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Jet001 [13]
2 years ago
8

Rotate the following triangle 90 degrees. A(4, -3) B(-12, 8) C(6, -4)

Mathematics
1 answer:
Snowcat [4.5K]2 years ago
4 0

Answer:

given vertices of triangle ABC

A(4, -3) B(-12, 8) C(6, -4)

Rotating through 90°

P (x , y) -----> P' (y , -x)

A(4, -3) ------> A' ( -3 , -4 )

B(-12, 8) -----> B' (8 , 12 )

C(6, -4) ------> C' (-4 , -6)

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X + x + x = 54<br> What’s the answer for this
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Answer:

x = 18

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x+x+x=54

(x+x+x)=54(Combine Like Terms)

3x=54

3x=54

Step 2: Divide both sides by 3.

3x  3 = 54

3 x=18

Answer:

x=18

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Calculate the effective annual interest rate if the annual interest rate, i, is 9%.
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The Great Pyramid of Giza is an example of a square pyramid and is the last
Verdich [7]

Answer:

The surface area of the pyramid is 466,137 squared cubits

Step-by-step explanation:

This is simply asking us to find the surface area of the square based pyramid with the given dimensions.

The first thing we need to know is the principle for finding the surface area of such pyramidal shapes. To get the surface area of a pyramid, we will have to add the base area to the area of the side faces ( lateral area)

The base area of the square based pyramid, will be the same as the area of a square which is = 453 cubits X 453 cubits =205209 cubits^{2}

The lateral area has already been given to us as 260,928 squared cubits.

The surface area of the pyramid is 260,928 + 205209 = 466137 squared cubits

Hence, the surface area of the pyramid is 466137 squared cubits

5 0
3 years ago
Which set of numbers could represent the lengths of the sides of a right triangle?
DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

<h3>Pair: 8, 15, 17</h3>

By the pythagorean theorem, a triangle is a right triangle if and only if

\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2.

In this case,

\text{longest side}^2 = 17^2 = 289.

\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}.

In other words, indeed \text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2. Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

<h3>Pair: 10, 15, 20</h3>

Factor out the common factor 2 to simplify the calculations.

\text{longest side}^2 = 20^2 = 400

\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}.

\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2.

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

<h3>Pair: 12, 18, 22</h3>

\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121.

\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}.

\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2.

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

<h3>Pair: 7, 9, 11</h3>

\text{longest side}^2 = 11^2 = 121.

<h3>\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}.</h3>

\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2.

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

6 0
3 years ago
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