Geometry

Problem 3901

MathXL for School: Practice and Problem-Solving
Points AA^{\prime} and BB^{\prime} are images of points AA and BB after a 270270^{\circ} rotation about the origin. If the slope of ABundefined\overrightarrow{A B} is -3 , what is the slope of ABundefined\widehat{A^{\prime} B^{\prime}} ? Explain.
Select the correct choice below and fill in the answer box to complete your chaice. A. A rotation of 270270^{\circ} would result in a line parallel to ABundefined\overrightarrow{A B}. Since the slopes of parallel lines are equal, the slope of ABundefined\overrightarrow{\mathrm{A}^{\prime} B^{\prime}} is \square 1. B. A rotation of 270270^{\circ} would result in a line perpendicular to ABundefined\overrightarrow{\mathrm{AB}}. Since the slopes of perpendicular lines are opposite reciprocals, the slope of ABundefined\overrightarrow{\mathrm{A}^{\prime} \mathrm{B}^{\prime}} is \square . C. A rotation of 270270^{\circ} would result in a line perpendicular to ABundefined\overrightarrow{A B}. Since the slopes of perpendicular lines are equal, the slope of ABundefined\overrightarrow{A^{\prime} B} is \square . D. A rotation of 270270^{\circ} would result in a line parallel to ABundefined\overrightarrow{A B}. Since the slopes of parallel lines are opposite reciprocals, the slope of ABundefined\overrightarrow{A^{\prime} B} is \square

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Problem 3902

In the given diagram, there is a quadrilateral ABCD.The angles are given as follows: A=65,B=55,D=115.The length of side CD is 10 cm.Solve for x, where C=x.\begin{array}{c} \text{In the given diagram, there is a quadrilateral } ABCD. \\ \text{The angles are given as follows: } \angle A = 65^\circ, \angle B = 55^\circ, \angle D = 115^\circ. \\ \text{The length of side } CD \text{ is } 10 \text{ cm.} \\ \text{Solve for } x \text{, where } \angle C = x. \end{array}

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Problem 3903

Determine the center and radius of the circle. (x+2)2+(y+1)2=144(x+2)^{2}+(y+1)^{2}=144

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Problem 3904

Determine if triangle JKLJ K L and triangle MNOM N O are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
SSS: three sides proportionate SSS: three sides congruent SAS: two sides proportionate, included angle congruent SAS: two sides + included angle congruent AA: two angles congruent

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Problem 3905

Determine if triangle GHIG H I and triangle JKLJ K L are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Answer Attempt 1 out of 2
The triangle \square similar . are

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Problem 3906

estion Watch Video Show Examples termine if triangle RSTR S T and triangle UVWU V W are or are not similar, and, if they are, state how you ow. (Note that figures are NOT necessarily drawn to scale.)
Answer Attempt 1 out of 2
The triangle \square similar . are Submit Answer are not

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Problem 3907

Determine if triangle RSTR S T and triangle UVWU V W are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Answer Attempt 2 out of 2
SSS: three sides proportionate SSS: three sides congruent SAS: two sides proportionate, included angle congruent SAS: two sides + included angle congruent AA: two angles congruent

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Problem 3908

Determine if triangle EFGE F G and triangle HIJH I J are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Answer Attempt 1 out of 2 \square SSS: three sides proportipnate SSS: three sides congruent SAS: two sides proportionate, included angle congruent SAS: two sides + included angle congruent AA: two angles congruent

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Problem 3909

Hilfsmittelteil (erlaubte Hilfsmittel: graphikfähiger Taschenrechner, Formelsammlung) Aufgabe 4: (37 Punkte) Die Abbildung zeigt den Würfel ABCDEFGH mit G(555)\mathrm{G}(5|5| 5) und H(055)\mathrm{H}(0|5| 5) in einem kartesischen Koordinatensystem. Die Punkte I(5|0|1), J(2|5|0), K(052)\mathrm{K}(0|5| 2) und L(105)L(1|0| 5) liegen jeweils auf einer Kante des Würfels.
8 多 (2P) - AA - e) Zeigen Sie, dass das Viereck IJKL ein Trapez ist, in dem zwei Seiten gleich lang sind. Weisen Sie nach, dass die Seite L\overline{\mathrm{L}} des Trapezes doppelt so lang ist wie die Seite JK. (7P) f) Berechnen Sie die Größe eines Innenwinkels des Trapezes IJKL. (6P) (4P)
Der Punkt P (4|0|2) liegt auf der Strecke IL\overline{\mathrm{IL}}. Die Strecke JP\overline{\mathrm{JP}} steht dabei senkrecht zur Strecke IL\overline{\mathrm{IL}}. g) Berechnen Sie den Flächeninhalt des Trapezes IJKL. (5P) h) Gegeben ist die Ebene S:x=v(155)+w(551)S: \vec{x}=v \cdot\left(\begin{array}{c}-1 \\ -5 \\ 5\end{array}\right)+w \cdot\left(\begin{array}{c}-5 \\ 5 \\ 1\end{array}\right) mit v,wRv, w \in \mathbb{R}.
Der Punkt K liegt in einer Ebene T, die parallel zu S ist. Untersuchen Sie, ob auch der Punkt L in T liegt. (5P)

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Problem 3910

4 AMC 12 B Problems 8
Equilateral ABC\triangle A B C with side length 14 is rotated about its center by angle θ\theta, where 0<θ600<\theta \leq 60^{\circ}, to form DEF\triangle D E F. See the figure. The area of hexagon ADBECFA D B E C F is 91391 \sqrt{3}. What is tanθ\tan \theta ? 如图所示, 边长为 14 的等边三角形 ABC\triangle A B C 绕其中心旋转 θ\theta 度得到 DEF\triangle D E F, 其中 0<θ600<\theta \leq 60^{\circ} 。若六边形 ADBECFA D B E C F 的面积为 91391 \sqrt{3}, 请问 tanθ\tan \theta 的值是多少?

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Problem 3911

The vector parametric equation for the line through the points (3,4,2)(-3,-4,-2) and (3,1,1)(-3,1,-1) is L(t)=L(t)=\square

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Problem 3912

Гурвалжны хоёр өнцөг нь 54,9854^{\circ}, 98^{\circ} бол гурав дахь өнцгийг ол.

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Problem 3913

The recreation department of a small town wants to over-seed an area of the local park, shown in the diagram. If it takes one 5-pound bag of seed to cover 3000 square feet, how many bags of seed will they need? A) 16 B) 17 C) 20 D) 22

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Problem 3914

(A) Find the parametric equations for the line through the point P=(5,5,3)\mathrm{P}=(5,-5,3) that is perpendicular to the plane 1x+3y+4z=11 x+3 y+4 z=1. x=y=z=\begin{array}{l} x=\square \\ y=\square \\ z=\square \end{array} (B) At what point QQ does this line intersect the yzy z-plane? Q=(,)\mathrm{Q}=(\square, \square) \square

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Problem 3915

a) Calculate the curved surface area. b) Calculate the total surface area.
Give each answer to 1 d.p. Watch video

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Problem 3916

Si un système est en mouvement rectiligne: (If a system is in rectilinear motion
Select one or more: Sa trajectoire est une droite. (Its trajectory is a straight line.) La norme de sa vitesse est constante. (The norm of its speed is constant) Le vecteur vitesse peut varier. (The velocity can vary)
Check

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Problem 3917

New Tab Sawas EasyEridge Sawas Realize savwasrealize.com/dashboard/classes/66bc15ca539fd973b19f1068/details/assignments/87cbb1 af6dda441 c8ea3efb551f839af/review/content/9d7d2847-015c-3b27-b840-9456113f28.. HMATOO2S18 GEOMETR) DUE 3-3: MathXL for School: Practice and Problem-Solving Nov 26 - 11:59 pm Late Part 1 of 2
Find the angle of rotation for the rotation that is the composition rnrmr_{n} \circ r_{m}. Then, draw the image.
The angle of rotation is \square ]]^{\circ}. (Simplify your answer.) Clear all Check answer Video Textbook Get more help -

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Problem 3918

A 5 T B C -3 E -2 2 D Find the composition of transformations that map ABCD to EHGF. Reflect over the [?]-axis, then translate (x+[ ], y+[ ]). 0 2 3 F Note: -2 G Enter x or y for axis

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Problem 3919

Using the formula V=lwhV=l w h, and given l=8 cm,w=7 cml=8 \mathrm{~cm}, w=7 \mathrm{~cm}, and h=2.5 cmh=2.5 \mathrm{~cm} which equation is set up correctly?

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Problem 3920

The cross-section of the prism below is a compound shape formed of two rectangles.
Work out the volume of the prism. Give your answer in cm3\mathrm{cm}^{3}. Not drawn accuratelv

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Problem 3921

The cross-section of the prism below is a compound shape formed of two rectangles.
Work out the volume of the prism. Give your answer in cm3\mathrm{cm}^{3}.
Not drawn accuratelv

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Problem 3922

، C( 32,24)), A( 0,0)) هو مُعيّن. معطى: ABCD (18) . الزَأس B يقع على الشّعاع الموجب المحور ABCD (ب) طول ضلع المعيّن هو 25 وحدة طول.
جدوا إحداثيّات النّقطة D. (ج) إحسبوا طول قطر المُعيّن الأصغر.

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Problem 3923

TWundefined\overleftrightarrow{T W} bisects UWY\angle U W Y and XV\angle X \cong \angle V. Complete the proof that TVWTXW\triangle T V W \cong \triangle T X W. \begin{tabular}{|c|c|c|c|c|} \hline & Statement & & Reason & \\ \hline 1 & TWundefined\overleftrightarrow{T W} bisects UWY\angle U W Y & & Glven & \\ \hline 2 & XV\angle X \cong \angle V & & Given & \\ \hline 3 & XWYUWV\angle X W Y \cong \angle U W V & & Vertical Angle Theorem & \\ \hline 4 & TWYTWU\angle T W Y \cong \angle T W U & & Definition of angle bisector & \\ \hline 5 & mTWX=mTWY+mXWYm \angle T W X=m \angle T W Y+m \angle X W Y & & Additive Property of Angle Measure & \\ \hline 6 & mTWV=mTWU+mUWVm \angle T W V=m \angle T W U+m \angle U W V & & | & - \\ \hline 7 & mTWX=mTWU+mUWVm \angle T W X=m \angle T W U+m \angle U W V & + & Substitution & \\ \hline 8 & mTWV=mTWXm \angle T W V=m \angle T W X & & Transitive Property of Equality & \\ \hline 9 & TWTW\overline{T W} \cong \overline{T W} & & Reflexive Property of Congruence & \\ \hline 10 & TVWTXW\triangle T V W \cong \triangle T X W & & & . \\ \hline \end{tabular}

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Problem 3924

Cheating Challenge in Sims 4 - Youlude Complete the proof that PTVRUS\triangle P T V \cong \triangle R U S. \begin{tabular}{|c|c|c|c|c|} \hline & Statement & \multicolumn{3}{|l|}{Reason} \\ \hline 1 & PTVRUS\angle P T V \cong \angle R U S & Given & & \\ \hline 2 & STUV\overline{S T} \cong \overline{U V} & Given & & \\ \hline 3 & PR\angle P \cong \angle R & Given & & \\ \hline 4 & TV=UV+TUT V=U V+T U & & & - \\ \hline 5 & SU=ST+TUS U=S T+T U & Additive & & \\ \hline 6 & TV=ST+TUT V=S T+T U & & & \\ \hline 7 & SU=TVS U=T V & Transitiv & & \\ \hline 8 & PTVRUS\triangle P T V \cong \triangle R U S & & - & \\ \hline \end{tabular}

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Problem 3925

Complete the proof that EFGEGF\triangle E F G \cong \triangle E G F. \begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & FG\angle F \cong \angle G & Given \\ 2 & FGFG\overline{F G} \cong \overline{F G} & Reflexive Property of Congruence \\ 3 & EFGEGF\triangle E F G \cong \triangle E G F & \\ \hline \end{tabular}

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Problem 3926

Use the Law of Cosines to determine the indi

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Problem 3927

36. (II) Two large snowcats are towing a housing unit north, as shown in Fig. 4-42. The sum of the forces FundefinedA\overrightarrow{\mathbf{F}}_{\mathrm{A}} and FundefinedB\overrightarrow{\mathbf{F}}_{\mathrm{B}} exerted on the unit by the horizontal cables is north, parallel to the line L, and FA=4200 NF_{\mathrm{A}}=4200 \mathrm{~N}. Determine FBF_{B} and the magnitude of FundefinedA+FundefinedB\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}.
FIGURE 4-42 Problem 36.

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Problem 3928

Use the Law of Cosines to determine the indicated a

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Problem 3929

What values of vv and ww make BCDTUS\triangle B C D \cong \triangle T U S ? v=w=\begin{aligned} v & =\square \\ w & =\square \end{aligned} Submit

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Problem 3930

For the following right triangle, find the side length xx.

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Problem 3931

Find the width of a rectangular painting with perimeter 108.34in108.34 \mathrm{in}, 5.23 in. taller than wide.

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Problem 3932

Find the width of a rectangular painting with perimeter 104.59 in and height 5.79 in taller than width.

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Problem 3933

John's painting has a perimeter of 104.59 in and is 5.79 in taller than wide. Find width ww and length ll.

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Problem 3934

Find the value of xx given that mMKL=83m \angle M K L=83^{\circ}, mJKL=127m \angle J K L=127^{\circ}, and mJKM=(9x10)m \angle J K M=(9 x-10)^{\circ}.

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Problem 3935

Find the measures of angles RST, RSU, and UST given mRST=(12x1)m \angle R S T=(12 x-1)^{\circ}, mRSU=(9x15)m \angle R S U=(9 x-15)^{\circ}, and mUST=53m \angle U S T=53^{\circ}.

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Problem 3936

Find xx and the measures of angles: mCDF=(3x+14)m \angle CDF = (3x + 14)^\circ, mFDE=(5x2)m \angle FDE = (5x - 2)^\circ, mCDE=(10x18)m \angle CDE = (10x - 18)^\circ.

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Problem 3937

If mABCm \angle A B C is 1 degree less than 3 times mABDm \angle A B D and mDBC=47m \angle D B C=47^{\circ}, find the angles.

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Problem 3938

If CDE\angle C D E is straight, DEundefined\overrightarrow{D E} bisects GDH\angle G D H with mGDE=(8x1)m \angle G D E=(8 x-1)^{\circ} and mEDH=(6x+15)m \angle E D H=(6 x+15)^{\circ}. Find xx, mGDHm \angle G D H, mFDHm \angle F D H, and mFDEm \angle F D E.

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Problem 3939

Find the hypotenuse of a right triangle with sides 14 and 11.5. Round your answer to the nearest tenth.

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Problem 3940

What is the floor area in ft2\mathrm{ft}^{2} if it needs 25.4 square yards of carpet? (3ft=1yd)(3 \mathrm{ft}=1 \mathrm{yd})

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Problem 3941

Identify the angle pairs that are neither complementary nor supplementary: 72,1872^{\circ}, 18^{\circ}; 72,2872^{\circ}, 28^{\circ}; 72,10872^{\circ}, 108^{\circ}.

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Problem 3942

Find the supplementary angle if one angle's measure is unknown and their sum is 180180^{\circ}.

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Problem 3943

Find the angle between the nitrogen-oxygen bonds in the nitrate ion NO3\mathrm{NO}_{3}^{-}.

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Problem 3944

Calculate the distance between the points (1,3)(1,3) and (4,2)(4,-2). Provide an exact answer and simplify any radicals.

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Problem 3945

Calculate the distance between the points (0,3)(0,-3) and (7,9)(7,9). Distance ==

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Problem 3946

Find the area of a triangle with vertices at (2,3), (2,-5), and (6,1) using the formula: Area = 12x1(y2y3)+x2(y3y1)+x3(y1y2)\frac{1}{2} | x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) |.

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Problem 3947

Find the area of the parallelogram with vertices at (-4,-5), (3,-3), (-4,-9), (3,-7).

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Problem 3948

Calculate the area of the triangle with vertices at (-4,1), (-6,-3), and (5,-3) using the formula: Area = 12x1(y2y3)+x2(y3y1)+x3(y1y2\frac{1}{2} |x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2|.

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Problem 3949

Find the area of the parallelogram with vertices at (-6,9), (-3,1), (1,9), and (4,1).

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Problem 3950

Find the functions for the diameter d(r)d(r) and radius r(d)r(d) of a sphere given the volume V(r)=43πr3V(r)=\frac{4}{3} \pi r^{3}.

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Problem 3951

Find the width of the path around a 40 ft by 60 ft pool if the total perimeter is 248 ft.

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Problem 3952

Example 3 The ple chart below shows the social media usage of a class per day, Find the are length of the following given that r=4r=4 units. a. over 4 hours b. 1 to 2 hours c. under 1 hour d. under 30 minutes Solutions
Use the percentace

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Problem 3953

Найдите квадрат расстояния от начала координат до центра окружности, заданной уравнением: x2+8x+y28y4=0x^{2}+8 x+y^{2}-8 y-4=0

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Problem 3954

Triangles JKLJ K L and PQRP Q R are congruent, where JJ corresponds to PP, and KK corresponds to QQ. The measure of angle JJ is 4545^{\circ}, the measure of angle KK is 1010^{\circ}, and the measure of angle LL is 125125^{\circ}. What is the measure, in degrees, of angle PP ? (Disregard the degree symbol when entering your answer.) \square Answer Preview:

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Problem 3955

x26x+y24y51=0x 2-6 x+y 2-4 y-51=0
In the xyx y-plane, the graph of the given equation is a circle. If this circle is inscribed in a square, what is the perimeter of the square? (A) 16 (B) 32 (C) 64 (D) 204

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Problem 3956

QQ is a point on segment PR\overline{P R}. If PQ=4x+3,QR=3x+8P Q=4 x+3, Q R=3 x+8, and PR=18P R=18, what is PQP Q ? Simplify your answer and write it as a proper fraction, mixed number, or integer.

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Problem 3957

34. (III) A small block of mass mm rests on the rough, sloping side of a triangular block of mass MM which itself rests on a horizontal frictionless table as shown in Fig. 5-44. If the coefficient of static friction is μ\mu, determine the minimum horizontal force FF applied to MM that will cause the small block mm to start moving up the incline.
FIGURE 5-44 Problem 34.

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Problem 3958

(I) A jet plane traveling 1890 km/h(525 m/s)1890 \mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s}) pulls out of a dive by moving in an arc of radius 4.80 km . What is the plane's acceleration in gg 's?

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Problem 3959

Classifying scalene, isosceles, and equilateral triangles by side lengths
For each triangle, check all that apply.

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Problem 3960

7. (II) At what minimum speed must a roller coaster be traveling so that passengers upside down at the top of a circle (Fig. 5-45) do not fall out? Assume a radius of curvature of 7.6 m .
FIGURE 5-45 Problem 47.

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Problem 3961

Triangular Swan Portfolio 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: ABC\triangle A B C is equilateral; KOFO,JNJODECEEFBCDBDCK O \cong F O, J N \cong J O D E \cong C E \cong E F \quad \angle B C D \cong \angle B D C; CGFCFG;HKNHNK;GCFGKFJHM;KFHKLH\angle 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
1. mABCm \angle A B C
9. mCEDm \angle C E D
17. mKFGm \angle \mathrm{KFG}
25. mHIMm \angle \mathrm{HIM}
33. mOKNm \angle O K N
18. mCKFm \angle C K F
26. mHMIm \angle \mathrm{HMI}
34. mLINO

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Problem 3962

Question 13 Mharianne K
Keiko is on vacation at a tropical bay that has three islands. She rents a boat on Island A and plans to navigate to Island C, which is 14 miles away. Based on the figure below, at what angle θ\theta should she navigate to go to Island CC ?
Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth of a degree.

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Problem 3963

Several unit vectors r,s,t,u,n\vec{r}, \vec{s}, \vec{t}, \vec{u}, \vec{n}, and e\vec{e} in the xy-plane (not threedimensional space) are shown in the figure.
Using the geometric definition of the dot product, are the following dot products positive, negative, or zero? You may assume that angles that look the same are the same. \square 1. ne\vec{n} \cdot \vec{e} ? ? ? ? \square ? \square ? ? \square
2. st\vec{s} \cdot \vec{t} (Click on graph to enlarge)

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Problem 3964

Find the midpoint of the line segment with the given endpoints. (6,3) and (1,5)(-6,-3) \text { and }(-1,-5)
The midpoint is \square (Type an ordered pair.)

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Problem 3965

Write the standard form of the equation of the circle with the given center and radius. Center (5,7),r=8(-5,7), r=8
Type the standard form of the equation of the circle. (Simplify your answer.)

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Problem 3966

The equation of an ellipse with center (2,3)(2,3) that passes through the points (6,3)(6,3) and (2,5)(2,5) has the form f(x,y)=1f(x, y)=1. Find f(x,0)f(x, 0).

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Problem 3967

Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and rand (x+5)2+(y1)2=36(x+5)^{2}+(y-1)^{2}=36
The center is \square . (Type an ordered pair. Simplify your answer.) The radius is \square \square. (Type an integer or a simplified fraction.) Graph the circle.
Express the domain of the relation in interval notation. \square Express the range of the relation in interval notation. \square

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Problem 3968

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equa x2+y2+6x2y26=0x^{2}+y^{2}+6 x-2 y-26=0
The equation of the circle in standard form is \square (Simplify your answer.) The center of the circle is \square (Type an ordered pair.) The radius of the circle is r=\mathrm{r}= \square .
Use the graphing tool to graph the circle.
Click to enlarge graph

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Problem 3969

Area of a tringer
Find the area of the triangle below. Be sure to include the correct unit in your answer. If necessary, refer to the list of geometry formulas. \square cm cm2\mathrm{cm}^{2} cm3\mathrm{cm}^{3}

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Problem 3970

Find the area of this parallelogram. Be sure to include the correct unit in your answer. If necessary, refer to the list of geometry formulas. \square

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Problem 3971

Find the perimeter of the figure below. Notice that one side length is not given. Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer.

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Problem 3972

Find the perimeter of the figure below. Notice that one side length is not given. Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer.

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Problem 3973

The circumference of a circular field is 216 yards. What is the radius of the field? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. yards

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Problem 3974

The circumference of a circular field is 200 yards. What is the diameter of the field? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. \square yards

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Problem 3975

The circumference of a circular lot is 204 yards. What is the diameter of the lot? Round your answer to the nearest hundredth. If necessary, refer to the list of geometry formulas. \square yards

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Problem 3976

Geomety Circumference and area of a cincle
The diameter of a circle is 8 ft . Answer the parts below. Make sure that you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact circumference and area of the circle. Write your answers in terms of π\pi.
Exact circumference: \square Exact area: \square ft2\mathrm{ft}^{2} ft3\mathrm{ft}^{3} (b) Approximate the circumference and area of the circle. To do the approximations, use the π\pi button on the ALEKS calculator and round your answers to the nearest hundredth.
Approximate circumference: \square Approximate area: \square

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Problem 3977

B. Refer to circle JJ when answering the following questions.
1. What is the value of xx ?
2. What are the measures of the following angles? a. NJO\angle N J O d. KJL\angle K J L b. LJM\angle L J M e. MJN\angle M J N c. KJN\angle K J N f. KJO\angle K J O
3. What are the major arcs? Name at least 5.
4. What are the minor arcs? Name at least 5 .
5. What are the semi-circles? Name at least 4.
6. What is arc length of each arc if r=3r=3 in? a. \overparen{N O} c. \overparen{L M} e. g. KMOundefined\widehat{K M O} b. KLundefined\widehat{K L} d. \overparen{M N} f. KONundefined\widehat{K O N} h. MOKundefined\widehat{M O K} C. Read and analyze the following problems. Find what are being asked.

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Problem 3978

For the right triangles below, find the exact values of the side lengths ss and qq. The figures are not drawn to scale.

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Problem 3979

Question 54 \square 1 equilateral tilangle is inseribed I lind the length of the imadius (in emi) of the equilateral inangle.
Marke10 Hegative Mark 1025

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Problem 3980

Question 67 Point P(1,2)P(-1,2) is the midpoint of segment ABA B. Co-ordinates of AA are (2,y)(-2, y) and BB are (x,3)(x, 3). What is the value of xx ? Marks:1.0 Negative Marks:0.25

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Problem 3981

```latex The figure ABCDEFABCDEF, not drawn to scale, represents a wedge (prism) with measurements as shown. BCBC is perpendicular to the plane FEDCFEDC.
Given: - BC=5cmBC = 5 \, \text{cm} - DC=12cmDC = 12 \, \text{cm} - ED=13cmED = 13 \, \text{cm}
Calculate: (i) the length, in cm, of BDBD (ii) the surface area, in cm2\mathrm{cm}^{2}, of the wedge (iii) the volume of the prism ```

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Problem 3982

The curved edge of the door mat below is half an ellipse, a "serni-ellipse". As shown in the figure below, the flat edge of the door mat measures 148 cm and the distance from the center (on the flat edge) to the curved edge is 54 cm . The distance from point pp to the curved edge is 21 cm . Find the distance from pp to the center.
Round your answer to the nearest hundredth. Do not round any intermediate computations. 148 cm\longmapsto 148 \mathrm{~cm} \square cm

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Problem 3983

(6.) Für ein Dreeick ABCA B C gilt: A(3/2),AB=(1/2),AC=(1/1)A(3 /-2), A B=(1 / 2), A C=(-1 / 1). Geben Sie die Koordinalen des Schwerpunkts SS des Dreiecks an.
9. Geben Sie die in kartesischer Binomialform gegebenen Punkte in Polarform an. A(5/2),B(0/5),C(6/0),D(6/3)A(-5 /-2), B(0 / 5), C(-6 / 0), D(-6 / 3)

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Problem 3984

|(^) شبه منحرف مساحة • ^ اسم † وارتفاعهُ . اسم جد طول القاعدتين إذا علمت أن طول أحدهما ضعف الأخرى .

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Problem 3985

ه تريدُ أملُ عَمَلَ شمعةٍ على شكل هرم رباعيّ قائم منتظم، من متوازي مستطيلات من الشمع أبعاده: (١٠سم ، ١٥سم ، ١٠سم). مساحة القواعقة × 20 أحسِبُ أن حسِبُ طول ضلع قاعدة الهرم، علماً بأنّ ارتفاع الهرم المطلوب هو ۲۰سم. ب احسِبُ نسبةً مِساحة قاعدة متوازي المستطيلات إلى مساحة قاعدة الهرم . E

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Problem 3986

Work out the volume of the water in the cuboid-shaped container below. Give your answer in millilitres (ml), and give any decimal answers to 1 d.p. (Hint: 1ml=1 cm31 \mathrm{ml}=1 \mathrm{~cm}^{3} )

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Problem 3987

A prism is 46 mm long. Its cross-section is a triangle with a base length of 17 mm and a perpendicular height of 24 mm .
What is the volume of the prism? Give your answer in mm3\mathrm{mm}^{3}.

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Problem 3988

Рівняння гіперболічного типу може визначати \square гіперболу спряжену гіперболу пару прямих, що перетинаються пару паралельних прямих \square точку

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Problem 3989

The compound shape below is formed from a rectangle and a sector of a circle.
Calculate the perimeter of the compound shape. Give your answer in centimetres (cm) to 1 d.p.

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Problem 3990

For Exercises 959895-98, find the exact area of the sector. Then round the result to the nearest tenth of a unit. (See Example 10) 95. 96. 97. 98.

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Problem 3991

Lupe's bedroom floor is a rectangle with an area of 195 square feet. The floor is 15 feet long. What is the width of Lupe's bedroom floor? (a) 12 feet (b) 13 feet (C) 14 feet (d) 15 feet

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Problem 3992

the line 4x+3y=54 x+3 y=5 is tanjent to the center of a circle 0(2,3)0(-2,3). What is the radias of thi's circle?

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Problem 3993

The diagram shows a solid cone with radius 7.6 cm and height 16 cm.\text{The diagram shows a solid cone with radius } 7.6 \text{ cm and height } 16 \text{ cm.} A cut is made parallel to the base of the cone and the top section is removed.\text{A cut is made parallel to the base of the cone and the top section is removed.} The remaining solid has height 12 cm as shown in the diagram.\text{The remaining solid has height } 12 \text{ cm as shown in the diagram.} Find the volume of the remaining shape.\text{Find the volume of the remaining shape.}

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Problem 3994

Using the pencil, plot the point (6,6)(6,-6).

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Problem 3995

(II) What is the minimum work needed to push a 950kg950-\mathrm{kg} car 510 m up along a 9.09.0^{\circ} incline? Ignore friction.

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Problem 3996

(II) A 380-kg piano slides 4.6 m down a 3030^{\circ} incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 7-21). Determine: (a) the force exerted by the man, (b) the work done on the piano by the man, (c) the work done on the piano by the force of gravity, and (d)(d) the net work done on the piano, Ignore friction.
FIGURE 7-21 Problem 16.

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Problem 3997

Given the equation of a line y=12x+10 y = -\frac{1}{2} x + 10 , find the equation of the diagonal OB OB . Assume that point O O is the origin (0,0)(0,0) and point B B lies on the line y=12x+10 y = -\frac{1}{2} x + 10 .

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Problem 3999

A person is standing 40 ft away from a street light that is 30 ft tall and casts a shadow that is 50 feet long. How tall is the person if his shadow is 10.ft10 . \mathrm{ft} long?

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Problem 4000

Find measre of each angle 9) 11) 13) 12) 14)

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