solve the equation ab=bc for A, a, assuming that a, b, and c are square matrices and b is invertible.

Simplified form of the polynomial -4(2a+7)+3a+18 is -5a - 10. It is a binomial.

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given expression,

-4(2a+7)+3a+18

using distributive property

-4(2a) -4(7) + 3a + 18

-8a - 28 + 3a + 18

Solving like terms

-5a - 10

The solved polynomial is a binomial, since it has two terms.

Hence, simplified form of the given polynomial is -5a - 10, it is a binomial

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Product of multiplication of (2+√-25) and (4-√-100) is 58.

Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1).

For example, 6+7i is a complex number, where 6 is a real number and 7i is an imaginary number.

Given complex numbers

(2+√-25) and (4 -√-100)

√-25 = √(5² . -1) = 5√-1

i = √-1

√-25  = 5i

√-100 = √(10² . -1)

√-100 = 10i

Multiplying both numbers

(2+√-25) . (4 -√-100)

then

= (2 + 5i) . (4 - 10i)

Using FOIL method

(a + b)(c + d) = ac + ad + bc + bd

= 8 - 20i + 20i - 50i²

= 8 - 50i²

i² = -1

= 8 + 50

= 58

Hence, 58 is the product of multiplication of (2+√-25)(4-√-100)

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The population of the town after 10 years is expected to be about 12766

We can use the formula for exponential decay to find the population of the town after 10 years.

The formula is:

P = P₀ * (1 - r)^t

Substituting the given values into the formula, we get:

P = 25000 * (1 - 0.065)^10

Simplifying and evaluating using a calculator:

P = 12766

Hence, the population is expected to be about 12766 .

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The inequality that represents the number of streamers x and balloons y the student council can buy is given as follows:

3.50x + 0.75y ≤ 100.

Each streamer costs $3.50, hence the total cost of purchasing x streamers is given as follows:

3.5x.

Each balloon costs $0.75, hence the total cost of purchasing y balloons is given as follows:

0.75y.

Then the total cost of purchasing x streamers and y balloons is given as follows:

3.50x + 0.75y.

The amount spent can be of at most $100, hence the inequality is given as follows:

3.50x + 0.75y ≤ 100.

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Answer:

Step-by-step explanation:

To find the surface area of the silo, we need to calculate the areas of the cylinder and hemisphere separately, and then add them together.

The formula for the surface area of a cylinder is:

A_cylinder = 2πrh + 2πr^2

where r is the radius of the base of the cylinder, and h is the height of the cylinder.

In this case, r = 15 feet and h = 30 feet, so we have:

A_cylinder = 2π(15)(30) + 2π(15)^2

A_cylinder = 900π + 450π

A_cylinder = 1350π

The formula for the surface area of a hemisphere is:

A_hemisphere = 2πr^2

where r is the radius of the hemisphere.

In this case, the radius of the hemisphere is also 15 feet, so we have:

A_hemisphere = 2π(15)^2

A_hemisphere = 450π

To find the total surface area of the silo, we add the surface areas of the cylinder and hemisphere:

A_total = A_cylinder + A_hemisphere

A_total = 1350π + 450π

A_total = 1800π

Using 3.14 for π, we can approximate the total surface area as:

A_total ≈ 5652 square feet

Therefore, the farmer will need to cover approximately 5652 square feet of surface area to paint the outside of the silo.

To select a sample of 50 students at your school in order to learn something about how many hours per week, on average, students at your school spend engaged in a particular activity, you could use random sampling.

Random sampling involves selecting a sample of individuals from a larger population in a way that ensures each individual has an equal chance of being selected. This helps ensure that the sample is representative of the larger population and can provide accurate results.

Here are the steps you could follow to select a random sample of 50 students at your school:

1. Obtain a list of all the students at your school. This could be a roster or a directory.
2. Assign each student a unique number.
3. Use a random number generator to select 50 numbers from the list of student numbers.
4. Select the students whose numbers were chosen by the random number generator as your sample.

By following these steps, you can ensure that your sample is randomly selected and representative of the larger population of students at your school. This will allow you to accurately estimate how many hours per week, on average, students at your school spend engaged in a particular activity.

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Answer: 125.4

llllljkjkjkjkkjkjkjkjkjkkjkjjkjkjkjkjkjkjjkjkjkjkjkkjkjkjjkjkjjkjkjkjkjkjkjkjkjkjkjkjkjkjjkjkjkjkjkjkjkjkjkjkkjjkkjkjkjkjkkjkjkjkjkjkjjkjkkjkjkjkjkjkjkjkjkjkjkjkkjkjkjkjkjkjkjkjkj

Answer:

Step-by-step explanation:1/9

Answer: The original price of the lawn mower was $649

Step-by-step explanation:

If Joaquin bought the lawn mower for $519.20 after a 20% discount, it means that he paid only 80% of the original price. We can use this information to calculate the original price of the mower by setting up the following equation:

0.8x = 519.20

where x is the original price of the lawn mower. To solve for x, we can divide both sides of the equation by 0.8:

x = 519.20 / 0.8

x = $649

The relative frequency is the proportion of the total numbers in a data set corresponds to a specific class interval and hence summing over all the relative frequencies must add up to 1, or 100%.

The frequency distribution table is made by building the class intervals of the raw data set, specifically when too many values are occurring many times; we group similar values in the same category, according to a pre-determined range of values. It is a two-column table in which the first column consists of class intervals and the second consists of the frequency corresponding to each interval.

The frequency distribution is made when the raw data is large and when the same number is repeated many times, that is where the concept of frequency comes into play.

Since, the frequency is the count of specific numbers in a data set, the sum of all frequencies corresponding to every class interval has to be the total number of values in the data set.

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The given question is incomplete, complete question is:

What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?

The simplification process of the expression 6(4y+8)−2y involves distributing '6' to '4y' and '8', and then combining like terms, yielding the simplified expression as 22y+48.

To rewrite the given expression in simplest terms, distribute the 6 to the terms inside the parentheses:

Now subtract 2y:

So, the expression 6(4y+8)−2y can be simplified to 22y + 48.

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The nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.

The nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr. To calculate the infusion rate, you can use the formula:

Infusion rate (mL/hr) = Volume to be infused (mL) / Infusion time (hr)

In this case, the volume to be infused is 750 mL and the infusion time is 6 hr. Plugging these values into the formula, we get:

Infusion rate (mL/hr) = 750 mL / 6 hr = 125 mL/hr

Therefore, the nurse should set the IV pump to deliver 125 mL/hr in order to administer the D5W 750 mL IV over 6 hr.

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Answer: You sold 16 bracelets and 21 necklaces

Step-by-step explanation

X# Bracelets        x+y=37     -2(x+y=37)     -2x-2y= -74      x+21=37

Y# Necklaces      2x+3y=95     [tex]\frac{+(2x+3y=95)}{y=21}[/tex]          x=16

              You sold 16 bracelets and 21 Necklaces

Answer:





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Class 11

>>Applied Mathematics

>>Number theory

>>Complex Numbers

>>The complex number z satisfying the equa

Question



The complex number z satisfying the equations ∣z∣−4=∣z−i∣−∣z+5i∣=0, is

This question has multiple correct options

A

3−i

B

23−2i

C

−23−2i

D

0

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Updated on : 2022-09-05

Solution



Verified by Toppr

Correct options are B) and C)

We have two equation ∣z∣−4=0 and ∣z−i∣−∣z+5i∣=0

Putting z=x+iy i.e x2+y2=16    ....(1)

and ∣x+iy−i∣=∣x+iy+5i∣

⇒x2+(y−1)2=x2+(y+5)2

⇒y=−2   ...(2)

Putting y=−2 in (1), 

x2+4=16⇒x=±2

Step-by-step explanation:

Hence the complex numbers z satisfying the given equation are 

z1=23−2i and z2=−23−2i

Answer:

21

Step-by-step explanation:

21

Answer:

3x - y - 2 = 0

Step-by-step explanation:

The line-3x - 9y - 12 is given in the general form of the equation of a line, Ax + By + C = 0, where A = -3, B = -9, and C = -12.

To find the equation of the line that passes through the point (2, -8) and is perpendicular to the line-3x - 9y - 12, we need to find the slope of the perpendicular line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.

The slope of the line-3x - 9y - 12 can be found using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Rearranging the general form equation:

-3x - 9y - 12 = 0

9y = 3x + 12

y = (3/9)x + 4

The slope of the line is m = 3/9. To find the slope of the perpendicular line, we find the negative reciprocal:

m_perpendicular = -1 / (3/9) = -9 / 3

We have the slope of the perpendicular line, now we need to find its equation. To do this, we use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is the point through which the line passes and m is the slope of the line. Plugging in the values for the point (2, -8) and the slope -9/3:

y - (-8) = -9/3 (x - 2)

y + 8 = -3x + 6

3x - y - 2 = 0

Using the secant-secant and tangent-secant formulas, the indicated measures are:

1. x = 1

2. y = 10.

3. SU = 30

4. x = 4

5. x = 1

6. CD = 12

The secant-secant and tangent-secant formulas relates the lengths of the segments formed when two secants or a secant and a tangent intersect outside a circle.

Using the formula, we can solve for the indicated measures as explained below.

1. To find x, apply the secant-secant formula:

(7 + 17) * 7 = (13x + 8x) * 8x

168 = 168x²

168/168 = 168x²/168

1 = x²

x = 1

2. To find y, apply the tangent-secant formula:

20² = y * (y + 30)

400 = y² + 30y

y² + 30y - 400 = 0

Factorize:

(y - 10)(y + 40) = 0

y = 10 or y = -40

y cannot be negative so, y = 10.

3. Apply the secant-secant formula to find the value of x:

(x + 10 + 9) * 9 = (x + 6 + 10) * 10

(x + 19) * 9 = (x + 16) * 10

9x + 171 = 10x + 160

9x - 10x = -171 + 160

-x = -11

x = 11

SU = x + 19 = 11 + 19

SU = 30

4. Apply the tangent-secant formula:

6² = x(x + 5)

36 = x² + 5x

x² + 5x - 36 = 0

Factorize:

(x - 4)(x + 9) = 0

x = 4 or x = -9

x must be positive, therefore, x = 4

5. Apply the secant-secant formula to find x:

18*10 = 20x * 9x

180 = 180x²

1 = x

x = 1

6. Apply the tangent-secant formula:

AB² = (CD + AC) * AC

Substitute the values:

8² = (CD + 4) * 4

64 = 4CD + 16

64 - 16 = 4CD

48 = 4CD

48/4 = CD

12 = CD

CD = 12

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The coordinates of P are (-0.82, 3.56).

The coordinates of M are (-2.1, -2.2).

The midpoint of a line segment is written as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) are the coordinates of the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

R = (4.3, 7.4)

T= (-8.5, -2.2)

S = (4.3, -2.2)

Segment RT is divided into 5 equal parts.

So,

TP : PR = 3 : 2 = m : n

The coordinates of P.

T= (-8.5, -2.2) = (a, b)

R = (4.3, 7.4) = (c, d)

x = [tex]\frac{mc + na}{m + n}[/tex]

x = [tex]\frac{3\times4.3 + 2\times-8.50}{5}[/tex]

x = [tex]\frac{12.9 - 17}{5}[/tex]

x = [tex]\frac{-4.1}{5}[/tex]

x = -0.82

And,

y = [tex]\frac{md + nb}{m + n}[/tex]

y = [tex]\frac{3\times7.4 + 2\times-2.2}{5}[/tex]

y = [tex]\frac{22.2 - 4.4}{5}[/tex]

y = 3.56

The coordinates of P are (-0.82, 3.56).

Now,

T= (-8.5, -2.2)

S = (4.3, -2.2)

M is the midpoint of TS.

So,

M = (x, y)

x = [tex]\frac{(4.3 - 8.5)}{2}[/tex] = [tex]\frac{x-4.2}{2}[/tex] = -2.1

y = [tex]\frac{-2.2 - 2.2}{2}[/tex] = [tex]\frac{-4.4}{2}[/tex] = -2.2

M = (x, y) = (-2.1, -2.2)

Thus,

The coordinates of P = (-0.82, 3.56).

The coordinates of M = (-2.1, -2.2).

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Answer:

The answer is (-3.38,1.64),(-0.82,-2.2)

Step-by-step explanation:

I just got it right on the test

Answer:

51,300 rupees

Step-by-step explanation:

Surface area of the 2 short walls = 2 x 30 x 2.5 = 150

Surface area of the 2 long walls = 2 x 50 x 2.5 = 250

Surface area of the floor = 50 x 30 = 1500

Total surface area = 150 + 250 + 1500 = 1900 m²

27 rupees/m² x 1900 m² = 51300 rupees

The method that can be used to prove that the triangles are congruent is B. AAS.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

There are two angles in the two triangles that are shown to be equal and there is also a side of one triangle that is equal to anther side. These triangles are therefore congruent.

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Answer:

$1,489.88 (nearest cent)

Step-by-step explanation:

To calculate gross pay, multiply the number of hours worked by the pay per hour.

Warren worked 36.5 hours one week and 32 hours the week before.

Therefore, the total number of hours Warren worked was:

Multiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:

Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).

Answer:

$1489.875

Step-by-step explanation:

Warren's gross pay for 36.5 hours last week can be calculated as follows:

Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875

Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:

Gross pay for 32 hours = $21.75/hour * 32 hours = $696

Adding the gross pay for the two weeks, we get:

Gross pay for 2 weeks = $793.875 + $696 = $1489.875

The expression (4a³b^4)³ when evaluated is 64a^9b^12

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

(4a³b^4)³

When expanded, we have

(4a³b^4)³ = 4³ * (a³)³ * (b^4)³

Evaluate the exponents

So, we have the following representation

(4a³b^4)³ = 64a^9b^12

Hence, the solution si 64a^9b^12

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Step-by-step explanation:

Nuclear: 6-20 cents per kWh

Coal: 5-17 cents per kWh

Gas: 5-15 cents per kWh

Wind: 2-9 cents per kWh

Hydro: 5-20 cents per kWh

Solar: 10-20 cents per kWh

The length of paper he used for wrapping paper is, 702 meters²

Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.

To calculate the amount of wrapping paper needed, we need to find the total surface area of the gift box. The surface area of a right rectangular prism is given by the formula:

surface area = 2(lw + wh + lh)

where l, w, and h are the length, width, and height of the prism, respectively.

In this case, the dimensions of the gift box are 9 meters, 9 meters, and 15 meters, so:

surface area = 2(9 x 9 + 9 x 15 + 15 x 9)

                     = 2(81 + 135 + 135)

                     = 2(351)

                     = 702 square meters

Therefore, Lavaughn used 702 square meters of wrapping paper for the gift box.

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Answer:

50%

12.5%

1%

10%

37.5%

87%

Answer:

27)50%

28)12.5%

29)1%

30)10%

31)38.4%

32)87%

your question is incomplete!

The reflex of angle A is 295 therefore, angle B is 295°

A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.

Given that angle B is the reflex angle of angle A, angle is measuring 65°

We need to find the measure of reflex Angle B

We know that,

To find the reflex angle of a given angle, we need to subtract the given measure from 360 degrees.

For example, the reflex angle of 110 degrees = 360 – 110 = 250.

Therefore,

Reflex Angle B = 360° - 65° = 295°

Hence, the reflex of angle A is 295 therefore, angle B is 295°

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