Hi I really need help on knowing how to solve this please help!

(200 - 100√2) / 16 is the rectangular form of the product c1*c2 for an equilateral triangle's vertices.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.

Here,

An equilateral triangle is a triangle with three equal sides. If 3-2i, 6-i, and c form the vertices of an equilateral triangle, then the distance between 3-2i and 6-i is equal to the distance between 3-2i and c.

The distance between two complex numbers a + bi and c + di can be found using the formula:

√((c - a)² + (d - b)²)

So, the distance between 3-2i and 6-i is:

√((6 - 3)² + (-1 - (-2))²) = √((3)² + (1)²) = √(9 + 1) = √10

And the distance between 3-2i and c is:

√((c - 3)² + (c - (-2))²) = √((c - 3)² + (c + 2)²)

Since these distances must be equal, we have:

√((c - 3)² + (c + 2)²) = √10

Squaring both sides:

(c - 3)² + (c + 2)² = 10

Expanding both sides:

c² - 6c + 9 + c² + 4c + 4 = 10

Combining like terms:

2c² + 10c + 5 = 10

Subtracting 10 from both sides:

2c² + 10c - 5 = 0

This is a quadratic equation, which can be solved using the quadratic formula:

c = (-b ± √(b² - 4ac)) / 2a

Where a = 2, b = 10, and c = -5. Plugging these values into the formula:

c = (-10 ± √(10² - 4 * 2 * -5)) / 2 * 2

c = (-10 ± √(100 + 40)) / 4

c = (-10 ± √(140)) / 4

c = (-10 ± 10√2) / 4

So there are two complex solutions, c1 = (-10 + 10√2) / 4 and c2 = (-10 - 10√2) / 4.

The product of these two solutions is:

c1 * c2 = ((-10 + 10√2) / 4) * ((-10 - 10√2) / 4)

= (100 - 100√2 + 100) / 16

= (200 - 100√2) / 16

(200 - 100√2) / 16 is the answer in rectangular form for the product c1*c2 for the vertices of an equilateral triangle.

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Answer:

height = 5 cm

Step-by-step explanation:

a cube has congruent sides (s)

the volume (V) of a cube is calculated as

V = s³

given V = 125 , then

s³ = 125 ( take cube root of both sides )

\(\sqrt[3]{s^3}\) = \(\sqrt[3]{125}\) = \(\sqrt[3]{5^3}\)

s = 5

then height = 5 cm

The area of the green region of the circle is 96.4 ft².

Area is the region bounded by a plane shape.

To calculate the area of the green region of the circle, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.

The sector of a circle is calculated as:

A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.

Given the following:

Central or reference angle (∅) = 180 - 27 = 153 degrees

Radius (r) = 17/2 = 8.5 feet

Plug in the values:

Area of the green region = 153/360 * π * 8.5²

Area of the green region ≈ 96.5 square feet.

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The man got an 18.92% discount on the jacket during the sale if he pays $150, saving $35 on the normal price.

What was the percentage discount on the jacket purchased by the man?

The discount can be calculated as follows:

Discount = Normal price - Sale price

Discount = $35

Normal price = Sale price + Discount

Normal price = $150 + $35

Normal price = $185

So, the percentage discount is:

Percentage discount = (Discount / Normal price) x 100

Percentage discount = ($35 / $185) x 100

Percentage discount = 18.92%

Therefore, the man got a discount of 18.92% on the jacket.

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Answer:

\(\displaystyle{f(x)=3^x-5}\)

Step-by-step explanation:

Being translated up-down means that the value exists outside of x. Therefore, we can cancel B and C choice since those are horizontal (left-right) translation.

Our only choice is A and D. However, D is being translated up since it's +5. Thus, the only correct answer that a function is being translated down is:

\(\displaystyle{f(x)=3^x-5}\)

or A choice.

So, the value of P (X=2 or X=0) is 0.4.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that it is certain to occur.

For example, if you flip a fair coin, the probability of it landing on heads is 0.5 or 50%, as there are only two possible outcomes (heads or tails) and they are equally likely to occur.

Probability is used extensively in fields such as statistics, mathematics, and science to model and analyze uncertainty and randomness. It is also used in practical applications such as gambling, risk assessment, and decision making.

o find the probability of X being 2 or 0, we need to add the probabilities of the two events.

P(X=2 or X=0) = P(X=2) + P(X=0)

From the given table, we can see that:

P(X=2) = 0.1

P(X=0) = 0.3

Therefore,

\(P (X=2 or X=0) = 0.1 + 0.3 = 0.4\)

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Answer:

                                                                                                ,

Step-by-step explanation:

.

The data in the table can be modeled by this linear equation in slope-intercept form: y = 8x - 5.

The slope is 8, which means the wages earned increases at rate of 8 dollars per hour as the time increases.

The y-intercept is -5 and it represent the initial wages earned.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (24.00 - 8.00)/(3 - 1)

Slope (m) = 16.00/2

Slope (m) = 8

At data point (1, 3), a linear equation in slope-intercept form for this line can be calculated as follows:

y - y₁ = m(x - x₁)

y - 3 = 8(x - 1)

y = 8x - 8 + 3

y = 8x - 5

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Answer:

thanks for the points

Step-by-step explanation:

The answer to the question Which THREE methods could be used to find the change in height, in feet, of the second drone is B Multiply −38.75 by 0.2

Since the first drone decreases a height of 38 ³/₄ feet, since this is a decrease, its change in height is h =  -38 ³/₄ feet = -38.75 feet. (The value is negative because it is a decrease in height).

Also, the second drone decreases by 20 % the decrease in height of the first drone, we have that the decrease in height of the second drone, h' = h × 20 % = -38.75 × 0.2

So, to find the change in height of the second drone we multiply -38.75 by 0.2.

So, the answer to the question Which THREE methods could be used to find the change in height, in feet, of the second drone is B Multiply −38.75 by 0.2

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Answer:

3.16 m

Step-by-step explanation:

2x² = 20

x² = 10

x = 3.16 m

check:

(3.16)(3.16) = 10

The length of each side of the square rounded to two decimal places will be 4.47 meters.

All the sides of a square are congruent. Let a be the side length of the square. Then the area of the square is the square of the side length of the square. Then the area of the square will be

Area of the square = a² square units

A square enclosure is to have an area of 20 square meters. Then the side length of the square will be given by the area of the square. Then the equation is given below.

20 = a²

a = √20

a = 4.47 meters

The length of each side of the square rounded to two decimal places will be 4.47 meters.

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Answer:

C. a reflection across the x-axis, and then a dilation by a scale factor of 2

Step-by-step explanation:

Transformations

If a given point (x,y) is reflected across the x-axis, it transforms to (x,-y).

If a given point (x,y) is rotated counterclockwise 90° about the origin, it transforms to (-y,x)

If a given point (x,y) is dilated by a factor scale of k, it transforms to (kx, ky).

We are given a shape called Image I formed by the points:

(4,-1) (6,-3) (3,-3) (3,-2)

The shape called Image II is formed by the points:

(8,2) (12,6) (6,6) (6,4)

Let's take the first point of Image I (4,-1).

A reflection across the x-axis will make it (4,1). A dilation by 2 will make it (8,2) which coincides with the first point of Image II.

Let's take the point (6,-3) of Image I.

A reflection across the x-axis will make it (6,3). A dilation by 2 will make it (12,6) which coincides with the second point of Image II.

Let's take the point (3,-3) of Image I.

A reflection across the x-axis will make it (3,3). A dilation by 2 will make it (6,6) which coincides with the third point of Image II.

Let's take the point (3,-2) of Image I.

A reflection across the x-axis will make it (3,2). A dilation by 2 will make it (6,4) which coincides with the fourth point of Image II.

Thus, both shapes are similar because of the following sequence of transformations:

C. a reflection across the x-axis, and then a dilation by a scale factor of 2

Answer:

ok

Step-by-step explanation:

graphed

The range of the function on the graph would be: D. all real numbers greater than or equal to 2

To obtain the range, observe the y values whose result can be obtained by the function of x. To obtain this range, we examine the graph and note that the range begins from 2 on the y-axis and extends upwards.

So, if we wish to define our range, we will enter all real numbers that are equal to or greater than 2 as seen in the direction of the graph.

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer:

Area of a rectangle = length x breadth

Given:

⇒ 134 cm² = length x 15cm

⇒ length = 134 ÷ 15

               = 8.93333333... cm

Reduction in length = original length - new length

                                 = 18 cm - 8.93333333... cm

                                 = 9.07 cm (nearest hundredth)

The depths below sea level, the rising speed, and the available air

supply, determine the minimum depth Ursula can wait.

Correct response;

The given parameters;

The initial depth of Prince Eric = 250 feet below sea level

Duration of air supply available = 10 minutes

Speed of ascent of Prince Eric = 20 ft./minute

The depth at which Ursula is forced to wait = 100 feet below sea level

The maximum ascent possible with the available air supply is given as follows;

Ascent = 20 ft./min × 10 min. = 200 ft.

Therefore, the air supply is insufficient to swim to the surface.

Level at which Ursula waits = 100 ft.

Level to which Prince Eric requires to ascent = 250 ft. - 100 ft. = 150 ft.

\(Time \ it \ takes \ to \ ascent \ to \ 150 \, ft. = \dfrac{150 \, ft.}{20 \, ft./min} = \mathbf{7.5 \,min}\)

The time it will take Prince Eric to ascend to Ursula's level is 7.5 minutes,

which is less than the 10 minutes, time to use the available air supply.

Therefore;

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However, I can still give you some general steps to solve a math problem in 200 words.

Step 1: Read the problem thoroughly and understand what it's asking you to find. This may involve identifying the given information and what you need to find. Also, identify any constraints on the problem, like time or cost.

Step 2: Plan how to solve the problem. Think about what mathematical operations or formulas you can use to find the answer. Make a list of the steps you need to take to solve the problem. Also, determine the units for your answer.

Step 3: Solve the problem. Use the mathematical operations or formulas you've identified in step 2 to find the answer. Show all of your work, including any calculations, so that you can easily check your work later.

Step 4: Check your answer. Make sure that your answer makes sense and that it satisfies any constraints given in the problem. Also, check that your units are correct. If your answer doesn't make sense, go back and review your work to see if you made an error.

Step 5: Reflect on what you've learned. Think about what you did well and what you could improve upon in future problem-solving situations. This will help you become a more effective problem solver in the future.

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Answer

20%

Step-by-step explanation:

Answer:

nice

Step-by-step explanation:

whats the rest of the problem or is it just that she rolled a dice

Answer:

- 0.7 m/s

Step-by-step explanation:

Because we are talking about "elevation", we assume that going upwards will result in a positive elevation change and going downwards will result in a negative elevation change.

We also assume, since we are talking about free-diving, that he starts from the surface (i.e elevation 0 m) and he free dives to a distance of 42 meters downwards (i.e elevation of -42)

In our case, the change in elevation

= final elevation - intital elevation

= -42 - 0

= -42 m

time elapsed is given as 60 sec.

Hence rate of change of elevation

= change in elevation ÷ time elapsed

= -42 ÷60

= - 0.7 m/s

Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for \(S_{n}\) , that is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then

S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188

The solution for the equation -2(2x + 5) - 3 = -3(x - 1) is x = - 16 which can be solved by the use the distributive property.

Distributive Property that when we multiply a number by a group of numbers that are added together, we can multiply each value in the group separately, then add the products of the multiplications.

-2(2x + 5) - 3 = -3(x - 1)

To solve this equation, we need to first use the distributive property to expand the left side of the equation.

We have:

-4x-10-3 = -3(x - 1)

-4x-13 = -3(x - 1)

Now, we can group the like terms on the left side and the right side of the equation.

On the left side, we have -4x - 13 and on the right side, we have -3x + 3.

-4x-13 = -3x + 3

To solve for x, we can add 3x to left side of the equation and add 13 to the right side.

This results in the equation:

-4x+ 3x  = 13 + 3

Now, we can add 3x with -4x of the equation to isolate the x-term.

We have:

-x = 16

x = - 16

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Answer:

8.154 - 0.05

751 602 - 50 000

1 567 324 896 - 500 000 000

Answer:

a) Find the angle, to 2 decimal places, between R and the vector 2i.

Step-by-step explanation:

Two forces, F1 and F2 are given by the vectors F1=(4i-5j)N and F2=(pi-qj)N. The resultant force, R=F1+F2 acts in the direction which is parallel to the vector (3i-j)