(-3+i)^2 in simplest a + bi form

The distance between the points (-3.5, 0), and (1.5, 0), shown on the coordinate plane, obtained using the distance formula; is 5 units

The correct option is; 5 units

The distance formula is a formula that can be used to calculate the distance between the points (x₁, y₁), and (x₂, y₂) on the coordinate plane using the following equation;

d = √((x₂ - x₁)² + (y₂ - y₁)²).

The distance between the points (-3.5, 0), and (1.5, 0), on the graph can be obtained using the distance formula which is; d = √((x₂ - x₁)² + (y₂ - y₁)²

Where;

(x₁, y₁) = (-3.5, 0)

(x₂, y₂) = (1.5, 0), we get;

d = √((1.5 – (-3.5))² – (0 – 0)²) = 5

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The perimeter of scale drawing of Central Park is 30 centimeter.

The area of scale drawing of Central Park is 31.25 square centimeters.

What is perimeter?

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

Given that Central Park is a rectangular park in New York City

The measured length is 12.5 centimeters

The measured width is 2.5 centimeters

The perimeter of scale drawing of Central Park is given as:

Given is a rectangular park

perimeter of rectangular = 2(length + width)

perimeter of rectangular = 2(12.5 + 2.5)

perimeter of rectangular = 2(15) = 30

Thus perimeter is 30 centimeter

The area of scale drawing of Central Park is given as:

area = length x width

area = 12.5 x 2.5 = 31.25 cm²

Thus area of rectangular park is 31.25 square centimeters

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Answer:

54

Step-by-step explanation:

16/4 + 56 - (3 + 4 - 1)

= 16/4 + 56 - (6)

= 4 + 56 - (6)

= 4 + 56 - 6

= 60 - 6

= 54

So, the answer is 54 !

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[tex] \sf \frac{16}{4} + 56 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \cancel \frac{16}{4} + 56 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \: 4 + 56 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \: 60 - (3 + 4 - 1)[/tex]

[tex] \: [/tex]

[tex] \sf \: 60 - (3 + 3)[/tex]

[tex] \: [/tex]

[tex] \sf \: 60 - 6[/tex]

[tex] \: [/tex]

[tex] \sf \fbox{ \: \sf \blue{ 54 }\: \: }[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps!:)

Answer:

oc

Step-by-step explanation:

(A). the current sale price of the computer system is $543.20.

Therefore, members of the store's loyalty club pay $488.88 for the computer system with their discount.

Find the current sale price. Round to the nearest cent if necessary.

• Members of the store's loyalty club get an additional 10% off their computer purchases. How much do club members pay for the computer with their discount?

To find the current sale price, we first need to calculate the markdown amount. We know that the markdown is 30% of the original selling price, which is $776, so the markdown amount is:

30% of $776 = 0.30 x $776 = $232.80

The sale price is then the original selling price minus the markdown amount:

Sale price = $776 - $232.80 = $543.20

Therefore, the current sale price of the computer system is $543.20.

Next, we need to calculate the price that club members pay after their discount. We know that club members get an additional 10% off the sale price, which is $543.20, so their discount amount is:

10% of $543.20 = 0.10 x $543.20 = $54.32

The price that club members pay is then the sale price minus their discount amount:

Price for club members = $543.20 - $54.32 = $488.88

Therefore, members of the store's loyalty club pay $488.88 for the computer system with their discount.

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Original Equation:

2x + 5y = 0

Explanation:

The slope intercept form is y = mx + b, so first we have to get x onto the other side, to do that, we subtract 2x from both sides and end up getting:

5y =  - 2x

Now we divide both sides by 5 to isolate y

[tex]y = -\frac{2}{5} x[/tex]

That's our equation!

(Hopefully that helps, and if you can later, please give me brainliest)

Answer:

6

Step-by-Step Explanation:

if you were to move the bottom triangle to the top, it would make the parallelogram a perfect rectangle.

the area is 60 units^2.

area=length*width

and the one side is 10. 60/10 =6 so 6 units is the answer

Using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

The right rectangular prism has four rectangle-shaped side faces and two parallel end faces that are perpendicular to each of the bases.

Parallelograms make up the sides of an oblique prism, a non-right rectangular prism.

A cuboid is yet another name for a right rectangle prism.

So, the volume of the right rectangular prism:

V = wlh

Insert values:

V = wlh

V = 6*8*4.5

V = 216cm³

Now, the volume of the cube:

V = a³

V = 2³

V = 8cm³

Then, the number of cubes that can be fitted in the right rectangular prism:

216/8 = 27

Therefore, using the volume formula we know that (B) 27 cubes can be fitted into the right rectangular prism.

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Correct question:

How many cubes, with side measures of 2 cm, will fit inside a right rectangular prism with dimensions of 6 cm by 8 cm by 4 1/2 cm?

Group of answer choices

a. 24

b. 27

c. 108

d. 54

Answer: The Missouri Compromise of 1820 was a landmark agreement in American history that temporarily resolved the issue of slavery in the western territories. The compromise was driven by a sense of nationalism among Americans in the early 1800s, who were concerned about preserving the unity of the country and avoiding the outbreak of civil war.

The Missouri Compromise reflected this sense of nationalism by seeking to maintain a balance of power between the slave states and the free states. The compromise allowed Missouri to enter the Union as a slave state, but it also admitted Maine as a free state, and prohibited slavery in any new states formed north of the 36°30′ parallel. By preserving this balance of power, the Missouri Compromise helped to ease tensions between the North and the South, and prevent the outbreak of civil war for several decades.

John Quincy Adams's diary entry provides some insights into the political climate of the time, and the debates surrounding the Missouri Compromise. In his diary entry of February 24, 1820, Adams writes:

"The Missouri question still hangs over us like a black cloud. The ground of the controversy is evidently an apprehension of the preponderance of power in the Union, which by some is feared to be passing from the South to the North."

This quote suggests that there was a growing concern among some Southerners about the balance of power in the Union, and that this concern was driving the debates over the Missouri Compromise. Adams goes on to describe the debates in Congress, noting that "the debates upon the Missouri question are exceedingly able, ingenious, and eloquent." He also provides some insights into the strategies being used by different sides of the debate, noting that "the argument for restriction upon Missouri, is that it will preserve the balance of power in the Union; that the balance of power is a fundamental principle of the Constitution; and that this principle is essential to the preservation of the Union."

These quotes suggest that the Missouri Compromise was a highly contentious issue, and that the debates surrounding it were marked by a strong sense of nationalism among both supporters and opponents of the compromise. The compromise ultimately reflected a desire among Americans to maintain the unity and stability of the country, even as it grappled with the divisive issue of slavery.

Step-by-step explanation:

Imaginary Numbers are 21. (5+2i)/ 4i is  -(5/4) + (1/2)i, 22. 3i/(-2+i) is -1.5i + 0.75. 23. (3-2i)/(4-3i) is 4/5 + (1/25)i, 24. 7/(5-2i) is (14/29) + (7/29)i.

In mathematics, imaginary numbers are a type of complex number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

Imaginary numbers were first introduced in the 16th century as a solution to certain polynomial equations that did not have real solutions. They were initially met with skepticism and derision, but eventually became widely accepted as a fundamental part of complex analysis and number theory.

One of the key properties of imaginary numbers is that when they are multiplied by themselves, the result is always a negative real number. For example, i * i = -1. This property is what makes imaginary numbers useful for representing certain physical quantities, such as the amplitude and phase of an oscillating system.

21. (5+2i)/ 4i = -(5/4) + (1/2)i

To divide complex numbers, we can multiply the numerator and denominator by the conjugate of the denominator. Here, the conjugate of 4i is -4i.

(5+2i)/ 4i = (5+2i)/4i * (-4i/-4i)

= -(20i - 8)/(-16)

= -(20i - 8)/16

= -(5/4) + (1/2)i

Therefore, (5+2i)/ 4i = -(5/4) + (1/2)i.

22. 3i/(-2+i) = -1.5i + 0.75

We can again use the conjugate to simplify the division of complex numbers.

3i/(-2+i) = 3i/(-2+i) * (-2-i)/(-2-i)

= (-6i -3)/(-5)

= 3/5 + 1.5i

Therefore, 3i/(-2+i) = -1.5i + 0.75.

23. (3- 2i)/(4-3i) = (18+5i)/25

Using the conjugate:

(3-2i)/(4-3i) = (3-2i)/(4-3i) * (4+3i)/(4+3i)

= (12+9i-8i-6i²)/(16+12i+12i-9i²)

= (20+i)/25

= 20/25 + (1/25)i

= 4/5 + (1/25)i

Therefore, (3-2i)/(4-3i) = (18+5i)/25 = 4/5 + (1/25)i.

24. 7/(5-2i) = (14/29) + (7/29)i

Using the conjugate:

7/(5-2i) = 7/(5-2i) * (5+2i)/(5+2i)

= (35+14i)/(29)

= (14/29) + (7/29)i

Therefore, 7/(5-2i) = (14/29) + (7/29)i.

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So, the quotient is. [tex]Q(x) = x^3 - x^2 - x + 1/(x - 2)[/tex], and the remainder is. [tex]R(x) = 1.[/tex]Therefore, we can write:

[tex]f(x) / d(x) = Q(x) + R(x) / d(x)\\f(x) / d(x) = x^3 - x^2 - x + 1/(x - 2) + 1/(x - 2)[/tex].

Algebraic division is the process of dividing one algebraic expression by another. It involves applying the same rules of arithmetic division but with algebraic terms instead of numbers.

In algebraic division, the dividend, which is the expression being divided, is written on the top, while the divisor, which is the expression doing the dividing, is written below it. The division process involves finding how many times the divisor can fit into the dividend, and then subtracting that amount from the dividend. This process is repeated until there is no remainder left.

To divide [tex]f(x) = x^4 - 2x^3 + x^2 - 2x + 1[/tex] by[tex]d(x) = x - 2,[/tex] we can use long division as follows:

[tex]x^3 - x^2 - x + 1/ (x - 2)[/tex]

[tex]x - 2 | x^4 - 2x^3 + x^2 - 2x + 1[/tex]

     [tex]-x^4 + 2x^3[/tex]

      -----------

      [tex]0 - x^2[/tex]

      [tex]0 + x^2[/tex]

          ----------

                [tex]- 2x[/tex]

               [tex]+ 2x[/tex]

                  -----

                      1

                      1

                      -

                      0

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Answer:

To solve 34x23 ≡ r (mod 13), we can first calculate the product 34x23 = 782. Next, we need to find the remainder when 782 is divided by 13. To do this, we can divide 782 by 13 and find the remainder: 782 ÷ 13 = 60 remainder 2 Therefore, 782 is equivalent to 2 (mod 13). So, the solution to the original equation is r ≡ 2 (mod 13).

To solve this problem, we can use the trigonometric functions sine, cosine, and tangent.

First, let's draw a diagram:

             A (top of the mountain)

            /|

           / |

         /    |  h (height of mountain)

       /      |

     / θ     |

B /_____|

   d (distance from base)

We are given that the distance from the base of the mountain to point B is 1/2 mile, or 2640 feet (since there are 5280 feet in a mile). We are also given that the angle of elevation from point B to point A is 65 degrees, and that the angle between the ski lift and the ground is 15 degrees.

Let's start by finding the height of the mountain h. We can use the tangent function, since we know the opposite (h) and the adjacent (d) sides of the right triangle formed by points A, B, and the foot of the mountain (call it point C):

tan(65) = h / d

h = d * tan(65)

Plugging in the values, we get:

h = 2640 * tan(65)

h ≈ 7855 feet

Next, let's find the length of the ski lift. We can use the cosine function, since we know the adjacent (d) and hypotenuse (L) sides of the right triangle formed by points B, the foot of the mountain, and the base of the ski lift (call it point D):

cos(15) = d / L

L = d / cos(15)

Plugging in the values, we get:

L = 2640 / cos(15)

L ≈ 2736 feet

Therefore, the length of the ski lift from the beginning to the end is approximately 2736 feet.

Answer:

then she will have 139.67 left

Answer: To make "w" the subject of the formula "P+aw=b", we need to isolate "w" on one side of the equation.

First, we can subtract "P" from both sides of the equation to get:

aw = b - P

Next, we can divide both sides of the equation by "a" to get:

w = (b - P) / a

Therefore, the solution is:

w = (b - P) / a

Step-by-step explanation:

The approximate perimeter of the entire shape is 77.69 inches.

The perimeter of a figure is the sum of the whole sides of the figure.

Therefore, the perimeter of the entire shape can be calculated as follows:

The shape is made of three sides of a square and half a circle.

Therefore,

circumference of the semi circle [tex]= \pi r[/tex]

[tex]r = 17 \div 2 = 8.5 \ \text{inches}[/tex]

circumference of the semi circle [tex]= 8.5\pi[/tex]

Hence,

perimeter of the shape [tex]= 17+17+17+ 8.5\pi[/tex]

perimeter of the shape [tex]= 51 + 8.5(3.14)[/tex]

perimeter of the shape [tex]= 51 + 26.69[/tex]

Therefore,

perimeter of the shape = 77.69 inches

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Volume of  6 3/4 cups of water is equal to 54 cups of water.

What is Volume?

One cup is equal to 8 fluid ounces. Therefore, to convert 6 3/4 cups to fluid ounces, we can multiply by 8:

6 3/4 cups = (6 x 8) + (3/4 x 8) cups = 48 + 6 = 54 cups

So, 6 3/4 cups of water is equal to 54 cups of water.

What is fluid?

A fluid is a substance that has the ability to flow and take the shape of its container. Fluids include liquids, gases, and plasmas.

Liquids are a common type of fluid that can flow and take the shape of their container, but have a definite volume. Some examples of liquids include water, oil, and milk.

Gases are another type of fluid that can flow and fill the entire volume of their container, taking on the shape of the container. Some examples of gases include air, oxygen, and nitrogen.

Plasmas are a unique type of fluid that occurs at very high temperatures, in which some or all of the atoms or molecules have been ionized, resulting in the presence of free electrons and positive ions. Some examples of plasmas include lightning, the sun, and neon lights.

Fluids are important in many fields, including physics, engineering, and biology. They play a critical role in many processes, such as the circulation of blood in the body, the flow of water in a river, and the movement of air in the atmosphere.

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The team that has the largest overall size hat for their players is the Seahawks; they have a larger mean value of about 23 inches. The correct option is b.

The two most frequently used measures of center are mean and median. When we compare the mean numbers for the Pelicans and Seahawks, we can see that the Pelicans have a mean of roughly 22 inches and the Seahawks have a mean of roughly 23 inches.

Nevertheless, when the data is skewed or contains outliers, the mean may not be the best approximation of the center because the mean can be altered by extreme values or outliers. Thus, we also need to compare the median values. The median is the midway value in the ordered set of data.

Thus, the correct option is b, Seahawks; they have a larger mean value of about 23 inches.

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Answer:

Step-by-step explanation:

the right answer is b 23 inches seahawkS BRAINLIST and verified answer wanted

The area of the triangle is 4.64 square meters and that of the trapezoid is 61.6 square inches.

A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle. An angle is formed between two sides.

A trapezoid is a polygon that has only one pair of parallel sides. These parallel sides are also called parallel bases of trapezoid. The other two sides of trapezoids are non-parallel and called legs of trapezoids.

The formula for the area of a triangle is:

A = (1/2) * b * h

where b is the base of the triangle and h is the height of the triangle.

Substituting the given values, we get:

A = (1/2) * 2.9 m * 3.2 m

A = 4.64 square meters

Therefore, the area of the triangle is 4.64 square meters.

The formula for the area of a trapezoid is:

A = (a + b) * h / 2

where a and b are the lengths of the parallel bases, and h is the height of the trapezoid.

Substituting the given values, we get:

A = (10 + 12) * 5.6 / 2

A = 22 * 2.8

A = 61.6 square inches

Therefore, the area of the trapezoid is 61.6 square inches.

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Answer:

22 * 100

Step-by-step explanation:

It would defintely be 22 * 100 because the other ones may be troubling to do mentally, especially 88 * 25. But with 22 * 100, you can easily get an answer of 2200.

A hemisphere over the cone with a radius of 10 cm and a height of 15 cm.

a) volume of the cone: V = 1570.8 cm³

b) volume of the hemisphere: V = 2093.33 cm³

c) voume of the entire figure : V= 3664.13 cm³

a) The formula V = (1/3)r2h, where r is the cone's radius and h is its height, determines the volume of the cone.

Substituting r = 10 cm and h = 15 cm, we get:

V = (1/3)π(10 cm)²(15 cm)

V ≈ 1570.8 cm³

The volume of the cone is approximately 1570.8 cm³.

b) The volume of the hemisphere is given by the formula V = (2/3)πr³, where r is the radius of the hemisphere. Since the hemisphere has the same radius as the cone, i.e., r = 10 cm, we get:

V = (2/3)π(10 cm)³

V = 2093.33 cm³

The volume of the hemisphere is approximately 2093.33 cm³.

c) The volume of the entire figure is the sum of the volume of the cone and the volume of the hemisphere. Adding the volumes of the two shapes, we get:

V = 1570.8 cm³ + 2093.33 cm³

V = 3664.13 cm³

The volume of the entire figure is approximately 5759.6 cm³.

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Answer:

60

Step-by-step explanation:

Since this is a right triangle, the longest side can be solved using the Pythagorean Theorem

x^2 + y^2 = z^2

So

15^2 + 20^2 = 225 + 400 = 625 = 25^2.

So 25 is hypotenuse.

Add them all together : 25+15+20 = 60.

So your answer is 60.

Answer:

60

Step-by-step explanation:

A squared + B squared = C squared

15 squared + 20 squared = C squared

225 + 400 = C squared

625  = C squared

Use radicals to find the square root of 625

Which is 25

C = 25

25 + 15 + 20 =

60

Without further context about the triangle and the lengths of its sides, it is not possible to solve for sin(B) using just the given information about cos(A).

As a result, point C's coordinates are (-3/2, -21/4) as the section formula to determine the coordinates of point C .

A point together in two-dimensional plane can be found using coordinates, which are pairs of numbers. Each point is represented by an ordered pair of absolute values (x,y), where x represents the horizontal coordinate and y represents the vertical coordinate, in the Cartesian geometry. The x-axis is the horizontal axis, while the y-axis is the vertical axis. The origin is the intersection of the two axes and bears the following coordinates: (0,0). A point's coordinates might be plus, negative, or zero depending on where it is in relation to the axes and the origin.

given

We may use the section formula to determine the coordinates of point C, which divides line segment AB in a ratio of 1:3.

Let point C's coordinates be (x, y). Next, we have

x = [(3/4) * (-2)] + [(1/4) * 6] = -3/2

y = [(3/4) * (-5)] + [(1/4) * 3] = -21/4

As a result, point C's coordinates are (-3/2, -21/4) as the section formula to determine the coordinates of point C .

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Answer: [tex]-3\sqrt{3}[/tex]

This the expression [tex]-3\times\sqrt{3}[/tex] or "-3 times the square root of 3"

[tex]\rule{300}{1.5}[/tex]

Work Shown:

Factor each term inside the square root so that a perfect square is one of the pieces. Then break up the roots and simplify as shown below.

[tex]-4\sqrt{12}+\sqrt{75}[/tex]

[tex]-4\sqrt{4\times3} +\sqrt{25\times3}[/tex]

[tex]-4\sqrt{4} \times\sqrt{3} +\sqrt{25} \times\sqrt{3}[/tex]

[tex]-4\times2\times\sqrt{3} +5\times\sqrt{3}[/tex]

[tex]-8\sqrt{3}+5\sqrt{3}[/tex]

[tex](-8+5)\sqrt{3}[/tex]

[tex]\bold{-3\sqrt{3}}[/tex]

Answer: Approximately $4,176.19 today for an investment that returns $800 each year for 6 years

Step-by-step explanation:

To calculate the present value of an investment that returns $800 each year for 6 years at a discount rate of 4 percent, we can use the formula for the present value of an annuity:

PV = C x [(1 - (1 / (1 + r)^n)) / r]

where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of years.

Plugging in the given values, we get:

PV = 800 x [(1 - (1 / (1 + 0.04)^6)) / 0.04]

PV = $4,176.19 (rounded to the nearest cent)

Therefore, if the discount rate is 4 percent, you would be willing to pay approximately $4,176.19 today for an investment that returns $800 each year for 6 years

To calculate the interest that Margo will pay, we first need to determine how much interest she will accrue over the 17-month period.

We can use the formula:

Interest = Principal x Rate x Time

Where:

Principal is the amount borrowed, which is $700 in this case.

Rate is the annual interest rate, which is 3% or 0.03 as a decimal.

Time is the time period expressed in years, which is 17/12 or 1.4167 years in this case (since there are 12 months in a year).

Therefore, the interest that Margo will pay can be calculated as:

Interest = $700 x 0.03 x 1.4167

Interest = $29.75

So Margo will pay $29.75 in interest. Rounded to the nearest cent, the answer is $29.8.

Answer:

there is no image so i cannot solve your question.

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

We can write the following equation to find the value of x based on above mentioned information:

10x - 20 = 7x + 4

10x - 7x = 20 + 4

3x = 24

x = 8

To find each angle measure, replace x with 8:

10x - 20 would be 10 × 8 - 20 = 60

Since angles are congruent the other one also would be 60°.