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jenyasd209 [6]
1 year ago
5

(Geometry course question) Explain why it is not possible to construct an equilateral triangle that has

Mathematics
1 answer:
Nutka1998 [239]1 year ago
6 0

Answer:

  √3 is irrational

Step-by-step explanation:

The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.

<h3 /><h3>Location of point C</h3>

With reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC <em>never passes through a point with integer coordinates</em>. (Any point with integer coordinates would be on a line with rational slope.)

<h3>Equilateral triangle</h3>

The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.

The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...

  \left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right]

Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...

  cos(60°)·x + sin(60°)·y

will be irrational.

As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.

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9. Write the number in place value table of 820245​
Lorico [155]

Answer:

Hello! The answer to your question will be below.

Step-by-step explanation:

Attached below....

Number form:820,245

Word form: eight hundred twenty thousand two hundred forty-five

Expanded form: 800,000+20,000+0+200+40+ 5

Place value chart below!!

Hope this helps! :)

⭐️Have a wonderful day!⭐️

3 0
3 years ago
Simplify the expression using the order of operations. 10^2/4 x 3
Setler [38]

Answer:

10^2 is exponent so do it first - 100

100/4=25

25x3=75

75

Parentheses

Exponents

Multiply - Multiply and Divide are interchangeable

Divide

Add - Adding and subtracting are interchangeable

Subtract

Step-by-step explanation:

6 0
3 years ago
I need some help checking and helping solve this project. So grateful this is such a good community.
liq [111]

\color{indigo}\rule{1pt}{1000000pt}

8 0
2 years ago
5) A positive plus a negative will (always, sometimes, never) be negative.
GREYUIT [131]

Hello logan693616!

\huge \boxed{\mathbb{QUESTION} \downarrow}

A positive plus a negative will (always, sometimes, never) be negative.

Give an example that proves your answer:

\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}

A positive plus a negative will <u>sometimes</u> be negative.

  • Suppose, we take a positive number whose value is greater than that of the negative number. While adding them, we'll take the sign of the greater number, which in this case is positive, so our answer will be a positive number. For example, <em>+4 + (-3) = <u>+1</u><u>.</u></em>
  • Now, if we take a negative number which is greater than the positive number, the sum of the two numbers will be negative. For example, (<em>-4) + 3 = <u>-</u><u>1</u><u>.</u></em>
  • So, the answer can actually depend based on the value of the numbers used.
  • Hence, our answer is ⇨ A positive plus a negative will <u>sometimes</u> be negative.

__________________

Hope it'll help you!

ℓu¢αzz ッ

5 0
2 years ago
The ray ‾ ⇀gj is the angle bisector of ∠fgh and m∠fgh = 75° how do you find ∠fgj
Anton [14]

For a better understanding of the solution/explanation given here please go through the diagram in the file attached.

By definition, an angle bisector is a ray that divides an angle into two congruent angles.

In our question we have been given that GJ is the ray that is the angle bisector and that has been shown in the diagram.

Now, since, m\angle FGH=75^{\circ}, therefore, the ray \underset{GJ}{\rightarrow} will divide the original angle m\angle FGH=75^{\circ} into two congruent angles, \angle GJH and \angle FGH. Since, the division is equal, the values of both these angles will be half of the original angle. Thus, we will have:

\angle FGJ=\angle HGJ=\frac{75^{\circ}}{2}=37.5^{\circ}

Thus, the required value of \angle FGJ=37.5^{\circ}

8 0
3 years ago
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