What is an equation of the line that is perpendicular to y + 1 = - 3 (x - 5) and passes through the point (4, -6)?

The ratio of perimeters is equal to the ratio of corresponding sides. The ratio of areas is the square of the ratio of corresponding sides.

The ratio of perimeters is equal to the ratio of corresponding sides. The ratio of areas is the square of the ratio of corresponding sides.

For a right triangle with legs of length 6 cm and 8 cm and a hypotenuse of length 10 cm, if each dimension is multiplied by 1/2 to form a similar triangle, the corresponding sides of the new triangle will be 3 cm, 4 cm, and 5 cm. The ratio of perimeters, 4 + 3 + 5 = 12, is equal to the ratio of corresponding sides, 6 + 4 + 5 = 15. So, the statement that the ratio of perimeters is equal to the ratio of corresponding sides is true.

The ratio of areas can be calculated by squaring the ratio of corresponding sides. So, the ratio of areas for the original right triangle will be (6 * 8) = 48 and for the similar triangle it will be (3 * 4) = 12. The ratio of areas, 48:12, simplifies to 4:1, which is indeed the square of the ratio of corresponding sides, 15:3.

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 cost price is 16500

Let's learn about the basic formula about Profit and Loss

[tex]\texttt{Profit = Selling Price - Cost Price}[/tex]

[tex]\texttt{Selling Price = Cost Price ( 100\% + Profit\% )}[/tex]

[tex]\texttt{Loss = Cost Price - Selling Price}[/tex]

[tex]\texttt{Selling Price = Cost Price ( 100\% - Loss\% )}[/tex]

Let us tackle the problem !

Given:

Gain Percentage = 5%

Loss Percentage = 5%

Difference of Sales Price = 1650

Unknown:

Cost Price = ?

Solution:

[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 100\% + \texttt{Gain Percentage} )[/tex]

[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 100\% + 5\% )[/tex]

[tex]\texttt{Initial Sales Price} = \texttt{Cost Price} \times ( 105\% )[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 100\% - \texttt{Loss Percentage} )[/tex]

[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 100\% - 5\% )[/tex]

[tex]\texttt{Final Sales Price} = \texttt{Cost Price} \times ( 95\% )[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{Difference of Sales Price} = \texttt{Initial Sales Price} - \texttt{Final Sales Price}[/tex]

[tex]1650 = \texttt{Cost Price} \times ( 105\% ) - \texttt{Cost Price} \times ( 95\% )[/tex]

[tex]1650 = \texttt{Cost Price} \times ( 105\% - 95\% )[/tex]

[tex]1650 = \texttt{Cost Price} \times ( 10\% )[/tex]

[tex]\texttt{Cost Price} = 1650 \div ( 10\% )[/tex]

[tex]\texttt{Cost Price} = 16500[/tex]

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces

The 'Share' plan will be enough for Liza with 650 minutes.

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, Lizzie makes 20 minutes of phone calls each day

There are 30 days in June,

Minutes required in the given month = 20*30 = 600

She should choose the Share plan with 650 minutes so that she will have enough minutes plus 50 minutes left.

Hence, The 'Share' plan will be enough for Liza with 650 minutes.

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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: 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:

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.

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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:25233

Step-by-step explanation:

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 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:

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.