Geometry

Problem 2001

Find the center $(h, k)$ and radius $r$ of the circle from $(x-h)^{2}+(y-k)^{2}=r^{2}$ . Derive the general equation of a circle.

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Problem 2002

Find the distance from the point $(-1, -3)$ to the circle defined by $x^{2}+y^{2}+2x+6y-6=0$ ; it's 4 units.

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Problem 2003

Сумма двух углов прямоугольного треугольника $126^{\circ}$ . Найдите острые углы.

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Problem 2004

Convert the circle equation $x^{2}+y^{2}+x-3y-\frac{1}{2}=0$ to standard form and find its center and radius.

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Problem 2005

Hitung luas bilik dalam $\mathrm{cm}^{2}$ jika 250 jubin berukuran $6.096 \times 10^{2} \mathrm{~mm}$ dan $3.048 \times 10^{2} \mathrm{~mm}$ .

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Problem 2006

Cari nilai $x$ jika $n(\xi)=52, n(P)=40, n(P \cap Q)=9$ dan $n\left(P^{\prime}\right)=x+7$ .

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Problem 2007

Найдите периметр равнобедренного треугольника, если одна сторона $a = 7$ дм, а другая $b = a + 8$ дм.

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Problem 2008

Постройте угол bisectrix с помощью циркуля и линейки.

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Problem 2009

Find a formula for the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

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Problem 2010

Can Arshad construct a unique quadrilateral with sides $AB=5 \mathrm{~cm}$ , $\angle A=50^{\circ}$ , $AC=4 \mathrm{~cm}$ , $BD=5 \mathrm{~cm}$ , and $AD=6 \mathrm{~cm}$ ? Explain why or why not.

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Problem 2011

Find the area of a circle with a radius of 10 inches using $A=\pi r^{2}$ and $\pi=3.14$ . Choices: A) $3.14 \mathrm{in}^{2}$ B) $31.4 \mathrm{in}^{2}$ C) $314 \mathrm{in}^{2}$ D) $3,140 \mathrm{in}^{2}$ E) $31,400 \mathrm{in}^{2}$

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Problem 2012

Find the volume of a right cone with a base diameter of $9.5 \mathrm{~cm}$ and a height of $16 \mathrm{~cm}$ .

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Problem 2013

Una gaviota observa un bote a $42^{\circ}$ de depresión desde 45 m de altura. ¿Cuál es la distancia horizontal al barco?

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Problem 2014

Find $m \angle Q O R$ if $m \angle P O Q=24$ and $m \angle P O R=59$ .

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Problem 2015

Find $m \angle R O S$ if $m \angle Q O S=46$ , $m \angle P O R=61$ , and $m \angle P O Q=28$ .

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Problem 2016

Desde una torre de 28 m, un salvavidas ve a una persona con un ángulo de depresión de $58^{\circ}$ . ¿Cuál es la distancia a la persona?

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Problem 2017

Find $m \angle P O S$ if $m \angle P O Q = 19$ , $m \angle Q O R = 31$ , and $m \angle R O S = 15$ .

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Problem 2018

Find the length of a segment with endpoints at $(-1, 11)$ and $(4, 5)$ .

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Problem 2019

In a pipeline with a 30 cm diameter and water speed of 1.5 m/s, find the speed at a 1 cm diameter.

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Problem 2020

The office floor plan is at a scale of $1:20$ . Find the actual length for $96 \mathrm{~cm}$ and pantry area in $\mathrm{cm}^{2}$ for $4.8 \mathrm{~m}^{2}$ .

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Problem 2021

In square $ABCD$ , area equals the sum of areas of triangles $ABE$ and $DCE$ . If $AB=6$ , find $CE$ . (a) 5 (b) 6 (c) 2 (d) 3 (e) 4

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Problem 2022

In square $ABCD$ with $AB=6$ , the area equals the sum of triangles $ABE$ and $DCE$ . Find length of $CE$ .

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Problem 2023

Find the area $x$ of hexagon $ABCDEF$ with rectangle $ABCD$ where $AB=9$ cm, $BC=16$ cm, $AE=8$ cm, and $FG=3$ cm.

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Problem 2024

Determine the location of the point $(-3,4)$ in the coordinate plane.

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Problem 2025

Berechne Volumen und Oberfläche einer Pyramide mit Grundfläche $a=15 \mathrm{~cm}, b=12 \mathrm{~cm}, h=20 \mathrm{~cm}$ .

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Problem 2026

Berechne den Umfang und Flächeninhalt eines runden Tisches mit $r=25 \mathrm{~cm}$ .

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Problem 2027

Find the missing angle in triangles ABE and DEC where $\angle ABE=25^{\circ}$ and $\angle EDC=100^{\circ}$ .

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Problem 2028

Clarence's garden is 20 ft by 40 ft. How many 4-yard fencing packages do they need for the perimeter?

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Problem 2029

Berechne das Volumen und die Oberfläche eines Quaders mit $a=4 \mathrm{~cm}, b=6 \mathrm{~cm}, c=12 \mathrm{~cm}$ .

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Problem 2030

已知圆O的半径为2.5，弦AB的长度为2，若三角形ABC为等腰三角形，则求 $BC^{2}=$ 。

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Problem 2031

1. Într-un triunghi dreptunghic $A B C$ cu $\angle C=60^{\circ}$ , găsiți măsura unghiului $A D C$ (bisectoarea $B A M$ ).
2. Calculați aria unui paralelogram cu laturile $A B=170 \mathrm{~m}, B C=80 \mathrm{~m}$ și diagonala $B D=150 \mathrm{~m}$ .

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Problem 2032

Calculați aria triunghiului $B O D$ și măsura unghiului $B A D$ în patrulaterul convex $A B C D$ cu datele date.

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Problem 2033

Determine the general equation of the circle defined by $x^{2}+y^{2}=16$ .

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Problem 2034

Find the perimeter of Central Park, given vertices at $(-1.25,-0.25)$ , $(-1.25,0.25)$ , and $(1.25,0.25)$ .

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Problem 2035

Calculate the volume and surface area of a cube with side length 3 units. Use $V = s^3$ and $A = 6s^2$ .

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Problem 2036

4. Într-un pătrat $A B C D$ , cu punctele $E, F, G$ pe laturi, arată că triunghiul $D E G$ este isoscel și află unghiul dintre $D F$ și $E G$ .

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Problem 2037

5. Într-un dreptunghi cu $AB=12 \mathrm{~cm}$ și $BC=4 \mathrm{~cm}$ , calculează aria triunghiului $CEO$ și unghiul $BFC$ .

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Problem 2038

Find the volume of a cuboid with dimensions 3, 3, and 4 units: $V = l \times w \times h$ .

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Problem 2039

What does the coefficient 7 represent in a rectangle with width $x$ and length $7x$ ? A. Length is 7 times width. B. Area is 7. C. Width is 7 times length. D. Length is 7.

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Problem 2040

Thando's bag is 35cm x 35cm x 30cm. How many 27cm x 27cm x 3.5cm pizza boxes fit in it? After a 15% size increase, can they still fit?

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Problem 2041

Find the total length of two semicircles with centers $R$ and $S$ , where $RS=12$ . Options are: (A) $8 \pi$ , (B) $9 \pi$ , (C) $12 \pi$ , (D) $15 \pi$ , (E) $16 \pi$ .

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Problem 2042

Determine the quadrant for a point with positive coordinates $(x > 0, y > 0)$ .

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Problem 2043

What conjecture about the triangle's perimeter could Maryanne have made after the translation $(x-10, y+17)$ ?

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Problem 2044

What could Maryanne's conjecture about the triangle's perimeter be after the translation $(x-5, y+11)$ ?

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Problem 2045

Translate Triangle RST with vertices $R (-4,2)$ , $S (5,3)$ , $T (2,-5)$ , 4 down and 3 left. Find new coordinates.

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Problem 2046

Un topógrafo mide el ángulo de elevación al cerro: $45^{\circ}$ y a $800$ m más, $30^{\circ}$ . ¿Cuál es la altura del cerro?

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Problem 2047

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5 \text{ km}$ , $AC=1.2 \text{ km}$ , and $\angle A=50^\circ$ .

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Problem 2048

等腰三角形一个底角为 45 度，问这个三角形的类型是？(1) 锐角 (2) 直角 (3) 钝角 (4) 无法确定

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Problem 2049

Elena has a rectangular aquarium with height $1 \frac{3}{4} \mathrm{ft}$ . If the painted area is $5 \frac{5}{6} \mathrm{ft}^{2}$ , find the length.

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Problem 2050

Find the volume of Lin's aquarium with dimensions $\frac{7}{2} \mathrm{ft}$ (length), $\frac{4}{3} \mathrm{ft}$ (width), and $\frac{3}{2} \mathrm{ft}$ (height).

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Problem 2051

Sebuah papan sasar bulatan dengan jejari $20 \mathrm{~cm}$ . Beza jejari antara bulatan $P, Q, R, S$ dan $T$ ialah $4 \mathrm{~cm}$ .
Hitung: (a) Beza lilitan bulatan $T$ dan $P$ . (b) Luas kawasan $P$ dan $R$ (gunakan $\pi=\frac{22}{7}$ ).

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Problem 2052

Hitung (a) beza lilitan bulatan $T$ dan $P$ dalam $\mathrm{cm}$ , (b) luas kawasan $P$ dan $R$ dalam $\mathrm{cm}^{2}$ . Gunakan $\left.\pi=\frac{22}{7}\right.$

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Problem 2053

Hitung beza lilitan bulatan $T$ dan $P$ , serta luas kawasan $P$ dan $R$ dengan $\pi=\frac{22}{7}$ .

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Problem 2054

A circle sector with radius 5 cm and angle 144° forms a cone. Find: 1) base radius, 2) height, 3) volume, 4) surface area, 5) vertical angle.

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Problem 2055

1. Într-o livadă sunt 160 de pomi. În prima zi s-au plantat $60\%$ meri și $40\%$ nuci, iar în a doua zi 76 pomi. Află procentul din prima zi și câți meri și nuci s-au plantat.
2. Consideră $E(x)=x^{2}-(x+1)^{2}-(x+2)^{2}+(x+3)^{2}$ . Arată că $E(x)=4$ pentru orice $x$ și calculează suma $S=1^{2}-2^{2}-3^{2}+4^{2}+\ldots+40^{2}$ .
3. În sistemul de axe $x O y$ , $A(3,2)$ , $B$ simetricul lui $A$ față de $O x$ , și $C$ simetricul lui $A$ față de $O$ . Arată că $C=(-3,-2)$ și determină funcția corespunzătoare lui $BC$ .
4. Semicercul de centru $D$ este tangent la laturile $A B$ și $A C$ ale triunghiului isoscel $A B C$ . Demonstrează că $D$ este mijlocul lui $B C$ și află raza semicercului, știind că $B C=30 \mathrm{~cm}$ și $A D=20 \mathrm{~cm}$ .

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Problem 2056

Calculați aria dreptunghiului $A B C D$ având $A C=6 \mathrm{~cm}$ și $\angle D O C=120^{\circ}$ . Care este aria?

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Problem 2057

Find the perimeter of triangle $ABC$ with $AD=4 \sqrt{3} cm$ , $BC=5 cm$ , and $BD=1 cm$ .

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Problem 2058

A rectangular prism A has dimensions: length = $4 \mathrm{~cm}$ , width = $3 \mathrm{~cm}$ , height = $2 \mathrm{~cm}$ .
a) How many cubes fit along the length?
b) How many cubes fit along the width?
c) How many layers of cubes?
d) What is the volume in cubes?

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Problem 2059

Christopher's fence is rectangular, with length $2 \mathrm{ft}$ longer than width. Points are $S(1, -2)$ , $R(6, -2)$ , $P(1, 8)$ , $Q(6, 4)$ .

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Problem 2060

Xavier's papaya trees cover $370 \mathrm{~m}^{2}$ . The perimeter for pineapple trees is $84 \mathrm{~m}$ . Find their area.

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Problem 2061

Find the length of a rectangular fishpond with a perimeter of $62 \mathrm{~m}$ and length 3 times its width.

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Problem 2062

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

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Problem 2063

Zeichne den Graphen für Anettes Inlinerfahrt: Ampelhalt, steiniger Weg, Auto vorlassen, dann Ankunft.

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Problem 2064

What is the area of this figure? $\square$ square meters Submit

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Problem 2065

13. The vertex of the parabola $y+16=(x-1)^{2}$ is located at (A) $(-1,-16)$ (B) $(-1,16)$ (C) $(1,-16)$ (D) $(1,16)$ (E) $(16,1)$
14. Find the axis of symmetry of parabola

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Problem 2066

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm . If the area of printed material on the poster is fixed at $1,536 \mathrm{~cm}^{2}$ , find the dimensions (in cm ) of the poster with the smallest area.

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Problem 2067

A solid sphere of radius 18.0 cm and mass 10.0 kg starts from rest and rolls without slipping a distance of $\mathrm{L}=7.0 \mathrm{~m}$ down a house roof that is inclined at $30^{\circ}$ .
What is the angular speed about its center as it leaves the house roof? $38.9 \frac{\mathrm{rad}}{\mathrm{s}}$
The height of the outside wall of the house is $h=9 \mathrm{~m}$ . What is the horizontal displacement of the sphere between the time it which it leaves the roof and the time at which it hits the ground? 15.2 m

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Problem 2068

Find the circumcenter of $\triangle E F G$ with $E(4,4), F(4,2)$ , and $G(8,2)$ . Hint: Draw a picture
Select one: A. $(6,3)$ B. $(4,2)$ C. $(4,4)$ D. $(3,6)$

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Problem 2069

Mason is training for the javelin-throw event. A coach created a graph that shows the height of the javelin over time for Mason's best throw.
How many seconds did it take for the javelin to reach its greatest height? A 4.1 s (B) 1.3 s
C 13 s (D) 2 s

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Problem 2070

What is true about all of the coordinate values in the first quadrant?
They are all.... You can earn 5 coins values of 0 or more values of 0 or less

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Problem 2071

Word bank: Not all words are used! $\operatorname{point}(s) \cdot \operatorname{Line}(s) \cdot \operatorname{Segment}(s) \cdot \operatorname{Ray}(\mathrm{s}) \cdot$ Plane(s) • Angles • Vertex Point • Acute Angle(s) Obtuse Angle $(s) \cdot$ Right Angle(s) • Midpoint • 0-Slope • Slope • Equal • Same • Parallel perpendicular • Inverse opposite • Adjacent Angle(s) • Complementary Angle(s) • Congruence Congruent • Supplementary Angle(s) • Vertical Angle(s) • $90^{\circ} \cdot 180^{\circ} \cdot 360^{\circ} \cdot$ Angle Bisector(s) Bisected • Perpendicular Bisector • Postulates • Theorems • Definitions • Given • Proof(s) Converse • Inverse • Contrapositive • Transversal • Alternate Interior • Alternate Exterior Same Side Interior • Same Side Exterior • Additive Angle Properties
The $\qquad$ of parallel lines is "two lines that have the same slope and never intersect. They are also always equidistant from each other."
If two lines intersect at 90 degrees they are $\qquad$
A transversal is a line that cuts across two $\qquad$ lines.
Postulate 1 states that "a $\qquad$ can be formed by any two points"
A midpoint will split a line into two $\qquad$ parts.
Two alternate exterior angles are always $\qquad$ .
Two same-side interior angles are always $\qquad$ .
Perpendicular bisectors have an inverse opposite slope and will always go through a segment's $\qquad$ .
The $\qquad$ is always given for a reason.
If not p , then not q is what an $\qquad$ statement should look like.
To prove "IF/THEN" statements, "IF" is your given and "THEN" should be your $\qquad$ .

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Problem 2072

EXERCICE 4 Ce n'est pas une figure en vraie grandeur. On donne: - Les points K, O, L sont alignés ; O est entre K et $\mathrm{L} ; \mathrm{OK}=2 \mathrm{~cm}$ ; $\mathrm{OL}=3,6 \mathrm{~cm}$ . - Les points J, O, N sont alignés ; $O$ est entre $J$ et $N ; O J=3 \mathrm{~cm}$ ; - Les triangles OKJ et OLN sont rectangle en $K$ et $L$ .
1. Démontrer que les droites (JK) et (LN) sont parallèles.
2. Calculer JK.
3. Calculer ON.

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Problem 2073

Find the measures triangle 3)
Find the meas

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Problem 2074

Show Examples
Question Triangle EFG is similar to triangle HIJ. Find the measure of side JH. Round your answer to the nearest tenth if necessary.

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Problem 2075

$\begin{array}{l} y=\frac{2}{3} x+3 \\ y=-\frac{4}{3} x-3 \end{array}$
Plot two lines by clicking the graph. Click a line to delete it.

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Problem 2076

Other than itself, which angle is congruent to $\angle A E B$ ? $\square$ Submit

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Problem 2077

The radius of a circle is 12.1 ft . Find the circumference to the nearest tenth.
Answer Attempt 1 out of 2 $C=$ $\square$ ft
Submit Answer

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Problem 2078

Graph the image of rectangle STUV after a translation 12 units down.

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Problem 2079

Reorder the steps of the proof to make sure that steps that are logically dependent on prior steps are in the proper order.
Given: $C$ is the midpoint of $\overline{A E}, \overline{A E} \perp \overline{F C}, \angle A \cong \angle E$ and $\angle B \cong \angle D$ .
Prove: $\angle B C F \cong \angle D C F$ . \begin{tabular}{|r|r|} \hline Step & Statement \\ \hline & $C$ is the midpoint of \\ 1 & $\overline{A E} \perp \overline{F C}$ \\ & $\angle A \cong \angle E$ \\ & $\angle B \cong \angle D$ \end{tabular} $2 \angle E C D$ and $\angle D C F$ are complementary Given $\left.\begin{array}{|c|l}\hline 2 & \angle E C D \text { and } \angle D C F \text { are complementary }\end{array} \begin{array}{l}\text { If two angles form a right angle, then they a } \\ \text { complementary }\end{array}\right\}$

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Problem 2080

Lesson 5.3 Example 3 Treat each red box of choices as a set of dropdown choices for each blank. Choose the best answer for each blank. You are given that $\overline{P Q} \cong \overline{P S}$ . By the Reflexive Property of Congruence Transitive Property of Congruence Symmetric Property of Congruence $\overline{R P} \cong \overline{R P}$ . definition of perpendicular lines congruent by the $\square$ triangle sum theorem the corresponding hypotenuse and leg of a right triangle three pairs of sides $\qquad$ So, $\qquad$ Two pairs of sides and their included angle . are congruent.
So, $\triangle P Q R$ and $\triangle P S R$ are congruent by the HL Congruence Theorem SAS Congruence Theorem SAS Congruence Theorem

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Problem 2081

\begin{tabular}{|c|c|} \hline & $V=\frac{1}{3} b h \quad$ for $b$ \\ \hline \end{tabular}

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Problem 2082

The diameter of a circle is 6 cm . Find its area to the nearest tenth.
Answer Attempt 1 out of 2 $A=$ $\square$ $\mathrm{cm}^{2}$
Submit Abser

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Problem 2083

Плошадь параллелограмма Вариант 2 №1. Высота параллелограмма равна 9 cm , а основание - 14 cm . Найдите площадь параллелограмма. N22. Найдите площадь параллелограмма, изображенного на рисунке 1. №3. Найдите площадь параллелограмма, изображенного на рисунке 2 , если размер клетки $1 \times 1.8$ №4. Площадь параллелограмма равна $42 \mathrm{~m}^{2}$ , а основание - 7 м. Найдите высоту параллелограмма. №5. На рисунке 3 изображен параллелограмм $\mathrm{ABCD}, \mathrm{AB}=6 \mathrm{~cm}$ , высоты BE и DF равны по 4 и 8 cm . Найдите сторону AD. №6. По данньмм рисунка 4 найдите площадь параллелограмма.
Рис. 1.
Рис.2.
Рис. 3. c
Рис.4.

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Problem 2084

1. Solve for $x$ . Find the measure of the exterior angle.

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Problem 2085

Two ants crawl around a circle of radius $r=7$ with both $x$ and $y$ measured in inches. Both start at the point ( 7,0 ) at the same time. One bug is moving at a rate of $2 \mathrm{in} / \mathrm{sec}$ . The other is moving twice as fast. When will one ant be directly above the other ant as shown below? (Give the first time this happens assuming they start at $t=0$ .)

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Problem 2086

9 Arty says that if you change a scale so that a unit represents a longer distance than in an original scale, then the lengths in the new scale drawing will be longer. Do you agree? Give an example of a scale and some measurements to support your answer.

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Problem 2087

Prove: $\angle B C F \cong \angle D C F$ . \begin{tabular}{|c|c|c|} \hline Step & Statement & Reason \\ \hline 1 & $C$ is the midpoint of $\overline{A E}$ $\begin{array}{l} \overline{A E} \perp \overline{F C} \\ \angle A \cong \angle E \\ \angle B \cong \angle D \end{array}$ & Given \\ \hline 2 & $\angle A C F$ is a right angle & Perpendicular lines form right angles \\ \hline 3 & $D$ and $\angle D C F$ are complementary & If two angles form a right angle, then they are complementary \\ \hline 4 & $\triangle A B C \cong \triangle E D C$ & AAS \\ \hline 5 & $\angle B C F \cong \angle D C F$ & If two angles are complements of the same angle (or congruent angles), then they are congruent \\ \hline 6 & $B$ and $\angle B C F$ are complementary & If two angles form a right angle, then they are complementary \\ \hline 7 & $\angle E C F$ is a right angle & Perpendicular lines form right angles \\ \hline 8 & $\overline{A C} \cong \overline{C E}$ & A midpoint divides a segment into two congruent segments \\ \hline 9 & - $\angle A C B \cong \angle E C D$ & Corresponding Parts of Congruent Triangles are Congruent (CPCTC) \\ \hline \end{tabular}

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Problem 2088

Figure 3
8. In this example, our two lines are not parallel. Drag Point $E$ to the left and to the right as you have in the previous examples. What is different about this figure? How does it affect the observations you made in the previous examples? Be specific in your explanation. - Vertical anglos.
9. Look at angles BGH and EGA. Why do these angles remain congruent even though the two lines are not parallel? Make a specific distinction between the relationships observed in the first two figures and this figure.

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Problem 2089

Tantukan kainiringan garis singgung graplt dingan parsamaan $r=3+3 \cos \theta$

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Problem 2090

Use the following information to answer the question.
Graph C
Graph B
Graph $\mathbf{D}$
Which of the graphs above represents exponential decay?
Select one: a. Graph A b. Graph B c. Graph C d. Graph D

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Problem 2091

(e) You rotate $\triangle N P Q$ with coordinates $N(12,-3), P(1,2)$ , and $Q(9,0)$ $180^{\circ}$ about the origin.

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Problem 2092

Write the equation in standard form for the circle with center $(1,0)$ passing through $\left(\frac{17}{2},-4\right)$ .

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Problem 2093

State the postulate or theorem you would use to prove e triangles cannot be proven congruent, write none. If triangles can be proven congruent then write the congruence statement. 5. 6. 7.

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Problem 2094

9. Find all of the numbered angles. (NOT drawn to scale!)
Given: $a / / b ; m \angle 5=63^{\circ}$ Show your work. $\begin{array}{c} m \angle 1= \\ m \angle 2= \\ m \angle 3= \\ m \angle 4= \\ m \angle 6= \\ m \angle 7= \end{array}$

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Problem 2095

Where can the medians of a triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle A. I only B. III only C. I or III only D. I, II, or II
Select one: A. A B. $B$ C. C D. $D$

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Problem 2096

\#12 Sarciex Listen
Find the measure of each acute angle in a right triangle where the measure of one acute angle is 3 times the sum of the measure of the other acute angle and 8.
The smaller acute angle measures $\square$ ${ }^{\circ}$ and the larger acute angle measures $\square$ ${ }^{\circ}$ .

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Problem 2097

The trapezoid $C^{\prime} D^{\prime} E^{\prime} F^{\prime}$ is a dilation of the trapezoid $C D E F$ . What is the scale factor of the dilation? Desk 1

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Problem 2098

```latex Find the measure of the numbered angle.
$m \angle 4=$
Angle 8 should equal 140.
Angles 1 and 3, and angles 2 and 4 are vertical.

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Problem 2099

The radius, $R$ , of a sphere is 9.3 m . Calculate the sphere's volume, $V$ . Use the value 3.14 for $\pi$ , and round your answer to the nearest tenth. (Do not round any intermediate computations.) $V=\square \mathrm{m}^{3}$

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Problem 2100

Is it possible for a triangle to have sides with the given lengths? Explain. 5 in., 8 in., 15 in. A. Yes; the sum of each pair is greater than the third. B. No; $5+8$ is not greater than 15 . C. $\mathrm{No} ; 15^{2}>5^{2}+8^{2}$ . D. Yes; $15^{2}>5^{2}+8^{2}$ .

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Geometry

Problem 2001

Find the center (h,k)(h, k)(h,k) and radius rrr of the circle from (x−h)2+(y−k)2=r2(x-h)^{2}+(y-k)^{2}=r^{2}(x−h)2+(y−k)2=r2. Derive the general equation of a circle.

Problem 2002

Find the distance from the point (−1,−3)(-1, -3)(−1,−3) to the circle defined by x2+y2+2x+6y−6=0x^{2}+y^{2}+2x+6y-6=0x2+y2+2x+6y−6=0; it's 4 units.

Problem 2003

Сумма двух углов прямоугольного треугольника 126∘126^{\circ}126∘. Найдите острые углы.

Problem 2004

Convert the circle equation x2+y2+x−3y−12=0x^{2}+y^{2}+x-3y-\frac{1}{2}=0x2+y2+x−3y−21​=0 to standard form and find its center and radius.

Problem 2005

Hitung luas bilik dalam cm2\mathrm{cm}^{2}cm2 jika 250 jubin berukuran 6.096×102 mm6.096 \times 10^{2} \mathrm{~mm}6.096×102 mm dan 3.048×102 mm3.048 \times 10^{2} \mathrm{~mm}3.048×102 mm.

Problem 2006

Cari nilai xxx jika n(ξ)=52,n(P)=40,n(P∩Q)=9n(\xi)=52, n(P)=40, n(P \cap Q)=9n(ξ)=52,n(P)=40,n(P∩Q)=9 dan n(P′)=x+7n\left(P^{\prime}\right)=x+7n(P′)=x+7.

Problem 2007

Найдите периметр равнобедренного треугольника, если одна сторона a=7a = 7a=7 дм, а другая b=a+8b = a + 8b=a+8 дм.

Problem 2008

Постройте угол bisectrix с помощью циркуля и линейки.

Problem 2009

Find a formula for the perimeter of a rectangle with area 100 m2100 \mathrm{~m}^{2}100 m2 as a function of one side's length.

Problem 2010

Can Arshad construct a unique quadrilateral with sides AB=5 cmAB=5 \mathrm{~cm}AB=5 cm, ∠A=50∘\angle A=50^{\circ}∠A=50∘, AC=4 cmAC=4 \mathrm{~cm}AC=4 cm, BD=5 cmBD=5 \mathrm{~cm}BD=5 cm, and AD=6 cmAD=6 \mathrm{~cm}AD=6 cm? Explain why or why not.

Problem 2011

Problem 2012

Find the volume of a right cone with a base diameter of 9.5 cm9.5 \mathrm{~cm}9.5 cm and a height of 16 cm16 \mathrm{~cm}16 cm.

Problem 2013

Una gaviota observa un bote a 42∘42^{\circ}42∘ de depresión desde 45 m de altura. ¿Cuál es la distancia horizontal al barco?

Problem 2014

Find m∠QORm \angle Q O Rm∠QOR if m∠POQ=24m \angle P O Q=24m∠POQ=24 and m∠POR=59m \angle P O R=59m∠POR=59.

Problem 2015

Find m∠ROSm \angle R O Sm∠ROS if m∠QOS=46m \angle Q O S=46m∠QOS=46, m∠POR=61m \angle P O R=61m∠POR=61, and m∠POQ=28m \angle P O Q=28m∠POQ=28.

Problem 2016

Desde una torre de 28 m, un salvavidas ve a una persona con un ángulo de depresión de 58∘58^{\circ}58∘. ¿Cuál es la distancia a la persona?

Problem 2017

Find m∠POSm \angle P O Sm∠POS if m∠POQ=19m \angle P O Q = 19m∠POQ=19, m∠QOR=31m \angle Q O R = 31m∠QOR=31, and m∠ROS=15m \angle R O S = 15m∠ROS=15.

Problem 2018

Find the length of a segment with endpoints at (−1,11)(-1, 11)(−1,11) and (4,5)(4, 5)(4,5).

Problem 2019

In a pipeline with a 30 cm diameter and water speed of 1.5 m/s, find the speed at a 1 cm diameter.

Problem 2020

The office floor plan is at a scale of 1:201:201:20. Find the actual length for 96 cm96 \mathrm{~cm}96 cm and pantry area in cm2\mathrm{cm}^{2}cm2 for 4.8 m24.8 \mathrm{~m}^{2}4.8 m2.

Problem 2021

In square ABCDABCDABCD, area equals the sum of areas of triangles ABEABEABE and DCEDCEDCE. If AB=6AB=6AB=6, find CECECE. (a) 5 (b) 6 (c) 2 (d) 3 (e) 4

Problem 2022

In square ABCDABCDABCD with AB=6AB=6AB=6, the area equals the sum of triangles ABEABEABE and DCEDCEDCE. Find length of CECECE.

Problem 2023

Find the area xxx of hexagon ABCDEFABCDEFABCDEF with rectangle ABCDABCDABCD where AB=9AB=9AB=9 cm, BC=16BC=16BC=16 cm, AE=8AE=8AE=8 cm, and FG=3FG=3FG=3 cm.

Problem 2024

Determine the location of the point (−3,4)(-3,4)(−3,4) in the coordinate plane.

Problem 2025

Berechne Volumen und Oberfläche einer Pyramide mit Grundfläche a=15 cm,b=12 cm,h=20 cma=15 \mathrm{~cm}, b=12 \mathrm{~cm}, h=20 \mathrm{~cm}a=15 cm,b=12 cm,h=20 cm.

Problem 2026

Berechne den Umfang und Flächeninhalt eines runden Tisches mit r=25 cmr=25 \mathrm{~cm}r=25 cm.

Problem 2027

Find the missing angle in triangles ABE and DEC where ∠ABE=25∘\angle ABE=25^{\circ}∠ABE=25∘ and ∠EDC=100∘\angle EDC=100^{\circ}∠EDC=100∘.

Problem 2028

Clarence's garden is 20 ft by 40 ft. How many 4-yard fencing packages do they need for the perimeter?

Problem 2029

Berechne das Volumen und die Oberfläche eines Quaders mit a=4 cm,b=6 cm,c=12 cma=4 \mathrm{~cm}, b=6 \mathrm{~cm}, c=12 \mathrm{~cm}a=4 cm,b=6 cm,c=12 cm.

Problem 2030

已知圆O的半径为2.5，弦AB的长度为2，若三角形ABC为等腰三角形，则求BC2=BC^{2}=BC2=。

Problem 2031

Problem 2032

Calculați aria triunghiului BODB O DBOD și măsura unghiului BADB A DBAD în patrulaterul convex ABCDA B C DABCD cu datele date.

Problem 2033

Determine the general equation of the circle defined by x2+y2=16x^{2}+y^{2}=16x2+y2=16.

Problem 2034

Find the perimeter of Central Park, given vertices at (−1.25,−0.25)(-1.25,-0.25)(−1.25,−0.25), (−1.25,0.25)(-1.25,0.25)(−1.25,0.25), and (1.25,0.25)(1.25,0.25)(1.25,0.25).

Problem 2035

Calculate the volume and surface area of a cube with side length 3 units. Use V=s3V = s^3V=s3 and A=6s2A = 6s^2A=6s2.

Problem 2036

4. Într-un pătrat ABCDA B C DABCD, cu punctele E,F,GE, F, GE,F,G pe laturi, arată că triunghiul DEGD E GDEG este isoscel și află unghiul dintre DFD FDF și EGE GEG.

Problem 2037

5. Într-un dreptunghi cu AB=12 cmAB=12 \mathrm{~cm}AB=12 cm și BC=4 cmBC=4 \mathrm{~cm}BC=4 cm, calculează aria triunghiului CEOCEOCEO și unghiul BFCBFCBFC.

Problem 2038

Find the volume of a cuboid with dimensions 3, 3, and 4 units: V=l×w×hV = l \times w \times hV=l×w×h.

Problem 2039

What does the coefficient 7 represent in a rectangle with width xxx and length 7x7x7x? A. Length is 7 times width. B. Area is 7. C. Width is 7 times length. D. Length is 7.

Problem 2040

Thando's bag is 35cm x 35cm x 30cm. How many 27cm x 27cm x 3.5cm pizza boxes fit in it? After a 15% size increase, can they still fit?

Problem 2041

Find the center $(h, k)$ and radius $r$ of the circle from $(x-h)^{2}+(y-k)^{2}=r^{2}$ . Derive the general equation of a circle.

Find the distance from the point $(-1, -3)$ to the circle defined by $x^{2}+y^{2}+2x+6y-6=0$ ; it's 4 units.

Сумма двух углов прямоугольного треугольника $126^{\circ}$ . Найдите острые углы.

Convert the circle equation $x^{2}+y^{2}+x-3y-\frac{1}{2}=0$ to standard form and find its center and radius.

Hitung luas bilik dalam $\mathrm{cm}^{2}$ jika 250 jubin berukuran $6.096 \times 10^{2} \mathrm{~mm}$ dan $3.048 \times 10^{2} \mathrm{~mm}$ .

Cari nilai $x$ jika $n(\xi)=52, n(P)=40, n(P \cap Q)=9$ dan $n\left(P^{\prime}\right)=x+7$ .

Найдите периметр равнобедренного треугольника, если одна сторона $a = 7$ дм, а другая $b = a + 8$ дм.

Find a formula for the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

Can Arshad construct a unique quadrilateral with sides $AB=5 \mathrm{~cm}$ , $\angle A=50^{\circ}$ , $AC=4 \mathrm{~cm}$ , $BD=5 \mathrm{~cm}$ , and $AD=6 \mathrm{~cm}$ ? Explain why or why not.

Find the volume of a right cone with a base diameter of $9.5 \mathrm{~cm}$ and a height of $16 \mathrm{~cm}$ .

Una gaviota observa un bote a $42^{\circ}$ de depresión desde 45 m de altura. ¿Cuál es la distancia horizontal al barco?

Find $m \angle Q O R$ if $m \angle P O Q=24$ and $m \angle P O R=59$ .

Find $m \angle R O S$ if $m \angle Q O S=46$ , $m \angle P O R=61$ , and $m \angle P O Q=28$ .

Desde una torre de 28 m, un salvavidas ve a una persona con un ángulo de depresión de $58^{\circ}$ . ¿Cuál es la distancia a la persona?

Find $m \angle P O S$ if $m \angle P O Q = 19$ , $m \angle Q O R = 31$ , and $m \angle R O S = 15$ .

Find the length of a segment with endpoints at $(-1, 11)$ and $(4, 5)$ .

The office floor plan is at a scale of $1:20$ . Find the actual length for $96 \mathrm{~cm}$ and pantry area in $\mathrm{cm}^{2}$ for $4.8 \mathrm{~m}^{2}$ .

In square $ABCD$ , area equals the sum of areas of triangles $ABE$ and $DCE$ . If $AB=6$ , find $CE$ . (a) 5 (b) 6 (c) 2 (d) 3 (e) 4

In square $ABCD$ with $AB=6$ , the area equals the sum of triangles $ABE$ and $DCE$ . Find length of $CE$ .

Find the area $x$ of hexagon $ABCDEF$ with rectangle $ABCD$ where $AB=9$ cm, $BC=16$ cm, $AE=8$ cm, and $FG=3$ cm.

Determine the location of the point $(-3,4)$ in the coordinate plane.

Berechne Volumen und Oberfläche einer Pyramide mit Grundfläche $a=15 \mathrm{~cm}, b=12 \mathrm{~cm}, h=20 \mathrm{~cm}$ .

Berechne den Umfang und Flächeninhalt eines runden Tisches mit $r=25 \mathrm{~cm}$ .

Find the missing angle in triangles ABE and DEC where $\angle ABE=25^{\circ}$ and $\angle EDC=100^{\circ}$ .

Berechne das Volumen und die Oberfläche eines Quaders mit $a=4 \mathrm{~cm}, b=6 \mathrm{~cm}, c=12 \mathrm{~cm}$ .

已知圆O的半径为2.5，弦AB的长度为2，若三角形ABC为等腰三角形，则求 $BC^{2}=$ 。

Calculați aria triunghiului $B O D$ și măsura unghiului $B A D$ în patrulaterul convex $A B C D$ cu datele date.

Determine the general equation of the circle defined by $x^{2}+y^{2}=16$ .

Find the perimeter of Central Park, given vertices at $(-1.25,-0.25)$ , $(-1.25,0.25)$ , and $(1.25,0.25)$ .

Calculate the volume and surface area of a cube with side length 3 units. Use $V = s^3$ and $A = 6s^2$ .

4. Într-un pătrat $A B C D$ , cu punctele $E, F, G$ pe laturi, arată că triunghiul $D E G$ este isoscel și află unghiul dintre $D F$ și $E G$ .

5. Într-un dreptunghi cu $AB=12 \mathrm{~cm}$ și $BC=4 \mathrm{~cm}$ , calculează aria triunghiului $CEO$ și unghiul $BFC$ .

Find the volume of a cuboid with dimensions 3, 3, and 4 units: $V = l \times w \times h$ .

What does the coefficient 7 represent in a rectangle with width $x$ and length $7x$ ? A. Length is 7 times width. B. Area is 7. C. Width is 7 times length. D. Length is 7.

Find the total length of two semicircles with centers $R$ and $S$ , where $RS=12$ . Options are: (A) $8 \pi$ , (B) $9 \pi$ , (C) $12 \pi$ , (D) $15 \pi$ , (E) $16 \pi$ .

Determine the quadrant for a point with positive coordinates $(x > 0, y > 0)$ .

What conjecture about the triangle's perimeter could Maryanne have made after the translation $(x-10, y+17)$ ?

What could Maryanne's conjecture about the triangle's perimeter be after the translation $(x-5, y+11)$ ?

Translate Triangle RST with vertices $R (-4,2)$ , $S (5,3)$ , $T (2,-5)$ , 4 down and 3 left. Find new coordinates.

Un topógrafo mide el ángulo de elevación al cerro: $45^{\circ}$ y a $800$ m más, $30^{\circ}$ . ¿Cuál es la altura del cerro?

Calculate the distance $BC$ in triangle $ABC$ where $AB=1.5 \text{ km}$ , $AC=1.2 \text{ km}$ , and $\angle A=50^\circ$ .

Elena has a rectangular aquarium with height $1 \frac{3}{4} \mathrm{ft}$ . If the painted area is $5 \frac{5}{6} \mathrm{ft}^{2}$ , find the length.

Find the volume of Lin's aquarium with dimensions $\frac{7}{2} \mathrm{ft}$ (length), $\frac{4}{3} \mathrm{ft}$ (width), and $\frac{3}{2} \mathrm{ft}$ (height).

Sebuah papan sasar bulatan dengan jejari $20 \mathrm{~cm}$ . Beza jejari antara bulatan $P, Q, R, S$ dan $T$ ialah $4 \mathrm{~cm}$ .
Hitung: (a) Beza lilitan bulatan $T$ dan $P$ . (b) Luas kawasan $P$ dan $R$ (gunakan $\pi=\frac{22}{7}$ ).

Hitung (a) beza lilitan bulatan $T$ dan $P$ dalam $\mathrm{cm}$ , (b) luas kawasan $P$ dan $R$ dalam $\mathrm{cm}^{2}$ . Gunakan $\left.\pi=\frac{22}{7}\right.$

Hitung beza lilitan bulatan $T$ dan $P$ , serta luas kawasan $P$ dan $R$ dengan $\pi=\frac{22}{7}$ .

Calculați aria dreptunghiului $A B C D$ având $A C=6 \mathrm{~cm}$ și $\angle D O C=120^{\circ}$ . Care este aria?

Find the perimeter of triangle $ABC$ with $AD=4 \sqrt{3} cm$ , $BC=5 cm$ , and $BD=1 cm$ .

A rectangular prism A has dimensions: length = $4 \mathrm{~cm}$ , width = $3 \mathrm{~cm}$ , height = $2 \mathrm{~cm}$ .
a) How many cubes fit along the length?
b) How many cubes fit along the width?
c) How many layers of cubes?
d) What is the volume in cubes?

Christopher's fence is rectangular, with length $2 \mathrm{ft}$ longer than width. Points are $S(1, -2)$ , $R(6, -2)$ , $P(1, 8)$ , $Q(6, 4)$ .

Xavier's papaya trees cover $370 \mathrm{~m}^{2}$ . The perimeter for pineapple trees is $84 \mathrm{~m}$ . Find their area.

Find the length of a rectangular fishpond with a perimeter of $62 \mathrm{~m}$ and length 3 times its width.

Find the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

What is the area of this figure? $\square$ square meters Submit

13. The vertex of the parabola $y+16=(x-1)^{2}$ is located at (A) $(-1,-16)$ (B) $(-1,16)$ (C) $(1,-16)$ (D) $(1,16)$ (E) $(16,1)$
14. Find the axis of symmetry of parabola

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm . If the area of printed material on the poster is fixed at $1,536 \mathrm{~cm}^{2}$ , find the dimensions (in cm ) of the poster with the smallest area.

Find the circumcenter of $\triangle E F G$ with $E(4,4), F(4,2)$ , and $G(8,2)$ . Hint: Draw a picture
Select one: A. $(6,3)$ B. $(4,2)$ C. $(4,4)$ D. $(3,6)$

Mason is training for the javelin-throw event. A coach created a graph that shows the height of the javelin over time for Mason's best throw.
How many seconds did it take for the javelin to reach its greatest height? A 4.1 s (B) 1.3 s
C 13 s (D) 2 s

What is true about all of the coordinate values in the first quadrant?
They are all.... You can earn 5 coins values of 0 or more values of 0 or less

Find the measures triangle 3)
Find the meas

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Question Triangle EFG is similar to triangle HIJ. Find the measure of side JH. Round your answer to the nearest tenth if necessary.