Simplify the expression to a + bi form:
(3+10i)-(-12-8i)

Answer:

Step-by-step explanation:

the lateral area of the drawing the lateral area of the drawing is 40 mi2. Area rectangle = w * l 5 * 2 = 10 mi² (area 1 rectangle) then you multiply by 4 10 * 4 = 40 mi² or 5 * 2 * 4 = 40 mi²

Answer:

  294 m²

Step-by-step explanation:

You want the lateral area of a regular hexagonal prism with side lengths 7 m and height 7 m.

The lateral area is the sum of the areas of the 6 square faces.

Each of the 6 faces is a square 7 m on the edge. Its area is ...

  (7 m)² = 49 m²

There are 6 of these square faces, so their total area is ...

  6 × 49 m² = 294 m²

The lateral area of the prism is 294 m².

The option that applies to 2cos(x)+sqrt2=0 less than x less than 2pi is options C and D:

c.5pi/4

d.7pi/4

To solve this equation, we can start by isolating the cosine term on one side of the equation:

[tex]2cos(x) = -\sqrt{2[/tex]

[tex]cos(x) = \sqrt{\frac{2}{2} } }[/tex]

The cosine function has a range of [-1, 1], so the only possible value for cos(x) is -sqrt(2)/2. This means that the only solution to the equation is x = acos(-sqrt(2)/2).

The inverse cosine function, denoted as "arccos," gives us the angle whose cosine is a given value. In this case, we want to find the angle whose cosine is -sqrt(2)/2. The domain of the arccos function is [-1, 1], so the range of the function is [0, pi]. This means that the solution x must be an angle in the range [0, pi].

Since the problem specifies that the solution must be in the range [0, 2pi], we need to consider all possible angles in that range that satisfy the equation. This means that the possible solutions are:

[tex]x = acos(-\sqrt (2)/2) + 2\pi *k[/tex]

where k is an integer.

Substituting the values from the given choices into this equation, we find that the possible solutions are:

[tex]a. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 0 = \pi /4 + 0 = \pi /4\\b. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 1 = \pi /4 + 2\pi = 3\pi /4\\c. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 2 = \pi /4 + 4\pi = 5\pi /4\\d. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 3 = \pi /4 + 6\pi = 7\pi /4[/tex]

Therefore, the correct answer is c. and d.

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Answer:

b.3pi/4 

c.5pi/4 

Step-by-step explanation:

Therefore ,the answer of this integration problem comes out to be  4/9.

To describe notions like displacement, area, volume, and other results of the combination of incredibly small inputs, an integral in mathematics imparts numerical values to functions. Integration is a method used in the process of integral discovery.

Here,

Given :

=>  [tex]\int\limits^9_7 {\frac{14}{(x-8)^{2} } } \, dx[/tex]

=> substitute x- 8 =u

=>du/dt =d(x-8)/dx = 1

=>du/dt =1

=> [tex]\int\limits^9_7 14{\frac{1}{(x-8)^{2} } } \, dx[/tex]

Substituting x- 8 =u

=> [tex]\int\limits^9_7 14{\frac{1}{(u)^{2} } } \, dx[/tex]

=> 14 [ [tex]\left \{ {{9} \atop {7}} \right. (\frac{-1}{u} )[/tex]  ]

=> 14( -1/9) + 1/7)

=> 14   ( ( 9 -7 ) / 63 )

=> 14 (2/63)

=> 28/63

=>4/9

Therefore ,the answer of this integration problem comes out to be  4/9.

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Answer:

False

Step-by-step explanation:

False. A material in which thermal energy is transferred slowly is actually an insulator. A conductor is a material that easily allows the transfer of thermal energy. This is because conductors have loosely bound electrons that can move freely through the material, allowing heat to be easily transferred. Examples of good conductors include metals such as copper, aluminum, and silver. On the other hand, insulators have tightly bound electrons that do not move easily, making them poor conductors of heat. Examples of good insulators include materials like glass, plastic, and rubber.

Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.

The point that divides a line segment into two equal halves is known as the midway in geometry. A point that divides a line segment into two equal halves is the midpoint of the segment. In other words, the line segment's midpoint is precisely in the middle. The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

Given,

VZ = s + 14

WY = s

VZ bisects WY

VZ = 2WY

s + 14 = 2(s)

s + 14 = 2s

2s - s = 14

s = 14

Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.

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By using properties of triangle, it can be calculated that-

t = 60°

u = 8

What is a triangle?

A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.

Based on the sides of a triangle, triangle may be classified as equilateral, isosceles and scalene

Triangle whose all three sides are equal is called equilateral

Triangle whose two sides are equal is called isosceles

Triangle whose all sides are unequal is called scalene

Here,

[tex]\angle[/tex]FGE = 90°

[tex]\angle[/tex]GFE = 30°

[tex]\angle FEG[/tex] = 180 - (90 + 30)

           = 180 - 120

           = 60°

t = 60°

Since FE = HE and [tex]\Delta[/tex]FGE and  [tex]\Delta[/tex]FGE are right angle triangles,

So FG = FH

u = 8

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The rent per unit should be $8,354.22 to generate a Net Operating Income (NOI) of $100,000, given the vacancy rate and operating expenses.

The operating expenses are costs that must be deducted from the gross operating income to arrive at the net operating income.

The operating expenses do not include some period expenses, which are indirect costs.

                                                                                            Total

Rent per unit (per month) = $696.19 ($8,354.22/12)   $150,376

Vacancy Rate (5% of Potential Gross Income)                   7,519

Effective Gross Income                                                $142,857

Operating Expenses (30% of Effective Gross Income) 42,857

Net Operating Income (NOI)                                      $100,000

Number of Units 18

Gross operating income = net operating income + operating expenses

Operating expenses = 30% of effective gross income

Net operating income = 70% of effective gross income (100 - 30%)

= $100,000

Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)

Vacancy rate = 5% of potential gross income

Effective Gross Income = 95% (100 - 5)

Potential gross income = $150,376 ($142,857 ÷ 95%)

Number of units = 18

Rent per unit = $8,354.22 ($150,376/18)

Rent per month = $696.19 ($8,354.22 ÷ 12)

Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.

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The angle in the similar triangles is as follows:

m∠N = 42 degrees

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

In other words, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Therefore, triangle JKL is similar to triangle NOP. This means the corresponding angles are congruent.

Hence,

∠J = ∠N

∠K = ∠O

∠L = ∠P

Therefore,

m∠N = 180 - 80 - 58(sum of angles in a triangle)

m∠N = 42 degrees

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According to question.

Given data,

The dilation of ABCD using centre D

And scale factor 1/3

Lebel the dilation IJKL.

With the help of figure,

The dilation of ABCD shown in the figure,

The centre of D shown in the figure,

when EFGH, IJKL are obtained from scaling factor ½,1/3 respectively,

then,

ABCD≈EFGH

and

ABCD≈IJKL

Therefore,

EFGH≈IJKL

(Quadrilaterals similar to the same quadrilateral)

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Answer:

The inequality has two prime solutions. To determine the number of prime solutions that the inequality has, we need to first solve the inequality to find its solutions. Since the inequality involves a polynomial, we can use the techniques of algebraic manipulation and factoring to solve it.

We begin by multiplying out the left-hand side of the inequality to obtain:

(n²-17)(n²-100)≤0

This expression can be further simplified by multiplying out the terms in the brackets, which gives us:

n⁴ - 117n² + 1700 ≤ 0

To solve this inequality, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting the expression equal to zero and then factoring it to obtain:

n⁴ - 117n² + 1700 = 0

n² (n² - 117) + 1700 = 0

(n² - 19)(n² - 90) + 1700 = 0

(n² - 19)(n² - 90) = -1700

To find the solutions of this equation, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting each factor equal to zero and solving for n:

n² - 19 = 0 or n² - 90 = 0

n² = 19 or n² = 90

n = ±√19 or n = ±√90

Since the problem states that n is a prime number, we need to consider only the solutions where n is a prime number. Of the solutions above, only n = ±√19 and n = ±√90 are prime numbers, so these are the only solutions that we need to consider. Since there are two such solutions, the inequality has two prime

The day and time that Thereas should take her 7th dose, given that she should take the dose every 12 hours is 9 am on Thursday.

From the first day that Therease took the dose which was 9 am on Monday, the table to show the days and times she takes the other doses, based on her taking them every 12 hours is:

                                       Day                                 Time

First dose                    Monday                               9 am

Second dose              Monday                               9 pm

Third dose                  Tuesday                               9 am

Fourth dose                Tuesday                               9 pm

Fifth dose                   Wednesday                          9 am

Sixth dose                  Wednesday                          9 pm

Seventh dose               Thursday                            9 am

Therese will therefore take the seventh dose at 9 am on Thursday.

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Step-by-step explanation:

The first, twelfth and last term of an arithmetic progression are and , respectively. Determine (a) the number of terms in the series, (b) the sum of all the terms and (c) the 80 th term

The results were as follows: a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.

Get a number that, when multiplied twice by itself, equals the original number in order to find the square root of any integer. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to get the cube root of any integer. equivalently for 4throots and so on.

We have

a)

[tex]x^{2}[/tex] = 36

so x= [tex]\sqrt{36}[/tex]

x = +6, -6

b)

[tex]x^{2}[/tex] = [tex]\sqrt{50}[/tex]

x = [tex]\sqrt[4]{50}[/tex]

x = +-2.6591

c)

[tex]x^{2}[/tex] = [tex]\sqrt{100}[/tex]

x = [tex]\sqrt[4]{100}[/tex]

x = +- 3.1622

d)

2[tex]x^{2}[/tex] = 50

[tex]x^{2}[/tex] = 50/2

[tex]x^{2}[/tex] = 25

x   =+-5

Thus a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.

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Assuming that the meal cost $50, the Shapley values (payments) for each player is: number of possible combination , Player 1: $15 , Player 2: $10 , Player 3: $10 , Player 4: $15

1. Calculate the marginal contribution of each player. This is the amount of money that each player adds to the total cost of the meal.

Player 1: $25

Player 2: $15

Player 3: $10

Player 4: $0

2. Calculate the Shapley Value for each player. This is calculated by taking the average of the marginal contribution of each player, weighted by the number of possible combinations they could have been in.

Player 1: ($25*3 + $15*2 + $10*1 + $0*0) / 6 = $15

Player 2: ($25*2 + $15*3 + $10*2 + $0*1) / 6 = $10

Player 3: ($25*1 + $15*2 + $10*3 + $0*2) / 6 = $10

Player 4: ($25*0 + $15*1 + $10*2 + $0*3) / 6 = $15

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Answer:

The number can be any value less than or equal to 100.

Thus, it can be any number in this range: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]

Step-by-step explanation:

Firstly, let's convert the word problem into a math expression:

[tex]\frac{x}{5}+25\leq45[/tex]

We can now solve this inequality for the variable x.

[tex]\frac{x}{5} \leq 20[/tex]

[tex]x \leq 100[/tex].

Therefore x is any value less than or equal to 100.

Geometric sequence has a common ratio.

Let's verify is the ratio of subsequent terms is common:

As wee se the ratio is common, it confirms that the sequence is geometric.

Common ratio is:

Answer:

Yes, the sequence is geometric.

[tex]\textsf{Common ratio}=\dfrac{2\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Given sequence:

[tex]2, \; \dfrac{4}{\sqrt{3}},\; \dfrac{8}{3},\;\dfrac{16}{3\sqrt{3}},\;...[/tex]

A geometric sequence has a common ratio.

Therefore, to check if the given sequence has a common ratio, divide each term by the previous term:

[tex]\boxed{\begin{aligned}\dfrac{16}{3\sqrt{3}} \div \dfrac{8}{3}&=\dfrac{16}{3\sqrt{3}} \times \dfrac{3}{8}\\\\&=\dfrac{48}{24\sqrt{3}}\\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}\dfrac{8}{3} \div \dfrac{4}{\sqrt{3}}&=\dfrac{8}{3} \times \dfrac{\sqrt{3}}{4}\\\\&=\dfrac{8\sqrt{3}}{12}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned} \dfrac{4}{\sqrt{3}} \div 2&= \dfrac{4}{\sqrt{3}} \times \dfrac{1}{2}\\\\&= \dfrac{4}{2\sqrt{3}} \\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]

As there is a common ratio, the sequence is geometric.

The common ratio is:

The population of the island after 10 years will be approximately 2385.

The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0e^{(-kt)}[/tex].

Increases in a population's or a dispersed group's membership are referred to as population growth. The actual annual increase in the human population is about 83 million, or 1.1%.

Given,  an island's population grows exponentially and the continuous growth rate is 3% per year and the current population is 1,767.

∴ The population be 10 years from now will be,

[tex]y_{10} = y_0e^{(0.03)\times10}[/tex].

We have written 3% as a decimal and it is the correct way of putting it into the formula for exponential growth or decaying equations.

[tex]y_{10} = 1767e^{0.3}[/tex].

[tex]y_{10} = 1767\times1.35[/tex].

[tex]y_{10} = 2385[/tex].

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Answer:

  1, 4, 5

Step-by-step explanation:

You want to identify correct proportions between the sides of similar isosceles trapezoids ABCD and WXYZ.

The similarity statement tells us the corresponding side pairs are ...

A proper proportion will be equate ratios of the corresponding sides in the same trapezoid, or the corresponding sides in different trapezoids.

AB/WX = DA/ZW . . . . . . correct

AB/WX = ZW/DA . . . . . . incorrect

CB/XY = WX/AB . . . . . . incorrect

AB/WX = CB/YX . . . . . . correct

DA/AB = ZW/WX . . . . . . correct

BC/AD = XY/YZ . . . . . . incorrect

Answer:

160 cm

Step-by-step explanation:

the question says twice this length

the length is 80 cm, therefore

[tex]80 \times 2 = 160[/tex]

This is because the question is dimply asking you to double the length of the shirt

The amount of money on the card decreases by $1.43 per week. The slope is a measure of the steepness of a line

The slope can be positive, negative, or zero. A positive slope means that the line slopes upward from left to right, which means that the value of the dependent variable (in this case, M) increases as the value of the independent variable (t) increases. A negative slope means that the line slopes downward from left to right, which means that the value of the dependent variable decreases as the value of the independent variable increases.

To find the linear equation that models the data, we need to find the slope of the line. The slope is calculated by using the formula:

slope =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]

Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points on the line. In this case, we can use week 0 and week 14 as our two points. Let's say that at week 0, M = $100 and at week 14, M = $80. Then the slope would be:

slope = ($80 - $100) / (14 - 0) = -$20 / 14 = -$1.43

So the linear equation that models the data is:

M = -$1.43 * t + $100

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The final score is of:

4-2 for the Blue team.

The number of ways that each score could have been obtained is of:

8.

These three bullet points are given:

The possible scores with six goals and the blue team winning are of:

If the team didn't score more than two goals in a row at any point of the game, the difference is of two, hence the score was 4 - 2.

The goals can be arranged as follows:

Then the total number is of ways that the goals could be obtained is of:

3! + 1 + 1 = 8.

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Answer:

7.5 minutes

4/3 km

Step-by-step explanation:

Use a proportion.

2 km is to 3 min as 5 km is to x min

2/3 = 5/x

2x = 3 × 5

2x = 15

x = 7.5

Answer: 7.5 minutes

2 km is to 3 min as x km is to 2 min

2/3 = x/2

3x = 2 × 2

3x = 4

x = 4/3

Answer: 4/3 km

Measure of angle ABE is 47°.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius.

Given

∠CBE = 43°

As we know, ∠ABC is a right angle

∠ABC = ∠ABE + ∠CBE

90 = ∠ABE +43

∠ABE = 90 - 43

∠ABE = 47

Measure of angle ABE is 47°.

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When Haresh weighs 54 pounds on Earth, his weigh on the moon will be 9 pounds.

From the information, person's weight varies directly with gravity. If a person weighs 180 pounds on Earth, they will weigh only 30 pounds on the moon.

The constant of proportionality will be:

= 180 / 30.

= 6..

Therefore, Haresh weighs 54 pounds on Earth, his weigh on the moon will be:

= 54 / 6

= 9 pounds.

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Answer:

32

Step-by-step explanation:

1536 divided by 48 is 32.

I'd say the answer is reasonable because the number is a positive number and also because each item/thing is equal to they are the same thing and nothing is too big or too small.

Answer:

4x + 1.9 = 22.2

22.2 - 4x = 1.9

Step-by-step explanation:

Define the variable:

Given information:

First equation

The cost of 4 tire patches and the amount remaining on the gift card equals the total amount on the gift card:

⇒ 4x + $1.90 = $22.20

⇒ 4x + 1.9 = 22.2

Second equation

The total amount on the gift card less the cost of 4 tire patches equals the amount remaining:

⇒ $22.20 - 4x = $1.90

⇒ 22.2 - 4x = 1.9

Answer:

4x + 1.9 = 22.2

22.2 - 4x = 1.9

Step-by-step explanation:

Answer:

number is 4

Step-by-step explanation:

let n be the number then 4 times the number is 4n and

4n = n + 12 ( subtract n from both sides )

3n = 12 ( divide both sides by 3 )

n = 4

that is the number is 4

The specified number of New Year's resolutions Harry makes which is 5 more than the resolutions Tim makes, and the total number of resolutions of 13 indicates a word problem with a solution that Harry makes 9 New Year's resolutions.

A word problem is a mathematics or science question, presented using complete sentences, rather that mathematical expressions or science symbols.

A word problem consists of presenting a problem in terms of a real  situation such, with the solution being obtained easiest through the use of mathematical or science procedures.

Let x represent the number of resolutions Tim makes

The number of resolutions Harry makes = x + 5

The number of resolutions Harry and Tim made together = 13

Therefore, we get; x + x + 5 = 13

2·x + 5 = 13

2·x = 13 - 5 = 8

x = 8 ÷ 2 = 4

The number of resolutions Tim makes, x = 4

The number of resolutions Harry makes = x + 5

Therefore, the number of resolutions Harry makes = 4 + 5 = 9

Harry made 9 New Year's resolutions

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