identify the real and imaginary parts of the complex number. -5 + 6i

To find the number of deluxe staterooms for each of the three ships, we can set up and solve an equation based on the given information.

Let's represent the number of deluxe staterooms on the Pacific Paradise ship as x.

The number of deluxe staterooms on the Caribbean Paradise is 29 more than the Pacific Paradise, so it can be represented as x + 29.

The number of deluxe staterooms on the Mediterranean Paradise is 30 fewer than twice the number of deluxe staterooms on the Pacific Paradise, so it can be represented as 2x - 30.

We can form an equation with the sum of the deluxe staterooms on all three ships: x + (x + 29) + (2x - 30) = 719.

Simplifying the equation gives us 4x - 1 = 719.

By adding 1 to both sides and dividing by 4, we can find the value of x which represents the number of deluxe staterooms on the Pacific Paradise ship.

Finally, we can substitute the value of x into the expressions for the other two ships to find their number of deluxe staterooms.

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formula for volume of a sphere is V=4/3 x pi x R63

if diameter = 16 than radius = 16/2 = 8

 so the equation would be 4/3 x pi x 8^3

Final answer:

To find m2, subtract m6 from 180 degrees.

Explanation:

To find m2 in this problem, we can use the fact that angles in a triangle sum up to 180 degrees. We know that m6 = 57° and m7 = 23°.

First, we can find m1 by subtracting m7 from 180 degrees: m1 = 180° - 23° = 157°.

Next, we can find m2 by subtracting m6 from 180 degrees: m2 = 180° - 57° = 123°. Therefore, m2 is equal to 123 degrees.

100-40= 60%

60% = 0.60

420/0.60 = 700

he had 700 peas

The answer is y = 5x + 7

here's how you get it:

Start with the base   y = mx + b

then imput the points and the slope:

-3 = 5 ( -2 ) + b

Then solve for b

-3 = 5 ( -2 ) + b

-3 = -10 + b

-b = -7

b = 7

so the equation is:

y = 5x + 7

Answer:

c. h+j+k over 3

Step-by-step explanation:

We know that,

[tex]\text{Average}=\frac{\text{Sum of observations}}{\text{Total number of observation}}[/tex]

Here, h, j and k represents the melting point of helium, hydrogen and Neon respectively,

Since, the sum of melting points = h + j + k,

Also, the total number of gases = 3,

Thus,

[tex]\text{Average melting points}=\frac{h+j+k}{3}[/tex]

Or (h+j+k) over 3

⇒ Option c is correct.

The algebraic expression which shows the average melting

points of helium, hydrogen, and neon is h+j+k over 3.

This is calculated with the sum of the items divided by the

number of items.

In this scenario, we were given the items as h, j and k. The

total number of items is 3.

The average will therefore be = h+j+k/3

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20-12 8

She has mailed 8 invitations.

Another way to state the transformation is D. R0, 360°

Given that the rotation is:

(x,y) --------> (x,y)

This shows that it goes back to its original position and there is a full rotation occurred.

Based on its full rotation to 360°, it can be noted that option D is another way to state the transformation as other given rotations would give different translations.

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Answer: I can confirm it’s D Ro, 360°

Step-by-step explanation:

Answer:

a) AAA.

Step-by-step explanation:

Triangles which are of the same shape and size are called congruent triangles. Triangles of same shape are similar triangles.

Two triangles can be proved congruent by SSS ,SAS AAS ,ASA ,HL  postulates.

Two triangles can be proved similar by AAA method.

All congruent triangles are similar but all similar triangles are not congruent.

Hence option a) AAA is not an appropriate method of proving triangles congruent.

The area of a rectangle with length l and width w is given by the product l * w.

The area of a rectangle is calculated by multiplying its length (l) by its width (w).

Therefore, the area (A) of a rectangle can be expressed as:

A = l * w

So, the area of a rectangle with length l and width w is given by the product l * w.

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the missing number should be the square root of the last number times 2 for a perfect trinomial

 so square root of 49 = 7

7*2 =14

 so the missing number should be 14

To solve the given task, change the Cartesian coordinates into spherical coordinates. Rewrite the integrand and the solid hemisphere limits according to these new variables. Evaluate the final triple integral using standard techniques.

To solve the given problem, the first step is to convert the Cartesian coordinates into spherical coordinates. In spherical coordinates, a point in three dimensions is represented by three parameters: ρ (rho) for the radial distance, θ (theta) for the azimuthal angle, and φ (phi) for the polar angle.

Here, given x² + y² + z² ≤ 4, z ≥ 0, the given region corresponds to a solid hemisphere centered at the origin and radius 2 in spherical coordinates, goes as 0 ≤ ρ ≤ 2, 0 ≤ θ ≤ 2π, and 0 ≤ φ ≤ π/2. Our spherical coordinates are x = ρsin(φ)cos(θ), y = ρsin(φ)sin(θ), and z = ρcos(φ).

Then, rewrite the integrand using spherical coordinates, (9 - x² - y²) becomes (9 - ρ²sin²(φ)) and dv becomes ρ²sin(φ)dρdφdθ.

The final integral that needs to be evaluated will read: ∫₀^2 ∫₀^π/2 ∫₀^2π (9 - ρ²sin²(φ))ρ²sin(φ) dθ dφ dρ. This is a triple integral in spherical coordinates that you can now solve using standard integration techniques.

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The given function  [tex]f(x) = \dfrac{ 3}{x + 2} -\sqrt{x-3}[/tex] The value of f(7) would be -1.67.

The function is a type of relation, or rule, that maps one input to a specific single output.

The given function

[tex]f(x) = \dfrac{ 3}{x + 2} -\sqrt{x-3}[/tex]

By substitute x = 7 to find f(7)

[tex]f(7) = \dfrac{ 3}{7 + 2} -\sqrt{7-3}\\\\f(7) = \dfrac{ 3}{9} -\sqrt{4}\\\\f(7) = \dfrac{ 1}{3} -2\\\\f(7) = \dfrac{ 1 - 6}{3}\\\\f(7) = \dfrac{ -5}{3}\\[/tex]

f(7)= -5/3 = -1.67

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