If you place a 45-foot ladder against the top of a 36-foot building, how many feet will the bottom of the ladder be from the bottom of the building?

Answer: An atom a fundamental piece of matter. ... An atom itself is made up of three tiny kinds of particles called subatomic particles: protons, neutrons, and electrons. The protons and the neutrons make up the center of the atom called the nucleus and the electrons fly around above the nucleus in a small cloud.

Step-by-step explanation:

Answer:

C. 29.46 years

Step-by-step explanation:

The other person is correct, thank you.

Saturn's mean distance from the Sun at 9.54 AU gives it an orbital period of about 29.46 Earth years.

The student is asking about the orbital period of Saturn based on its average distance from the Sun, expressed in astronomical units (AU). According to Kepler's third law of planetary motion, there is a relationship between the orbital period of a planet and its average distance from the Sun. For Saturn, its mean distance from the Sun is approximately 9.54 AU, and its orbital period is roughly 29.46 Earth years.

Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This can be expressed mathematically as p² = a³, where p is the orbital period in Earth years and a is the semi-major axis in AU. By checking Saturn's given values for p² (29.46 * 29.46 = 867.9) and a³ (9.54 * 9.54 * 9.54 = 868.3), we can see that Saturn's data approximates the relation of Kepler's third law effectively, confirming that an orbital period of 29.46 years for Saturn's distance from the Sun is consistent.

The vertex is (-1,0), range is (-inf,0], increasing on (-inf,-1), decreasing on (1,inf)

The key aspects of the function [tex]f(x) = - x^2 - 2x - 1[/tex] are as follows:

Vertex: The vertex of a quadratic function is the point where the function changes from increasing to decreasing, or vice versa. To find the vertex, we can complete the square or use the vertex formula. In this case, the vertex is (-1,0).

Range: The range of a function is the set of all possible output values. Since the leading coefficient in f(x) is negative, the parabola opens downwards, so the range is all numbers less than or equal to 0, or (-inf,0].

Increasing/Decreasing: A quadratic function is increasing to the left of its vertex and decreasing to the right of its vertex. Therefore, f(x) is increasing on (-inf,-1) and decreasing on (-1,inf).

Domain: The domain of a function is the set of all possible input values. For quadratic functions, the domain is all real numbers, so the domain of f(x) is all real numbers.

Therefore, The vertex is (-1,0), range is (-inf,0], increasing on (-inf,-1), decreasing on (1,inf).

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The answer is <w and <v; <x and <y. hope that helps

Answer:

<w, <v; <x, <y

Step-by-step explanation:

I just took the test. May I have Brainiest? I still need four to level up... TwT

Answer:  The given statement is FALSE.

Step-by-step explanation:  We are given to check whether the following statement is TRUE of FALSE :

"There are values of t so that [tex]\sin t=\dfrac{5}{4}.[/tex]"

We know that the range of sine function is the close interval [-1, 1].

That is,

the value of sine of any angle cannot be less than -1 and greater than 1.

According to the given information, we have

[tex]\sin t=\dfrac{5}{4}=1.25>1.[/tex]

So, no such values of t exists for which [tex]\sin t=\dfrac{5}{4}.[/tex]

Hence, the given statement is FALSE.

To find the total number of students in the school district, set up a proportion using the given information. Cross multiply to solve for x.

To find the total number of students in the school district, we can set up a proportion using the given information. If 240 students represent 5% of the total students, we can write the proportion as:
x/240 = 100/5
Cross multiplying, we get:
x = (240 * 100) / 5
Simplifying, we find:
x = 4800
Therefore, there are 4800 students in the school district.

To find the total number of students in the school district, divide the number of students at Misty's school (240) by the percentage they represent (5%), resulting in a total of 4800 students in the school district.

If Misty's school has 240 students, which represents 5% of the total students in the school district, we can calculate the total number of students in the school district using percentages and equivalent fractions. We can set up an equation where 240 students is 5% of the total number of students (let's call this total x).

The equation is 240 = 0.05 * x. To find x, divide 240 by 0.05, which gives us x = 240 / 0.05. This calculation yields x = 4800. Therefore, there are 4800 students in the school district.

Answer:

To return to the top of the canyon he rappelled 40 ft above .

Step-by-step explanation:

Given  : Manoj rappelled 30 ft down from the top of a canyon. He then rappelled an additional 10 ft down the canyon.

To find : What must he do to return to the top of the canyon.

Solution : We have given

Manoj rappelled down from the top of a canyon = 30 ft.

Again he rappelled an additional down the canyon = 10ft.

So, total distance he covered = 30 ft + 10 ft = 40 ft .

Now , He is 40 ft down from the top of the canyon .

To return to the top of the canyon he rappelled 40 ft above .

Therefore, To return to the top of the canyon he rappelled 40 ft above .

The bottom of the ladder will be 27 feet from the bottom of the building.

To find the distance from the bottom of the ladder to the bottom of the building, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the ladder forms the hypotenuse, and the building forms one of the other sides of the right triangle. Let's denote the length from the bottom of the ladder to the bottom of the building as x.

According to the Pythagorean theorem:

[tex]\[ \text{Hypotenuse}^2 = \text{Adjacent side}^2 + \text{Opposite side}^2 \][/tex]

Given:

- Length of the ladder (hypotenuse) = 45 feet

- Height of the building (opposite side) = 36 feet

We need to find the length of the adjacent side (the distance from the bottom of the ladder to the bottom of the building).

[tex]\[ 45^2 = x^2 + 36^2 \][/tex]

2025 = [tex]x^2[/tex] + 1296

[tex]x^2[/tex] = 2025 - 1296

[tex]x^2[/tex] = 729

x = [tex]\sqrt{729}[/tex]

x = 27

The term that correctly labels the blank in the graphic organizer depends on the specifics of the organizer itself. It could either be a square, quadrilateral, pentagon, or triangle.

Without seeing the graphic organizer, it is difficult to provide a specific answer. However, each option represents a different type of bidimensional figure in mathematics. A square is a specific type of quadrilateral with all sides equal and all angles being 90 degrees. A quadrilateral is a polygon with 4 sides, which can be of different lengths and angles. A pentagon is a polygon with 5 sides. A triangle is a polygon with 3 sides. Depending on what the graphic organizer is showing, any one of these could be the correct answer.

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Answer:B Quadrilateral

Step-by-step explanation:

Answer:B Quadrilateral

Step-by-step explanation:

Answer:  The required greatest common factor of the given expressions is [tex]6wy^2.[/tex]

Step-by-step explanation:  We are given to find the greatest common factor of the following two expressions :

[tex]E_1=60w^5y^3,\\\\E_2=78wy^2.[/tex]

The factorization of the given expressions can be written as :

[tex]E_1=2^2\times3\times5\times w^5\times y^3,\\\\E_2=2\times3\times13\times w\times y^2.[/tex]

Therefore, the greatest common factor of the given expressions is

[tex]GCD(E_1,E_2)=2\times3\times w\times y^2=6wy^2.[/tex]

Thus, the required greatest common factor of the given expressions is [tex]6wy^2.[/tex]

The new coordinates after a dilation with scale factor 2 are: V'(12, 4), W'(-4, 8), X'(-6, -4), Y' (6, -10). The new coordinates are calculated by multiplying both the x and y coordinates of the original points by the scale factor.

Dilation is a transformation that alters the size of the figure without changing its shape. It's accomplished by multiplying the original coordinates of the vertices by a specified scale factor.

The original coordinates of quadrilateral VWXY are V(6, 2), W(–2, 4), X(–3, –2), and Y(3, –5). The scale factor given is 2. Let's find the coordinates of each point after dilation.

1. First, we'll start with point V. Its coordinates are (6,2). After dilation with a scale factor of 2, we multiply each coordinate by the scale factor. The new coordinates are (6 × 2, 2 × 2) which gives us (12, 4).

2. The coordinates of point W are (–2, 4). After dilation, we obtain the new coordinates as (–2 × 2, 4 × 2), which gives us (–4, 8).

3. Now we move onto point X. Its coordinates are (–3, –2). After dilation, the new coordinates become (–3 × 2, –2 × 2), which is (–6, –4).

4. Lastly, we have point Y. Its coordinates are (3, –5). After dilation, the new coordinates become (3 × 2, –5 × 2), which gives us (6, –10).

Therefore, the coordinates of the quadrilateral V'W'X'Y' after dilation with the scale factor of 2 are V'(12, 4), W'(–4, 8), X'(–6, –4), and Y'(6, –10).

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To solve Euler's formula for the number of edges E, you rearrange the formula to E = V + F - 2. This solution requires the basic operations of adding and subtracting from both sides of the equation.

Euler's formula states that V (vertices) minus E (edges) plus F (faces) equals 2 for any polyhedron without holes. Therefore, to solve for E, we need to rearrange the equation as follows:

Starting with the original formula: V - E + F = 2.

Add E to both sides: V + F = E + 2.

Subtract 2 from both sides to solve for E: E = V + F - 2.

This rearranged formula gives us the number of edges E in terms of the number of vertices V and the number of faces F.

The formula for the number of edges (E) in terms of the number of vertices (V) and faces (F) is E = 2 + V - F.

To solve Euler's formula V − E + F = 2 for E, we need to isolate E on one side of the equation. Here's how we can do that:

Add E to both sides of the equation to move the term containing E to one side:

V − E + F + E = 2 + E

V + F = 2 + E

Subtract V and F from both sides:

V + F - V - F = 2 + E - V - F

0 = 2 + E - V - F

Rearrange the terms:

2 = E - V + F

Finally, isolate E by adding V and subtracting F from both sides:

E = 2 + V - F

Therefore, the formula for the number of edges (E) in terms of the number of vertices (V) and faces (F) is E = 2 + V - F.

Answer:

6 feet

Step-by-step explanation:

A soccer ball is kicked from the ground in an arc defined by the function,

[tex]h(x) = -2x^2 + 8x[/tex]

h(x) is the height of the ball and time is t.

we need to find out the height when t= 3 seconds

Plug in 3 for t

[tex]h(x) = -2x^2 + 8x[/tex]

[tex]h(3) = -2(3)^2 + 8(3)[/tex]

[tex]h(3) =-18+24=6[/tex]

The height of the ball after 3 seconds is 6 feet.

7 2/45 would be the correct answer