Area  

Wing Area determined by using the wingspan and aspect ratio of the Boeing. Where the Aspect ratio of the wing written as,
AR=S^ 2/A
Here s is the wingspan, A is the Wing area and AR is the Aspect ratio.
A=S^ 2/AR=195.7^ 2/6.5=5510.57 FT^ 2
Therefore the wing area is determined as 5511 ft2


2) Average Elliptical chord

Elliptic chord of the Boeing wing determined by the elliptical wing Aspect
ratio,
AR=4xspan/π x chord
chord=4x span/π x AR
chord=4x 195.7/πx6.95=35.87f t
Therefore, the elliptic chord length is determined as35.87 f t


3) Reynolds Number
Reynolds number for the given wing is determined by the average speed and the average chord length
Re=9324xVxc
Here V is the average speed and c is the chord length using the determined values we can find the Reynolds number as,
Re=9324x500x35.87=1.67225x10^ 8
Therefore, the Reynolds number for the given elliptical wing is 1.672 X 10^8


4) Cruise Speed

Where the Speed of the cruise is given as 500 mph to convert the speed mph into the f t/s,
Speed=500x5280/3600=733.33 f t/s
Here 1 mile = 5280 f t and 1 hour = 3600 seconds

So, the speed of the plane is determined in the f t/s as 733.33 f t/s.

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Hey there!

Answers;

For part (a):

[tex]v=669,883[/tex]  [tex]miles/day[/tex]

[tex]r=44,423[/tex] [tex]miles[/tex]

[tex](a)V=rw[/tex]

[tex]w=\frac{v}{r}[/tex] [tex]=\frac{669883}{44423}[/tex][tex]=15.0796[/tex] [tex]radians/day[/tex]

[tex]15[/tex] [tex]radians/day[/tex]

For part (b):

[tex]Circumference=2\pi r[/tex]

[tex]2*3.14*44423[/tex]

[tex]278976*44[/tex]

Number of rotations = [tex]\frac{669883}{278976*44}[/tex] =  [tex]2*40[/tex] ⊥ ≈ [tex]2[/tex]

Hence:

(a) [tex]15[/tex] [tex]radiations/day[/tex]

(b) Number of rotations = [tex]2[/tex]

___________________________________________

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Answer: THE CORRECT ANSWER IS 30  

Step-by-step explanation:

The congruence theorems used in this problem are given as follows:

9. AAS.

10. SAS.

11. Not similar.

12. SSS.

For item 9, the AAS theorem is used, as the two angles, the 72º and the vertical angle, are congruent, along with the another side.

For the item 10, we have that the SAS theorem is used, as we have that the sides between the same angle are proportional.

For item 11, the triangles are not similar, as the side lengths are not proportional.

For item 12, the SSS theorem is used, as the three angles of the similar triangles have the same measure.

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Answer:hewwo

Step-by-step explanation:hewwo

Answer: The answer is b and c

Step-by-step explanation:

15 divided by eight and seven fifty eight thousandths will give a quotient of one and seven hundred and three thousandths

One of the four fundamental operations, along with addition, subtraction, and multiplication, is division. A number is split using the straightforward method of division.

The division (/) operator creates the product of its operands, where the dividend is the left operand and the divisor is the right operand.

In the problem written the words the division is done by writing in figure as below

15 ÷ 8.758

Using calculator the quotient is 1.7127 = 1.713 to the nearest thousandth

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The population after 12 years is 98448 and the formula is[tex]P(t) = 25000(1.121)^{t}[/tex].

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the population of the town is 25000 and increasing at the rate of 1.121.

The expression will be written as:-

[tex]P(t) = 25000(1.121)^{t}[/tex]

[tex]P(12) = 25000(1.121)^{12}[/tex]

P(12) = 98448

Hence, the population after 12 years will be 98448.

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