Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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find parametric equations for the line through the point ( p_0(0, 2, -4…
\( x(t) = -2t \), \( y(t) = 2 - 5t \), \( z(t) = -4 - 4t \)
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progress: the movement of the progress bar may be uneven because questi…
First, find the area of the parallelogram: base = 6 mm, height = 4 mm, so area = \( 6 \times 4 = 24 \) square millimeters. Then, find the area of the triangle: base = 8 - 4 = 4 mm…
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the measure of central angle ycz is 80 degrees. what is the sum of the …
First, note that the radius of the circle \( r = 9 \). The total degrees in a circle is \( 360^\circ \). The central angle for the two shaded sectors: since angle \( \angle YCZ = …
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question 5 of 10 what is the area of the polygon given below? a. 66 squ…
C. 186 square units
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given: $overline{de} perp overline{ef}$, $angle dfe$ is complementary t…
To prove \( \overleftrightarrow{DF} \parallel \overleftrightarrow{GH} \), we can follow these steps: ## Step 1: Identify the given information We are given that \( \overline{DE} \…
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line segment wx is the radius of circle x, and line segment zy is the r…
# Explanation: ## Step1: Find diameter of circle X The radius of circle X (WX) is 8, so diameter is \( 2\times8 = 16 \). ## Step2: Find diameter of circle Y The radius of circle Y…
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question 4 of 10 to the nearest square unit, what is the area of the re…
1783 square units (Option A)
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the area of circle z is ( 64pi \text{ ft}^2 ). what is the value of ( r…
\( r = 8 \, \text{ft} \) (corresponding to the option \( r = 8 \, \text{ft} \))
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what is the sum of the areas of circle c and circle d? 7π units² 14π un…
\( 98\pi \) units\(^2\) (corresponding to the option "98π units²")
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which statements are true regarding the area of circle d? select two op…
The area of the circle depends on the square of the radius. The area of circle D is \( 324\pi\space\text{cm}^2 \)
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the movement of the progress bar may be uneven because questions can be…
First drawing (A and B on a line with arrows both ends): Line AB Second drawing (A as endpoint, arrow at B end): Ray AB Third drawing (A and B with no arrows, just a segment): Lin…
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in circle g, r = 3 units. maria draws a circle with double the area of …
18π units²
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in the diagram, ∠jkm is a straight angle. which statements about the di…
- $\overrightarrow{KQ}$ is an angle bisector: False (no info to confirm it bisects an angle) - $\angle LKQ$ is bisected: False (no info about bisecting $\angle LKQ$) - $m\angle JK…
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point g is the center of the small circle. point x is the center of the…
\( 49\pi\space cm^{2} \) (corresponding to the option \( 49\pi\space cm^{2} \))
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fiona draws a circle with a diameter of 14 meters. what is the area of …
\( 49\pi\space m^{2} \) (corresponding to the option: \( 49\pi\space m^{2} \))
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the measure of central angle rst is π radians. what is the area of the …
\( 8\pi \) units\(^{2}\) (corresponding to the option "8π units²")
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in the diagram below, ∠dab and ∠dac are adjacent angles. if ( mangle da…
For \( m\angle DAB \): 60° For \( m\angle BAC \): 85°
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which term describes the number of square units contained in the interi…
A. Area
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find the volume of the object shown below, consisting of a hemisphere w…
4900
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the radius of circle c is 6 units and the measure of central angle acb …
\( 113.04 \) ### Second Question: Area of the sector created by central angle \( \angle ACB \)
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question 10 of 10 which term describes the number of square units conta…
A. Area
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a sculptor started with a solid cube and then carved out a pyramid from…
144
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the area of the rectangle below is ____ sq. units. a. 21 b. 34 c. 68 d.…
C. 68
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coordinates (noun) co·or·di·nate kō-ˈȯr-də-nət \you can use a gps track…
D. a set of numbers that show an exact position
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what is the area of the rectangle below? image of a rectangle with heig…
A. 136 sq. units
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8. find the value of x. diagram: two parallel lines, transversal, angle…
\(x = 15\) ### Problem 9:
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bob wants to find the volume of the three - dimensional figure below. i…
a cube and a pyramid
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question 7 of 10 what is the area of the triangle below? image of a rig…
B. 60 sq. units
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arc lm on circle o has a measure of 40°. which statements are true? che…
The true statements are: - The central angle measure created by the shaded region is \(40^\circ\). - The ratio of the measure of \(\angle LOM\) to the measure of the whole circle …
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question 6 of 10 what is the area of the triangle given below? image of…
D. 35 sq. units
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what is the area of the triangle given below? a. 8 sq. units b. 12 sq. …
A. 8 sq. units
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what is the area of the shown triangle given below? diagram of triangle…
21 sq. units (assuming the base is 14 and height is 3, since the area of a triangle is $\frac{1}{2} \times base \times height = \frac{1}{2} \times 14 \times 3 = 21$)
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what is the area of the obtuse triangle given below? image of triangle …
B. 97.5 sq. units
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question 2 of 10 the area of the triangle below is ____ sq. units. tria…
B. 34
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the area of a triangle is 40 sq. inches. if the base of the triangle is…
D. 8 inches
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what is the sector area created by the hands of a clock with a radius o…
27π in² (corresponding to the option "27π in.²")
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find the volume of the solid below, composed of a cone and a cylinder. …
To find the volume of the solid composed of a cone and a cylinder, we calculate the volume of each part and then sum them. ### Volume of the Cylinder: The formula for the volume o…
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beginnings - 600 bce: unit test which best explains the mesopotamian pr…
A. Leaders valued religion and wanted a prominent place to pay tribute to local gods
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question 10 of 10 is the following shape a square? how do you know? a. …
D. Yes, the opposite sides are parallel, and all sides are the same length.
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constructing segments practice complete this assessment to review what …
14
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a soup company is looking at two designs for a new can. can a has a dia…
First, recall the formula for the volume of a cylinder, \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. For Can A: - Diameter = 8 cm, so radius \( r_A …
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question 4a find the volume of a cone with a radius of 3 millimeters an…
66 The formula for the volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \). Substituting \( r = 3 \), \( h=7 \) and \( \pi=\frac{22}{7} \), we get \( V=\frac{1}{3}\times\frac{22}{7}…
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what is the distance formula? $\boldsymbol{\text{option a: } sqrt{(x_2 …
C. $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
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chapter 1 test: solving equations you must show your work for full cred…
\(B = \frac{4}{5}\) ### Problem 2: Solve \(-4 = 3x + 5\)
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question 8 of 10 how do you know if two line segments are perpendicular…
B. Their slopes are negative reciprocals.
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the diameter of an official soccer ball is approximately 22 centimeters…
5500 To find the volume of the soccer ball (a sphere), we use the formula for the volume of a sphere \( V=\frac{4}{3}\pi r^{3} \). The diameter is 22 cm, so the radius \( r=\frac{…
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if abcde is translated 3 units to the right and 4 units down, what will…
D. It will move but won't change shape or size.
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use the diagram to answer the questions. what is the area of the circle…
\( 121 \) ### Second Question: Measure of the central angle of the shaded sector
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question 6 of 10 is the following shape a rectangle? how do you know? a…
C. Yes, the adjacent sides are perpendicular, and the opposite sides are parallel.
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give the coordinates of point a. image of a coordinate plane with point…
C. \((-1, 3)\)
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classifying angles a goniometer may be used to measure the range of mot…
acute; \(0\); \(90\)
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what is the polygon being rotated to create the brown quilt block patte…
C. Triangle
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match each name of a solid on the left to every property that applies t…
pyramid: polygonal base, triangular faces cone: circular base rectangular prism: rectangular faces cylinder: circular base, rectangular faces
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what is the approximate circumference of the circle? what is the height…
\( \approx 18.8 \) (or \( 18.84 \), depending on precision) ### 2. Height of the Parallelogram
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question 9 of 19 lines m and p are perpendicular. if the slope of line …
A. $-\frac{1}{3}$ (assuming the slope of line \( m \) is \( 3 \), and lines \( m \) and \( p \) are perpendicular, the slope of \( p \) is the negative reciprocal, so \( -\frac{1}…
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if the radius is doubled, what is the effect on the area of sector xyz?…
The sector area will be 4 times greater. (The option corresponding to this statement, e.g., if the last option is "The sector area will be 4 times greater", then the answer is tha…
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what is the ratio of the sector area to the area of the entire circle? …
\(\frac{1}{5}\) (corresponding to the option \(\boldsymbol{\frac{1}{5}}\))
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find the volume of the solid below, composed of two pyramids connected …
To find the volume of the solid composed of two pyramids with the same square base, we use the formula for the volume of a pyramid, \( V = \frac{1}{3}Bh \), where \( B \) is the a…
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timothy built a base for a circular tabletop. the base can support a ta…
Smallest possible area: 113 square inches Largest possible area: 1662 square inches
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warmup: write the converse, inverse and contrapositive statement for th…
Converse: If it is a quadrilateral, then it is a square (False) Inverse: If it is not a square, then it is not a quadrilateral (False) Contrapositive: If it is not a quadrilateral…
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find the volume of the silo if the radius of the hemispherical top is 2…
80000
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the canopy of a parachute is a semicircle with a radius of 13 feet. a c…
B. \( 88.5 \, \text{ft}^2 \)
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find the volume of the solid shown below. (image: pyramid with rectangu…
264
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lines a and b are perpendicular. if the slope of line a is 3, what is t…
C. $-\frac{1}{3}$
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question 7 of 10 the lines shown below are parallel. if the green line …
A. -1
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question 3 3 of 6 find the volume of the solid shown below. use 3.14 fo…
\( 75.4 \)
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which statement is true regarding the two shaded sectors of circle o? e…
The area of sector AOB is equal to the area of sector DOC because the central angle measures are equal.
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question 4 of 10 if two lines have the same slope, they are parallel. a…
B. False
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which statements are true regarding the area of circles and sectors? ch…
- The area of a circle depends on the length of the radius. - The area of a sector depends on the ratio of the central angle to the entire circle. - The area of a sector depends o…
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the lines shown below are parallel. if the green line has a slope of $-…
A. $-\frac{1}{2}$
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a garden is represented by the figure (with labeled dimensions: 3x + 2,…
# Explanation: ## Step1: Analyze the figure structure The figure can be divided into two rectangles. The first rectangle has length \(3x + 2\) and height \(x + (3x - 1)-(3x - 1)\)…
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the two polygons in the image are scaled copies. explain how to find th…
To find the scale factor, identify corresponding sides of the two scaled polygons. Measure (or determine from the grid) their lengths. The scale factor is the ratio of the length …
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question 1 of 10 if the slopes of two lines are negative reciprocals, t…
A. True
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polygon b is a scaled copy of polygon a. what is the missing length of …
B. 3
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the measure of central angle mnl is π radians, and the measure of the e…
\( \frac{1}{2} \) ### Second Blank (Area of Entire Circle)
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lesson 5 constructing segments part 2 lucia constructed \\(\\overline{c…
\(AB = CD\) (the option with this statement, likely the last one marked with a dot in the image)
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which statements are true? check all that apply. the ratio of the measu…
- The ratio of the measure of the central angle to the measure of the entire circle is \(\frac{5}{2\pi}\). - The area of the sector is \(250\) units\(^{2}\). - The area of the sec…
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hotspot answer listen triangles d and e are scaled copies of each other…
\(\frac{5}{2}\)
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practice: running track measures circle with radius \\( \\frac{1}{10} \…
The distance once around the running track is \( 0.628 \) miles. ### Problem 2 #### Part b: How I calculated the answer:
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matching list listen use your completed table in your math notebook to …
To solve this matching problem, we analyze the corresponding parts of the original railroad - crossing sign and its copies (Copy 1 and Copy 2) by looking at the positions and shap…
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name the marked angle in 2 different ways.
$\angle MNL$, $\angle N$
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name the marked angle in 2 different ways. diagram with points r, s, q,…
\( \angle RSQ \), \( \angle S \)
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4、 in a figure, m∠a = 15x + 81 and m∠c = 10x + 24. if ∠a and ∠c are sup…
First, since ∠a and ∠c are supplementary, their measures add up to 180 degrees. So we set up the equation: \( (15x + 81) + (10x + 24) = 180 \) Combine like terms: \( 25x + 105 = 1…
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choose the correct answer which of these is a unit used to measure volu…
A. cubic centimeters
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review: find the indicated length. a---14---b---3x - 4---c ac = 4x + 4 …
28
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name the marked angle in 2 different ways. p o m n answer attempt 1 out…
$\angle ONM$, $\angle N$
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multiple choice question 4 listen in the image below, each small square…
D. Figure A: $7\frac{1}{2}$ units², Figure B: 10 units²
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bisecting a segment given $overline{ed} \\cong \\overline{db}$, which s…
A is the midpoint of \(\overline{FC}\), \(FA = \frac{1}{2}FC\) (the options with these statements, assuming the checkboxes correspond to: the second option, the fifth option, and …
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what is the area of the shaded sector? 24π 45π 72π 576π
\( 72\pi \) (corresponding to the option "72π")
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name the marked angle in 2 different ways. diagram with points o, m, n …
\( \angle MON \), \( \angle O \)
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consider the figure below. complete each statement. 1. ∠a and ∠d are - …
s: 1. Supplementary Angles 2. A Linear Pair 3. Vertical Angles Wait, but maybe I made a mistake. Let's check again. Wait, 1. $\angle a$ and $\angle d$: are they a linear pair? No,…
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practice: running track measures 1. the formula to find the circumferen…
The distance once around the running track is \( 0.628 \) miles.
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name the figure below in two different ways. v t r symbol: and
Symbol: \( \overrightarrow{} \) \( \overrightarrow{VR} \) and \( \overrightarrow{VT} \)
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name the figure below in two different ways. symbol: ▼ and □ and □
$\overrightarrow{MF}$ and $\overrightarrow{MX}$ (or $\overrightarrow{MF}$ and $\overrightarrow{MF}$? No, that's not right. Wait, maybe the ray is $\overrightarrow{MF}$ and also ca…
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the movement of the progress bar may be uneven because questions can be…
- \(4x - 3>9\) or \(-8x\geq16\) matches the second graph (with open circle at 3, closed at - 2). - \(8x\geq - 24\) and \(10>2x + 6\) matches the first graph (closed at - 3, open a…
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date______ period______ independent practice classify the angles as acu…
Obtuse ### Problem 3
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determining a missing length which expression represents the measure of…
\( x + 5 \) (corresponding to the option with this expression)
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name the figure below in two different ways. a • ——— • h symbol: dropdo…
\(\overline{AH}\) and \(\overline{HA}\)
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the movement of the progress bar may be uneven because questions can be…
15 inches
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name the figure below in two different ways. symbol: and
Line \( QM \) and Line \( QK \) (or Line \( QM \) and Line \( KM \), etc. as long as two points on the line are used) (Note: The symbol for a line is \( \overleftrightarrow{} \), …