John has pet rabbits in an enclosure that has an area of 30.72 square feet. The enclosure Taylor is planning to build for his rabbits will be 2.2 times as large as John's. How many more square feet will Taylor's enclosure have than John's enclosure?

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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Answer:

Step 2 has an error

Step-by-step explanation:

Given equation,

2(10 - 13x) = -34x + 60

By distributive property,

20 - 26x = -34x + 60

Now, we need to isolate x on the left side of the equation,

For this we need to eliminate constant term from the left side,

20 will be eliminated by subtracting 20 from both sides ( subtraction property of equality )

I.e. Step 2 has an error,

We need to use subtraction property of equality instead of using addition property of Equality,

Note : The correct steps would be,

Step 2 : 20 - 26x = -34x + 60 ( Subtraction property of equality )

Step 3 : 8x = 40  ( addition property of Equality )

Step 4 :  x = 5  (  Division Property of Equality )

Answer:

[tex]15.99x+12.54y\leq 125[/tex]

Step-by-step explanation:

Let

x------> the number of purchased plants

y------> the number of purchased bags of soil

we know that

The inequality that represent the situation is equal to

[tex]15.99x+12.54y\leq 125[/tex]

The solution is the triangular shaded area

see the attached figure

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 speed of an ostrich is 2 miles/hr.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, a roadrunner bird can run 14 miles per hour, which is 14 miles/hr and it is faster by 7 times than an ostrich.

∴ The speed of ostrich is (14/7) miles/hr.

= 2 miles/hr.

learn more about the unitary method here :

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Final answer:

It takes 3.75 minutes for a copy machine that makes 36 copies per minute to make 135 copies.

Explanation:

To calculate how long it takes to make 135 copies with a machine that copies at the rate of 36 copies per minute, you can use a simple division. First, divide the total number of copies needed by the number of copies the machine can make per minute.

So, the calculation would be: 135 copies divided by 36 copies per minute = 3.75 minutes.

Therefore, it would take 3.75 minutes for the copy machine to make 135 copies.

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

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 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

7 2/45 would be the correct answer

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:

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:

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.

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.