High School Geometry Examples and Practice Questions

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High school geometry

Recent questions in High school geometry

snaketao0g 2022-10-19

Distance between (-3,-2) and (4,7)?

bergvolk0k 2022-10-19

There's a circle of diameter $d$ that is on a wall, and touches a block. Find the value of $d$ .
I'm really unsure how to go about solving this. I wanted to first approach this by using the arc length, but I'm really unsure how to proceed. Anyone have ideas?

robbbiehu 2022-10-19

Distance between (-2,2,6) and (-1,1,3)?

Yazmin Sims 2022-10-19

Number of r-polygons in an n-polygon with no side coinciding
Here is the full question:
r-sided polygons are formed by joining the vertices of an n - sided polygon. Find the number of polygons that can be formed, none of whose sides coincide with those of the n sided polygon.
I imagined $(n - r)$ vertices in a closed polygon. There are $(n - r)$ possibilities for adding r vertices between them. (If we add r vertices here then no 2 vertices will be together). This leads me to $(\binom{n - r}{r})$ . But the correct answer wants me to multiply it with $\frac{n}{n - r}$ . What is the need for the last step?

Ayanna Jarvis 2022-10-19

Distance between (8,6,0) and (-1,4,-2)?

limfne2c 2022-10-19

Evaluating min/max probability with Geometric random variables
Suppose that $X_{1}, \dots, X_{n}$ are independent, ${geometric}_{1} (p)$ random variables. Evaluate $P (min (X_{1}, \dots, X_{n}) > l)$ and $P (max (X_{1}, \dots, X_{n}) \leq l)$
The textbook solution is as follows:
$\begin{aligned} P (min (X_{1}, \dots, X_{n}) > l) & = P (⋂_{k = 1}^{n} {X_{k} > l}) \\ = \prod_{k = 1}^{n} P (X_{k} > l) \\ = \prod_{k = 1}^{n} p^{l} \\ = p^{l n} \end{aligned}$
and $\begin{aligned} P (max (X_{1}, \dots, X_{n}) \leq l) & = P (⋂_{k = 1}^{n} {X_{k} \leq l}) \\ = \prod_{k = 1}^{n} P (X_{k} \leq l) \\ = \prod_{k = 1}^{n} (1 - p)^{l} \\ = (1 - p^{l})^{n} \end{aligned}$
I'm having trouble understanding pretty much the entire solution. If I were to summarize what's particularly puzzling me:
1) How was the first line of each solution derived (i.e. $P (min (X_{1}, \dots, X_{n} > l) = P (\cap_{k = 1}^{n} {X_{k} > l})$ and the corresponding equation for max)?
2) The PMF for ${Geometric}_{1} (p)$ is given as $p_{X} (k) = (1 - p) p^{k - 1}$ . How is $P (X_{k} > l) = p^{l}$ ? The same applies for the max case as well.

Raiden Barr 2022-10-19

Probability question about geometric distribution
Let X have a geometric distribution. Show that $P (X > k + j | X > k) = P (X > j)$ , where k and j are nonnegative integers.

taumulurtulkyoy 2022-10-19

Distance between (3,-1,1) and (1,-2,0)?

raapjeqp 2022-10-19

ABC is a triangle with a right angle at C, if the median of the side c is the geometric mean of sides a and b, prove that one of the acute angles of ABC is $15^{o}$

Hunter Shah 2022-10-18

Finding volume using disks/washers
Find the volume of a solid obtained by rotating the region bounded by $y = \sqrt{x}$ and $y = x$ about $y = 2$ .

hogwartsxhoe5t 2022-10-18

In hyperbolic geometry, ideal triangles are all congruent to each other.
Convex Ideal quadrilaterals ( a quadrilateral where all $4$ points are ideal points) all have the same area ( $(2 π)$ )

Brianna Schmidt 2022-10-18

What is the distance between (15,24) and (12,14)?

Danika Mckay 2022-10-17

On the interval [0, 5] we randomly and independently choose two numbers that divide this interval into three sections. The smaller number is denoted by a and the larger number by b. What is the probability event that section [a, b] will be the shortest and section [0, a] the longest?

Amira Serrano 2022-10-17

Distance between (-5,13,4) and (2,-16,-2)?

cousinhaui 2022-10-17

A rectangular pool measures 100 meters by 30 meters. What is the area of the pool in ares? $1 a = 100 m^{2}$

Christopher Saunders 2022-10-17

Translate this congruence statement into English sentence $\bar{T O} ≅ \bar{B E}$ .

Valery Cook 2022-10-17

Distance between (−73,−22) and (-61,−14)?

Chaim Ferguson 2022-10-17

Median from Probability distribution formula
How i can get formula for median of geometric distribution with this probability mass function formula $P_{r} = \frac{(1 - α) α^{C W}}{1 - α^{C W}} . α^{- r}$

podvelkaj8 2022-10-17

Distance between (4,-5) and (-6,7)?

Cale Terrell 2022-10-17

What is the distance between (18,5) and (6,2)?

Geometry help for high school students is one of the most popular requests online as Geometry always requires examples to learn. It is one of the reasons why high school geometry examples that have been provided will help you find the answers to the most common questions, be it graphs or the use of algebraic equations. If you require help with high school geometry, compare your instructions with the questions that have been shared below. The same relates to high school geometry test questions that are provided with multiple-option examples. Dealing with analytical geometry problems, always focus on word challenges.

Expert Help with High School Geometry