# Tagged Questions

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### How to prove this assertion about $\mathbb{R}^k$?

Suppose $k \geq 3$, $x$, $y \in \mathbb{R}^k$, $|x-y| = d > 0$, and $r > 0$. Then how to prove the following assertions? (a) If $2r > d$, then there are infinitely many $z \in \mathbb{R}^k$ ...
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### can you help me solve my menu board dilemma?

If I have a menu board that measures 35 3/8 $\times$ 71 5/8 and I need to cut in 3 equal pieces, what measurements should each piece be?
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### How to determine the length of $x$ in this sketch?

Consider the following construction: Assume that you are given the lengths of the sides $a,b,c,d,e$ as well as the size of the angle $\phi$. The task is to determine the length of $x$ in terms of the ...
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### How to do you find missing vertix in right triangle in a graph?

![enter preformatted text here][2]I'm graphing a line segment. The end points are $A$ and $B$. Then I"m using $10 \%$ of the length of line segment $AB$ to form ...
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### How would you prove that the graph of a linear equation is a straight line, and vice versa, at a “high school” level? [duplicate]

This is something I've been wondering about. Namely, I've always accepted "on intuition" that the equation $$ax + by = c$$ is, when graphed, a line. You can plot the points $(x, y)$ satisfying the ...
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### Find the shaded area

Find the shaded area Here is the equation that i've made \begin{align*} S&=\pi R^2\\ S_1&=\pi {R_1}^2\left(\frac{24}{360}\right)\\ S_2&=\pi{R_2}^2\left(\frac{24}{360}\right) \end{align*} ...
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### Inequality regarding areas of triangles

BdMO Nationals 2013: There is a point O inside ∆ABC. After joining A,O; B,O and C,O extend those line and they will intersect BC, AC and AB at points D, E and F respectively. ...
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### Solve $10x+2x^2+x^3=20$ using only algebra and geometry?

The cubic formula and modern math is not allowed, only algebra, geometry, and the like. Supposedly this problem was given to Fibbonaci. Here is the whole paragraph I read: In Flos Fibonacci gives ...
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### Existance and uniqueness of solution for a point with fixed distances to three other points

I have two sets of known points in $\mathbb{R}^2$: Four points $\mathbf{p_1}, \mathbf{p_2}, \mathbf{p_3}, \mathbf{p_x}$ , and three other points $\mathbf{q_1}, \mathbf{q_2}, \mathbf{q_3}$. I would ...
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### how to calculate the area of ​​a rhombus is in $cm^2$

How do I calculate the area of ​​a rhombus is in $cm^2$? Is the formula $\frac12 \times 17 \times 16$? Anyone can help me to solved this? I don't know the rhombus formula. Based on my exercise ...
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### Calculate dimensions of inner box

This is my first post here and also i'm bad with math so don't be mad at me :) Here is my issue, i have a box and i have another box inside, now i want that box inside to be at exactly same distance ...
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### Making a circle with paper folding, scissors, pencil, and a straightedge

Can we make a circle using paper folding, scissors, straightedge, anda pencil, allowing an infinite number of operations? I think my chemistry teacher have show me once how to make it during the ...
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### Solving Triangles (finding missing sides/angles given 3 sides/angles)

What is a general procedure for "solving" a triangle—that is, for finding the unknown side lengths and angle measures given three side lengths and/or angle measures?
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### Systems of equations finding right triangles

I need help setting up the equation for the question, "Find all right triangles for which the perimeter is $24$ units and the area is $24$ square units." I know that the area is $A = \frac12 b h$ ...