Geometry

Problem 4001

RIANGLE SUM CONJECTURE The sum of the measures of the angles of every triangle is $\qquad$ .
ISOSCELES TRIANGLE CONJECTURE If a triangle is isosceles then the base angles are $\qquad$

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Problem 4002

Complete the statement if $\triangle B I G \cong \triangle T O P$ .
9. $\overline{I G} \cong$ $\qquad$ 10. $\qquad$ $\cong$ TO
11. $\angle I \cong$ $\qquad$
12. $\qquad$ $\cong m \angle P$
13. $\triangle \mathrm{IBG} \cong$ $\qquad$ 14. $\qquad$ $\cong \triangle \mathrm{OPT}$

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Problem 4003

Two similar triangles are shown. $\triangle M N O$ was dilated, then $\qquad$ , to create $\triangle \mathrm{YHQ}$ . rotated reflected translated dilated

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Problem 4004

6. a. What are the dimensions of the box at the right? b. On centimeter grid paper, sketch two nets for the box. c. Find the area, in square centimeters, of each net. d. Find the total area of all the faces of the box. How does your answer compare with the areas you found in part (c)?

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Problem 4005

, find the surface area of each object. 41.

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Problem 4006

Which equation gives the value of the circumference, $C$ , of a circle with a diameter of 48 feet? CLEAR CHECK $C=\pi \cdot 48^{2}$ $C=48 \cdot \pi$
$C=\frac{48}{\pi}$ $C=24 \cdot \pi$

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Problem 4007

The ratios of corresponding sides in the two triangles are equal.
What other information is needed to prove that $\triangle F G E$ $\sim \triangle \mathrm{IJH}$ by the SAS similarity theorem? $\angle F \cong \angle J$ $\angle I \cong \angle F$ $\angle E \cong \angle H$ $\angle G \cong \angle I$

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Problem 4008

Which would prove that $\triangle A B C-\triangle X Y Z$ ? Select two options. $\frac{B A}{Y X}=\frac{B C}{Y Z}=\frac{A C}{X Z}$ $\frac{B A}{Y X}=\frac{B C}{Y Z}, \angle C \geq \angle Z$ $\frac{A C}{x z}=\frac{B A}{y x}, \angle A \cong \angle x$ $\frac{B A}{Y X}=\frac{A C}{Y Z}=\frac{B C}{X Z}$ $\frac{B C}{X Y}=\frac{B A}{Z X}, \angle C \approx \angle X$

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Problem 4009

Level 1 Question 1 Use what you know about Pythagoras' Theorem to write an equation which describes the relationship between the sides of this triangle. Simplify and solve your equation.
Question 2 A triangle has a base length of $(x-1) \mathrm{cm}$ and a height of $(x+1) \mathrm{cm}$ . Find its height if it has an area of $7 \mathrm{~cm}^{2}$ 。
Question 3 A rectangle has perimeter 20 cm and area $21 \mathrm{~cm}^{2}$ . What are its dimensions, in centimetres? (A) 1 and 20 (B) 4 and 6 (C) 9 and 2 (D) 3 and 7 (E) 6 and $3 \frac{1}{2}$
Question 4 The formula for the number of diagonals, $N$ , of a polygon with $n$ sides is $N=\frac{n(n-3)}{2}$ . How many diagonals would a polygon with 23 sides have?

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Problem 4010

34. On the grid below, draw a three-sided figure with two equal sides and one right angle

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Problem 4011

a) Si le périmètre d'un carré est de 20 hm , quelle est la mesure d'un de ses côtés?

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Problem 4012

Given $AEC$ is a straight line and $\triangle ABC \sim \triangle ECD$ , find $m$ and $n$ where $AB=9$ , $AE=n$ , $EC=6$ , $ED=8$ , $\angle ABC=62^\circ$ , $\angle BAC=72^\circ$ , and $\angle EDC=m$ . Also, is $AB \parallel DC$ ? Explain.

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Problem 4013

In square $ABCD$ , points $E$ on $AB$ and $F$ on $BC$ satisfy $AF = DE$ . Show: (a) $\triangle ABF \cong \triangle DAE$ ; (b) Is $AF$ perpendicular to $DE$ ? Why? (c) Prove $\triangle ABF \sim \triangle AGE$ .

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Problem 4014

Prove that $\triangle ABC \sim \triangle DEC$ given $\angle BAC = \angle CDE$ . Find if $\triangle ABC$ is right-angled and the area of $ABDE$ .

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Problem 4015

In rectangle $ABCD$ , with $AB = 20$ and $BC = 15$ :
(a) Find $AC$ . (b) Prove $\triangle ABC \sim \triangle CMD$ . (c) Find $MC$ . (d) Find ratio $AM : MC$ .

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Problem 4016

Find the orientation, center, vertices, conjugate axis ends, foci, and lengths of the axes for $\frac{y^{2}}{16}-x^{2}=1$ . Graph it.

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Problem 4017

Determine the center, vertices, foci, and axis of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and graph it.

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Problem 4018

Graph the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and determine its asymptotes.

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Problem 4019

Determine the transverse and conjugate axes of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and sketch its graph.

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Problem 4020

(a) Find $AD$ given $\tan 50^{\circ} = \frac{AD}{12}$ , where $AD = 14.30$ . (b) Calculate angle $BAC$ and verify it rounds to $40.42^{\circ}$ . (c) Determine the area of quadrilateral $ABCD$ . (d) Find the shortest distance from $B$ to line $AC$ .

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Problem 4021

Find the actual area of a park (8 cm² on a 1:25000 map) in m², expressed in scientific notation.

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Problem 4022

A farmer has 200 ft of fence for a 2000 sq ft area made of squares with sides $x$ and $y$ . Find $x$ and $y$ .

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Problem 4023

A farmer has 100 feet of fence to enclose 500 sq ft with adjoining squares. Find $x$ and $y$ where $y$ is the big square's side. $x=$ $y=$

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Problem 4024

In triangle $ABC$ , with $AB \parallel AC$ , if $\angle BAC = 5x$ and $\angle ABC = 2x$ , find $x$ .

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Problem 4025

In triangle $ABC$ , with points $D$ on $AB$ and $E$ on $BC$ , find angles given $\angle ABC=28^{\circ}$ , $\angle BED=38^{\circ}$ .
(a) Find $\angle ACD$ . (b) Express $\angle DFE$ in terms of $\theta$ where $\angle CAE=\theta$ .

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Problem 4026

Calculate the volume of a triangular prism with side lengths of 8yd, 10yd, and 12yd.

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Problem 4027

A farmer has 250 ft of fence for two adjoining squares with area 3125 sq ft. Find side lengths $x$ and $y$ .

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Problem 4028

A farmer has 250 ft of fencing for 3125 sq ft in two adjoining squares. Find the side lengths $x$ and $y$ .

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Problem 4029

A farmer has 150 feet of fence to enclose 1125 sq ft with squares of sides $x$ and $y$ . Find $x$ and $y$ . $x=$ $y=$

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Problem 4030

Calculate the volume of a rectangular prism with dimensions 20 in, 10 in, and 12 in using the formula $V = l \times w \times h$ .

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Problem 4031

Name a pair of angles that add up to 180 degrees.

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Problem 4032

Prove that $\frac{AC}{AE}=\frac{\cos \phi}{\cos \theta}$ for rectangle $ABCD$ with point $E$ on $BC$ .

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Problem 4033

Étudiez le cas où $\mathbf{b}_{1}=\mathbf{b}_{2}=\mathbf{b}$ . Pour un disque de rayon $5 \mathrm{~mm}$ éclairant un disque de $5 \mathrm{~cm}$ à $50 \mathrm{~cm}$ , calculez les largeurs de l'ombre et de la pénombre à $2 \mathrm{~m}$ . Expliquez les éclipses.

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Problem 4034

In the figure, lines $A C$ and $B D$ intersect at $E$ . Given $\angle A C B=32^{\circ}$ and $\angle A E D=108^{\circ}$ , find $\angle B A C$ .

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Problem 4035

A farmer has 300 feet of fence for a 4500 sq ft area of adjoining squares with sides $x$ and $y$ . Find $x$ and $y$ . $x=$ $y=$

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Problem 4036

A farmer has 450 feet of fence for two adjoining squares with area 10,125 sq ft. Find the side lengths $x$ and $y$ . $x=$ $y=$

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Problem 4037

In a regular $n$ -sided polygon, the interior angle exceeds the exterior angle by $156^{\circ}$ . Find $n$ .

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Problem 4038

In hexagon $A B C D E F$ and square $C D G H$ , find angles: (a) $\angle G H I$ and (b) $\angle B I F$ .

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Problem 4039

In triangle $ABC$ , with points $D$ on $AB$ and $E$ on $BC$ , find angles given $\angle ABC=28^{\circ}$ , $\angle BED=38^{\circ}$ . (a) Find $\angle ACD$ . (b) Express $\angle DFE$ in terms of $\theta$ where $\angle CAE=\theta$ .

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Problem 4040

Find the supplementary angle to $(11x+3)^\circ$ .

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Problem 4041

Find the supplementary angle of $\frac{(14x+2)^\circ}{(11x+3)^\circ}$ when $x=19$ .

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Problem 4042

Find two complementary angles where $(2x-9)^{\circ} + (9x)^{\circ} = 90^{\circ}$ . Simplify your answers.

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Problem 4043

A customer slides a mug off a counter 1.38 m high, landing 0.80 m away. Find the exit velocity and impact direction (below horizontal).

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Problem 4044

Sketch the graph of the quadratic function $f(x)=(x+1)^{2}-9$ . Find the axis of symmetry, domain, and range.

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Problem 4045

How many inches will a 7-foot wall be represented in blueprints if studs are marked every 1.5 feet? Round to the nearest tenth.

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Problem 4046

Find the length of each side of an equilateral triangle with a perimeter of 31.5 inches. Each side is $x$ inches.

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Problem 4047

Travis has a 4" x 6" photo. a) If enlarged to 16" wide, what is the new height? b) Can it be enlarged to 8" x 10"? Answer y or $n$ .

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Problem 4048

Find the width and length of a rectangular area fenced along a river, where length is 7 ft greater than width, using 91 ft of fencing.

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Problem 4049

The sides of a triangle are in a ratio of $2:3:4$ . If the perimeter is $63$ in, find the longest side.

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Problem 4050

Calculate the volume of a rectangular prism with length $14.25 \, \text{ft}$ , width $13 \, \text{ft}$ , and height $4 \frac{1}{5} \, \text{ft}$ using $V=lwh$ .

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Problem 4051

Find $R S$ if $S$ is the midpoint of $\overline{R T}$ , $R S=5 x+17$ , and $S T=8 x-31$ .

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Problem 4052

If $J L=10 x-2$ , $J K=5 x-8$ , and $K L=7 x-12$ , what is the value of $K L$ ?

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Problem 4053

Find angles $\angle 1$ and $\angle 2$ where $\angle 2$ is supplementary to $\angle 1$ and $m \angle 2 = 2m \angle 1 + 36^\circ$ .

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Problem 4054

Un poisson voit un disque lumineux de rayon $r=3.0 \, m$ à la surface d'un lac (indice $n=1.33$ ). Quelle est sa profondeur?

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Problem 4055

Solve for $h$ in the equation $A=\frac{1}{2}(B+b) h$ .

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Problem 4056

Find $D E$ given that $B$ is the midpoint of $A C$ , $A C=C D$ , $A B=3 x+4$ , $A C=11 x-17$ , and $C E=49$ .

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Problem 4057

Solve for $x$ if $\angle NKL = 3x - 10$ and $\angle NKM = 2x + 20$ , with KN bisecting $\angle LKM$ .

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Problem 4058

Solve for $x$ if angle $LKM=7x-8$ and angle $NKM=x+1$ , with KN bisecting angle LKM. What are $x$ and angle $LKM$ ?

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Problem 4059

Name a point that is not in the same plane as points A, B, and C.

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Problem 4060

Find the side length of a square with the same area as a right triangle with sides 6, 8, and 10.

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Problem 4061

Solve for $x$ and angle $LKM$ given that angle $LKM = 7x - 8$ and angle $NKM = x + 1$ .

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Problem 4062

Find $A C$ if line $y$ bisects $A C$ , where $A B=4-5 x$ and $B C=2 x+25$ . Solve: $4-5 x=2 x+25$

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Problem 4063

Find the length of $A C$ if line $y$ bisects $A C$ , $A B=4-5 x$ , and $B C=2 x+25$ .

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Problem 4064

Find the shortest distance between Stan and Wei, given Jeff's locations: 12 miles east of Stan and 16 miles north of Wei.

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Problem 4065

Determine the type of triangle formed by sides 60 cm, 100 cm, and 40 cm: unique, similar, or none?

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Problem 4066

Solve for $h$ in the formula $A=\frac{1}{2}(B+b) h$ .

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Problem 4067

Find the length of the line segment $\overline{EF}$ where $E(-7,-5)$ and $F(-2,7)$ . Options: 21, 13, 15, 17 units.

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Problem 4068

Find the volume of a cylinder with radius 8 cm and height 6 cm using $\pi \approx 3.14$ . Choices: $301.44 \mathrm{~cm}^{3}$ , $150.72 \mathrm{~cm}^{3}$ , $904.32 \mathrm{~cm}^{3}$ , $226.08 \mathrm{~cm}^{3}$ .

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Problem 4069

Find the volume of an oblique cylinder with radius 5 cm and height 12 cm using $\pi \approx 3.14$ . Options: 1) $377 \mathrm{~cm}^{3}$ 2) $1,021 \mathrm{~cm}^{3}$ 3) $534 \mathrm{~cm}^{3}$ 4) $942 \mathrm{~cm}^{3}$

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Problem 4070

Reflect the point $P(-6,6)$ over the $y$ -axis. What are the coordinates of $P^{\prime}$ ?

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Problem 4071

Given points $A(5,19)$ , $B(17,3)$ , $C(11,1)$ , and $D(20.6,8.2)$ , which slopes confirm diameter $\overline{A B}$ bisects chord $\overline{C D}$ ?

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Problem 4072

Find the equation of the line through $(-2,3)$ and perpendicular to $5x - y = 12$ . Choose from the options.

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Problem 4073

Graph the reflection of the point $T(10,-2)$ over the $x$ -axis.

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Problem 4074

Reflect the point $S(0,2)$ over the $x$ -axis. What are the coordinates of $S^{\prime}$ ?

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Problem 4075

Reflect the point $T(-3,2)$ over the $y$ -axis. What are the coordinates of $T^{\prime}$ ?

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Problem 4076

What shape is formed by two non-collinear rays $\overrightarrow{A B}$ and $\overrightarrow{A C}$ ?

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Problem 4077

Identify the angle measures that can form an acute scalene triangle from these sets: $46^{\circ}, 67^{\circ}, 67^{\circ}$ $46^{\circ}, 57^{\circ}, 67^{\circ}$ $36^{\circ}, 57^{\circ}, 87^{\circ}$ $36^{\circ}, 47^{\circ}, 97^{\circ}$

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Problem 4078

What is the scale of Paco's drawing if the longest side is 5 inches and the original is 10 inches with a length of 4 in. : 5 yd?

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Problem 4079

Find the area of a poster with length $6x$ inches and width $5x + 6$ inches. Simplify your expression.

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Problem 4080

Find the diagonal length of a monitor with dimensions 24 inches (length) and 18 inches (height) to the nearest inch. Use $d = \sqrt{24^2 + 18^2}$ .

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Problem 4081

Find the area of a poster with length $6x$ inches and width $5x + 6$ inches.

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Problem 4082

Draw Utah to scale on paper, where 1 cm = 50 miles. Find Utah's length and width in miles first.

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Problem 4083

Find the length of $OM$ given that $O$ is the center of a circle, $OA=20 \mathrm{~cm}$ , and $AB=24 \mathrm{~cm}$ .

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Problem 4084

Find $x$ if $AP=x$ , $AB=16$ , $CP=4$ , and $DP=7$ using the intersecting chords theorem.

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Problem 4085

B) Une cuve a un observateur à $\mathrm{O}$ (1.20 m au-dessus de AB) et un poisson à $\mathrm{P}$ (0.80 m en dessous).
3) Quelle distance l'observateur pense-t-il voir le poisson ? Quelle distance le poisson voit-il l'observateur ?
4) Avec un miroir au fond (CD) et une épaisseur d'eau $\mathrm{e}=1.20 \mathrm{~m}$ , à quelle distance l'observateur voit-il son image ?
Comment cela change-t-il si l'eau s'écoule ?

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Problem 4086

\begin{tabular}{|l|l} & \\ \hline & $(2,5) \&(-4,-6)$ \end{tabular} a. Plot the above two points: b. Work out the midpoint: c. Work out the distance: d. Work out the linear equation:

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Problem 4087

Gabrielle knows that a fir tree that is 8 feet tall casts a shadow that is 15 feet long. She wants to calculate the height of a nearby plum tree. If its shadow is 30 feet long, how tall is the plum tree?
Write your answer as a whole number or a decimal. Do not round. 新 $\square$ feet Submit

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Problem 4088

[*].] An ash tree is 9 meters tall and its shadow is 12 meters long. A nearby lemon tree is 6 meters tall. How long is the lemon tree's shadow? ） Write your answer as a whole number or a decimal. Do not round. \& $\square$ meters Submit

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Problem 4089

```latex The swan below is composed of several triangles. Use the given information and the figure to find each angle measure. Note: Figure not drawn to scale.
Given: $\triangle ABC$ is equilateral; $\overline{KO} \cong \overline{FO}; JN \cong JO, \overline{DE} \cong CE \cong \overline{EF}$ ; $\angle BCD \cong \angle BDC$ ; $\angle CGF \cong \angle CFG; \angle HKN \cong \angle HNK; \triangle GCF \cong \triangle GKF \cong \triangle JHM; \triangle KFH \cong \triangle KLH$ .
1. $m \angle ABC = 60^\circ$
2. $m \angle BCA = 60^\circ$
3. $m \angle CAB = 60^\circ$
4. $m \angle BCD = 70^\circ$
5. $m \angle BDC = 70^\circ$
6. $m \angle CBD = YO$
7. $m \angle EDC = 7 \not 2$
8. $m \angle ECD \sim \Omega$
9. $m \angle CED = 36$
10. $m \angle ECF = 30^\circ$
11. $m \angle EFC = 30$
12. $m \angle CEF = 120$
13. $m \angle CGF$
14. $m \angle CFG$
15. $m \angle GCF = 20$
16. $m \angle KGF = Q0$
17. $m \angle KFG = 80^\circ$
18. $m \angle GKF = \eta$
19. $m \angle FKH = YI$
20. $m \angle FHK = 80$
22. $m \angle KHL$
23. $m \angle HKL$
24. $m \angle KLH$
25. $m \angle HJM$
26. $m \angle HMJ$
27. $m \angle JHM$
28. $m \angle OFK$
29. $m \angle OKF$
30. $m \angle KOF$
31. $m \angle HKN$
32. $m \angle HNK$
33. $m \angle OKN$
34. $m \angle JNO$
35. $m \angle JON$
36. $m \angle NJO$
Additional extracted text:
19. $m \angle \mathrm{FKH}$
(4x), (7x), D, (4y), (62), (3z), (102), E, (Zz + 6), (16), (8x + 2), (4z - 7), (8y), (4y), M, H, (x+6).

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Problem 4090

The swan below is composed of several triangles. Use the given information and the figure to find each angle measure. Note: Figure not drawn to scale.
Given: $\triangle A B C$ is equilateral; $\overline{D E} \cong \overline{C E} \cong \overline{E F}$ loverline $\{\mathrm{DE}\}$ \{congloverlinc $\{\mathrm{CE}\}$ /congloverline $\{\mathrm{EF}\} ; \overline{K O} \cong \overline{F O}$ loverline $\{\mathrm{KO}\}$ \congloverline $\{\mathrm{FO}\} ; \overline{J N} \cong \overline{J O}$ loverline $\{\mathrm{JN}\}$ /congloverline $\{\mathrm{JO}\} ; \angle B C D \cong \angle B D C ; C G F \cong \angle C F G ; \angle H K N \cong$ $\angle H N K ; \triangle G C F \cong \triangle G K F \cong \triangle J H M ; \triangle K F H \cong \triangle K L H$
Triangular Swan Portfolio Print the document so that you can write on it and mark the pictureshowin congruent sides - (2 points)
1. $m \angle \mathrm{ABC}=$ 60
2. $m \angle B C A=$ 60 $\square$
3. $m \angle \mathrm{CAB}=$ 60 $\square$
4. $m \angle B C D=$ 70 $\square$
5. $m \angle \mathrm{BDC}=\mid 70$

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Problem 4091

$\text{Дан параллелепипед } A B C D A_{1} B_{1} C_{1} D_{1}, \text{ два противоположных основания которого, } A B C D \text{ и } A_{1} B_{1} C_{1} D_{1} \text{ являются квадратами со стороной } 12 \sqrt{2} \text{ см, а остальные грани прямоугольниками. Известно, что } C C_{1}=2 \sqrt{7} \text{ см. На стороне } A_{1} B_{1} \text{ отметили точку } M \text{ так, что } A_{1} M=M B_{1}.$ $\text{Найди периметр сечения параллелепипеда плоскостью } AMC.$

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Problem 4092

Дан прямоугольный параллелепипед $A B C D A_{1} B_{1} C_{1} D_{1}$ , у которого известны длины ребер: $A B=8, A D=7$ и $A A_{1}=24$ .
Определите площадь сечения параллелепипеда плоскостью $A B C_{1}$ .
Введите целое число или десятичную дробь...
Определите периметр сечения параллелепипеда плоскостью $A B C_{1}$ .
Введите целое число или десятичную дробь...

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Problem 4093

Дан тетраэдр $S A B C$ , все рёбра которого равны 16 . На ребре $A B$ отмечена точка $K$ так, что $A K=K B$ . Найдите площадь сечения данного тетраэдра плоскостью, проходящей через точку $K$ и перпендикулярной ребру $S A$ .
Полученный ответ умножьте на $\sqrt{2}$ .

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Problem 4094

Exercice 01 : Detx points $A$ et $B$ , ont pour coordonnées cartésiennes dans l'espace : $A(2,3,-3), B(5,7,2)$ Déterminer les composantes du vecteur $\overrightarrow{A B}$ ainsi que son module, sa direction et son sens.

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Problem 4095

Exercice 01 : Detx points $A$ et $B$ , ont pour coordonnées cartésiennes dans l'espace : $A(2,3,-3), B(5,7,2)$ Déterminer les composantes du vecteur $\overrightarrow{A B}$ ainsi que son module, sa direction et son sens.

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Problem 4096

Впишите правильный ответ. Сторона равностороннего треугольника равна $8 \sqrt{3}$ . Найдите радиус окружности, описанной около этого треугольника.

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Problem 4097

42. До гіперболи належить $M_{0}(-5,3)$ , а ексцентриситет гіперболи дорівнює $\sqrt{2}$ . Скласти канонічне рівняння гіперболи та побудувати ії.
43. Скласти рівняння і побудувати гіперболу, якщо вона має асимптоти $y= \pm \frac{2}{3} x$ і їй належить точка $M_{1}(9 / 2,-1)$ .

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Problem 4098

11. Classify point $C$ . A. Circumcenter B. Incenter C. Centroid

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Problem 4099

Exercice5: Soit $A B C$ un triangle tel que $A B=6, A C=\sqrt{13}$ et $B C=7$ .
1: Montrer que : $A B C$ est rectangle en $A$ . 2: Soit $H$ le projeté orthogonal de $A$ sur $(B C)$ . . $a$ : Montrer que : $A B \times A C=A H \times B C$ . .b: Calculer $\mathrm{AH}, \mathrm{CH}$ et BH .

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Problem 4100

اوجد كل المثلثات الفيثاغورية البدانية التي طول احد الساقين فيها يساوي 80 .

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1 ...38 39 40 41 42 43 44 ...61

Geometry

Problem 4001

RIANGLE SUM CONJECTURE The sum of the measures of the angles of every triangle is \qquad .ISOSCELES TRIANGLE CONJECTURE If a triangle is isosceles then the base angles are \qquad

Problem 4002

Problem 4003

Two similar triangles are shown. △MNO\triangle M N O△MNO was dilated, then \qquad , to create △YHQ\triangle \mathrm{YHQ}△YHQ. rotated reflected translated dilated

Problem 4004

6. a. What are the dimensions of the box at the right? b. On centimeter grid paper, sketch two nets for the box. c. Find the area, in square centimeters, of each net. d. Find the total area of all the faces of the box. How does your answer compare with the areas you found in part (c)?

Problem 4005

, find the surface area of each object. 41.

Problem 4006

Which equation gives the value of the circumference, CCC, of a circle with a diameter of 48 feet? CLEAR CHECK C=π⋅482C=\pi \cdot 48^{2}C=π⋅482 C=48⋅πC=48 \cdot \piC=48⋅πC=48πC=\frac{48}{\pi}C=π48​ C=24⋅πC=24 \cdot \piC=24⋅π

Problem 4007

Problem 4008

Problem 4009

Problem 4010

34. On the grid below, draw a three-sided figure with two equal sides and one right angle

Problem 4011

a) Si le périmètre d'un carré est de 20 hm , quelle est la mesure d'un de ses côtés?

Problem 4012

Problem 4013

In square ABCDABCDABCD, points EEE on ABABAB and FFF on BCBCBC satisfy AF=DEAF = DEAF=DE. Show: (a) △ABF≅△DAE\triangle ABF \cong \triangle DAE△ABF≅△DAE; (b) Is AFAFAF perpendicular to DEDEDE? Why? (c) Prove △ABF∼△AGE\triangle ABF \sim \triangle AGE△ABF∼△AGE.

Problem 4014

Prove that △ABC∼△DEC\triangle ABC \sim \triangle DEC△ABC∼△DEC given ∠BAC=∠CDE\angle BAC = \angle CDE∠BAC=∠CDE. Find if △ABC\triangle ABC△ABC is right-angled and the area of ABDEABDEABDE.

Problem 4015

In rectangle ABCDABCDABCD, with AB=20AB = 20AB=20 and BC=15BC = 15BC=15:(a) Find ACACAC. (b) Prove △ABC∼△CMD\triangle ABC \sim \triangle CMD△ABC∼△CMD. (c) Find MCMCMC. (d) Find ratio AM:MCAM : MCAM:MC.

Problem 4016

Find the orientation, center, vertices, conjugate axis ends, foci, and lengths of the axes for y216−x2=1\frac{y^{2}}{16}-x^{2}=116y2​−x2=1. Graph it.

Problem 4017

Determine the center, vertices, foci, and axis of the hyperbola y216−x2=1\frac{y^{2}}{16}-x^{2}=116y2​−x2=1 and graph it.

Problem 4018

Graph the hyperbola y216−x2=1\frac{y^{2}}{16}-x^{2}=116y2​−x2=1 and determine its asymptotes.

Problem 4019

Determine the transverse and conjugate axes of the hyperbola y216−x2=1\frac{y^{2}}{16}-x^{2}=116y2​−x2=1 and sketch its graph.

Problem 4020

Problem 4021

Find the actual area of a park (8 cm² on a 1:25000 map) in m², expressed in scientific notation.

Problem 4022

A farmer has 200 ft of fence for a 2000 sq ft area made of squares with sides xxx and yyy. Find xxx and yyy.

Problem 4023

A farmer has 100 feet of fence to enclose 500 sq ft with adjoining squares. Find xxx and yyy where yyy is the big square's side. x= x= x= y= y= y=

Problem 4024

In triangle ABCABCABC, with AB∥ACAB \parallel ACAB∥AC, if ∠BAC=5x\angle BAC = 5x∠BAC=5x and ∠ABC=2x\angle ABC = 2x∠ABC=2x, find xxx.

Problem 4025

Problem 4026

Calculate the volume of a triangular prism with side lengths of 8yd, 10yd, and 12yd.

Problem 4027

A farmer has 250 ft of fence for two adjoining squares with area 3125 sq ft. Find side lengths xxx and yyy.

Problem 4028

A farmer has 250 ft of fencing for 3125 sq ft in two adjoining squares. Find the side lengths xxx and yyy.

Problem 4029

A farmer has 150 feet of fence to enclose 1125 sq ft with squares of sides xxx and yyy. Find xxx and yyy. x= x= x= y= y= y=

Problem 4030

Calculate the volume of a rectangular prism with dimensions 20 in, 10 in, and 12 in using the formula V=l×w×hV = l \times w \times hV=l×w×h.

Problem 4031

Name a pair of angles that add up to 180 degrees.

Problem 4032

Prove that ACAE=cos⁡ϕcos⁡θ\frac{AC}{AE}=\frac{\cos \phi}{\cos \theta}AEAC​=cosθcosϕ​ for rectangle ABCDABCDABCD with point EEE on BCBCBC.

Problem 4033

Problem 4034

In the figure, lines ACA CAC and BDB DBD intersect at EEE. Given ∠ACB=32∘\angle A C B=32^{\circ}∠ACB=32∘ and ∠AED=108∘\angle A E D=108^{\circ}∠AED=108∘, find ∠BAC\angle B A C∠BAC.

Problem 4035

A farmer has 300 feet of fence for a 4500 sq ft area of adjoining squares with sides xxx and yyy. Find xxx and yyy. x= x= x= y= y= y=

Problem 4036

A farmer has 450 feet of fence for two adjoining squares with area 10,125 sq ft. Find the side lengths xxx and yyy. x= x= x= y= y= y=

Problem 4037

In a regular nnn-sided polygon, the interior angle exceeds the exterior angle by 156∘156^{\circ}156∘. Find nnn.

Problem 4038

In hexagon ABCDEFA B C D E FABCDEF and square CDGHC D G HCDGH, find angles: (a) ∠GHI\angle G H I∠GHI and (b) ∠BIF\angle B I F∠BIF.

Problem 4039

Problem 4040

Find the supplementary angle to (11x+3)∘(11x+3)^\circ(11x+3)∘.

Problem 4041

Find the supplementary angle of (14x+2)∘(11x+3)∘\frac{(14x+2)^\circ}{(11x+3)^\circ}(11x+3)∘(14x+2)∘​ when x=19x=19x=19.

Problem 4042

Find two complementary angles where (2x−9)∘+(9x)∘=90∘(2x-9)^{\circ} + (9x)^{\circ} = 90^{\circ}(2x−9)∘+(9x)∘=90∘. Simplify your answers.

Problem 4043

A customer slides a mug off a counter 1.38 m high, landing 0.80 m away. Find the exit velocity and impact direction (below horizontal).

Problem 4044

Sketch the graph of the quadratic function f(x)=(x+1)2−9f(x)=(x+1)^{2}-9f(x)=(x+1)2−9. Find the axis of symmetry, domain, and range.

RIANGLE SUM CONJECTURE The sum of the measures of the angles of every triangle is $\qquad$ .
ISOSCELES TRIANGLE CONJECTURE If a triangle is isosceles then the base angles are $\qquad$

Two similar triangles are shown. $\triangle M N O$ was dilated, then $\qquad$ , to create $\triangle \mathrm{YHQ}$ . rotated reflected translated dilated

Which equation gives the value of the circumference, $C$ , of a circle with a diameter of 48 feet? CLEAR CHECK $C=\pi \cdot 48^{2}$ $C=48 \cdot \pi$
$C=\frac{48}{\pi}$ $C=24 \cdot \pi$

In square $ABCD$ , points $E$ on $AB$ and $F$ on $BC$ satisfy $AF = DE$ . Show: (a) $\triangle ABF \cong \triangle DAE$ ; (b) Is $AF$ perpendicular to $DE$ ? Why? (c) Prove $\triangle ABF \sim \triangle AGE$ .

Prove that $\triangle ABC \sim \triangle DEC$ given $\angle BAC = \angle CDE$ . Find if $\triangle ABC$ is right-angled and the area of $ABDE$ .

In rectangle $ABCD$ , with $AB = 20$ and $BC = 15$ :
(a) Find $AC$ . (b) Prove $\triangle ABC \sim \triangle CMD$ . (c) Find $MC$ . (d) Find ratio $AM : MC$ .

Find the orientation, center, vertices, conjugate axis ends, foci, and lengths of the axes for $\frac{y^{2}}{16}-x^{2}=1$ . Graph it.

Determine the center, vertices, foci, and axis of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and graph it.

Graph the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and determine its asymptotes.

Determine the transverse and conjugate axes of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and sketch its graph.

A farmer has 200 ft of fence for a 2000 sq ft area made of squares with sides $x$ and $y$ . Find $x$ and $y$ .

A farmer has 100 feet of fence to enclose 500 sq ft with adjoining squares. Find $x$ and $y$ where $y$ is the big square's side. $x=$ $y=$

In triangle $ABC$ , with $AB \parallel AC$ , if $\angle BAC = 5x$ and $\angle ABC = 2x$ , find $x$ .

A farmer has 250 ft of fence for two adjoining squares with area 3125 sq ft. Find side lengths $x$ and $y$ .

A farmer has 250 ft of fencing for 3125 sq ft in two adjoining squares. Find the side lengths $x$ and $y$ .

A farmer has 150 feet of fence to enclose 1125 sq ft with squares of sides $x$ and $y$ . Find $x$ and $y$ . $x=$ $y=$

Calculate the volume of a rectangular prism with dimensions 20 in, 10 in, and 12 in using the formula $V = l \times w \times h$ .

Prove that $\frac{AC}{AE}=\frac{\cos \phi}{\cos \theta}$ for rectangle $ABCD$ with point $E$ on $BC$ .

In the figure, lines $A C$ and $B D$ intersect at $E$ . Given $\angle A C B=32^{\circ}$ and $\angle A E D=108^{\circ}$ , find $\angle B A C$ .

A farmer has 300 feet of fence for a 4500 sq ft area of adjoining squares with sides $x$ and $y$ . Find $x$ and $y$ . $x=$ $y=$

A farmer has 450 feet of fence for two adjoining squares with area 10,125 sq ft. Find the side lengths $x$ and $y$ . $x=$ $y=$

In a regular $n$ -sided polygon, the interior angle exceeds the exterior angle by $156^{\circ}$ . Find $n$ .

In hexagon $A B C D E F$ and square $C D G H$ , find angles: (a) $\angle G H I$ and (b) $\angle B I F$ .

Find the supplementary angle to $(11x+3)^\circ$ .

Find the supplementary angle of $\frac{(14x+2)^\circ}{(11x+3)^\circ}$ when $x=19$ .

Find two complementary angles where $(2x-9)^{\circ} + (9x)^{\circ} = 90^{\circ}$ . Simplify your answers.

Sketch the graph of the quadratic function $f(x)=(x+1)^{2}-9$ . Find the axis of symmetry, domain, and range.

Find the length of each side of an equilateral triangle with a perimeter of 31.5 inches. Each side is $x$ inches.

Travis has a 4" x 6" photo. a) If enlarged to 16" wide, what is the new height? b) Can it be enlarged to 8" x 10"? Answer y or $n$ .

The sides of a triangle are in a ratio of $2:3:4$ . If the perimeter is $63$ in, find the longest side.

Calculate the volume of a rectangular prism with length $14.25 \, \text{ft}$ , width $13 \, \text{ft}$ , and height $4 \frac{1}{5} \, \text{ft}$ using $V=lwh$ .

Find $R S$ if $S$ is the midpoint of $\overline{R T}$ , $R S=5 x+17$ , and $S T=8 x-31$ .

If $J L=10 x-2$ , $J K=5 x-8$ , and $K L=7 x-12$ , what is the value of $K L$ ?

Find angles $\angle 1$ and $\angle 2$ where $\angle 2$ is supplementary to $\angle 1$ and $m \angle 2 = 2m \angle 1 + 36^\circ$ .

Un poisson voit un disque lumineux de rayon $r=3.0 \, m$ à la surface d'un lac (indice $n=1.33$ ). Quelle est sa profondeur?

Solve for $h$ in the equation $A=\frac{1}{2}(B+b) h$ .

Find $D E$ given that $B$ is the midpoint of $A C$ , $A C=C D$ , $A B=3 x+4$ , $A C=11 x-17$ , and $C E=49$ .

Solve for $x$ if $\angle NKL = 3x - 10$ and $\angle NKM = 2x + 20$ , with KN bisecting $\angle LKM$ .

Solve for $x$ if angle $LKM=7x-8$ and angle $NKM=x+1$ , with KN bisecting angle LKM. What are $x$ and angle $LKM$ ?

Solve for $x$ and angle $LKM$ given that angle $LKM = 7x - 8$ and angle $NKM = x + 1$ .

Find $A C$ if line $y$ bisects $A C$ , where $A B=4-5 x$ and $B C=2 x+25$ . Solve: $4-5 x=2 x+25$

Find the length of $A C$ if line $y$ bisects $A C$ , $A B=4-5 x$ , and $B C=2 x+25$ .

Solve for $h$ in the formula $A=\frac{1}{2}(B+b) h$ .

Find the length of the line segment $\overline{EF}$ where $E(-7,-5)$ and $F(-2,7)$ . Options: 21, 13, 15, 17 units.

Find the volume of a cylinder with radius 8 cm and height 6 cm using $\pi \approx 3.14$ . Choices: $301.44 \mathrm{~cm}^{3}$ , $150.72 \mathrm{~cm}^{3}$ , $904.32 \mathrm{~cm}^{3}$ , $226.08 \mathrm{~cm}^{3}$ .

Find the volume of an oblique cylinder with radius 5 cm and height 12 cm using $\pi \approx 3.14$ . Options: 1) $377 \mathrm{~cm}^{3}$ 2) $1,021 \mathrm{~cm}^{3}$ 3) $534 \mathrm{~cm}^{3}$ 4) $942 \mathrm{~cm}^{3}$

Reflect the point $P(-6,6)$ over the $y$ -axis. What are the coordinates of $P^{\prime}$ ?

Given points $A(5,19)$ , $B(17,3)$ , $C(11,1)$ , and $D(20.6,8.2)$ , which slopes confirm diameter $\overline{A B}$ bisects chord $\overline{C D}$ ?

Find the equation of the line through $(-2,3)$ and perpendicular to $5x - y = 12$ . Choose from the options.

Graph the reflection of the point $T(10,-2)$ over the $x$ -axis.

Reflect the point $S(0,2)$ over the $x$ -axis. What are the coordinates of $S^{\prime}$ ?