Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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find the area of each polygon. 1. square with side 8 m 2. rectangle wit…
The area of the square is \( 64 \, \text{m}^2 \). ### Problem 2: Find the area of the rectangle (7 in by 12 in)
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determine the coordinates of each point after the shaded pre-image is r…
| Pre - Image Coordinates | Image Coordinates | | ---- | ---- | | \((-2,0)\) | \((-2,0)\) | | \((-2,2)\) | \((-2,-2)\) | | \((-1,3)\) | \((-1,-3)\) | | \((1,3)\) | \((1,-3)\) | | …
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9. modeling with mathematics you are going for a hike in the woods. you…
### Part a # Explanation: ## Step1: Define Coordinates Let the car be at the origin \((0,0)\). The waterfall is 4 miles east, so its coordinates are \((4,0)\). The lookout point i…
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problem 6 point ((x, y)) is reflected over the (y)-axis, and then trans…
\((-x + 5,y - 2)\)
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view policies current attempt in progress one end of a long straight ro…
\( \langle14.3, 16.7, 8.12 angle \) (rounded to a reasonable number of significant figures. If we use more precise calculations: \( \cos(55^{\circ})\approx0.5735764364 \), \( \cos…
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1) find m∠klm if m∠klb = 26° and m∠blm = 60°.
\( 86^\circ \)
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14. use structure sketch a graph given the following key features. doma…
The graph is a curve (or piece - wise function graph) with open circles at \((-4,-4)\), \((4,-4)\), closed circle at some point near \(y = 6\) (e.g., \((1,6)\) as a peak), passing…
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7. j(-3, 4), k(4, 4), l(3, -3)
The area of triangle \(JKL\) is \(\boldsymbol{24.5}\) (or \(\boldsymbol{\frac{49}{2}}\))
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3. points a, b, c, and d are collinear and positioned in that order. so…
\( x = - 61 \)
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en la escuela ¿eres formal o informal? a. circle the phrases below that…
### Part A To determine which phrases are for teachers (circled) and students (underlined): - **For teachers (circled)**: Phrases using formal address ("Ud." or respectful terms l…
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for #5-8, find the area of the polygon with the given vertices. 5. e(3,…
The area of the polygon (right triangle) is \( 7.5 \) (or \( \frac{15}{2} \)).
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a triangle has side lengths of (6g + 10) centimeters, (5g − 7) centimet…
\(-7 + 11g + 2h\) (corresponding to the option \(-7 + 11g + 2h\))
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2. ac is 6 units long. point b is on ac. if ab=18x and bc=6x, a.) what …
\( x = \frac{1}{4} \) ### Part b)
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the rectangle below has an area of ( x^2 - 15x + 56 ) square meters and…
\( x - 8 \)
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the rectangle below has an area of ( x^2 - 11x + 30 ) square meters and…
\( x - 6 \)
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a triangle has side lengths of (2b + 5c) centimeters, (10b + 7d) centim…
\( 12b + 2c + 11d \) (corresponding to the option "12b + 2c + 11d")
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a triangle has side lengths of (5k − 3) centimeters, (k + 1) centimeter…
\(m - 9 + 6k\) (the option with this expression)
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- a-level: solve the following problems for \x\ using the segmen 1. ist…
\( x = 13 \)
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a triangle has side lengths of (9v − 7w) centimeters, (7v + 10x) centim…
\( 18x - 2w + 16v \) (corresponding to the option "18x − 2w + 16v")
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a triangle has side lengths of (4m + 3n) centimeters, (8m + 10p) centim…
\(5n + 12p + 12m\) (the first option)
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3. f •———11———• e • d (2x - 9 above e to d) and ←——3x - 3——→ below f to…
\( x = 5 \)
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25. before aaron can be a real estate agent, he must obtain a license. …
256 square feet
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2. j•———x———•i———2x - 13———•h |<——————————17——————————>|
\( x = 10 \)
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4. b •——• c ———• d, where the length from b to c is ( x + 2 ), from c t…
\( x = 0 \)
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v = b · h cylinder h = 10 r = 4 cm
The volume of the cylinder is \( 160\pi\space cm^{3} \) (or approximately \( 502.4\space cm^{3} \))
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for #1-4, find the perimeter of the polygon with the given vertices. 1.…
22
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2. the height of a baseball hit in the air is given by the graphed para…
5; \( y \)-intercept (circle \( y \)-intercept) #### Part b
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figure j, the large hexagon, was dilated with the origin as the center …
- Statement: "A scale factor of 5 was applied to Figure J to create Figure K." → False (check the "False" box) - Statement: "If \((x, y)\) represents a point on Figure J, then the…
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1 triangle abc was dilated by a scale factor of 3 with the origin as th…
\((3x, 3y)\)
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1. l • 2x - 4 • k -2 + x • j, with a horizontal double - arrow labeled …
\( x = 7 \)
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3. l •——2——• m ——?——• n ←——7——→
5
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square a was transformed to create square b. which of the following rul…
B. \((x,y)\to(x + 7,y)\) C. \((x,y)\to(-x,y)\) E. \((x,y)\to(y,-x)\)
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2. a • — ? — • b — 5 — • c ←—— 12 ——→
7
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checkpoint 2. use the line segment addition postulate to solve for a mi…
\( x = 7 \) ### B-level Problem 2:
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express x in terms of a, b, and c
\(\boldsymbol{\frac{ac}{b - c}}\) (Note: If the proportion was set up incorrectly, but based on the similar triangles with the given labels, this is the solution. If the correct p…
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express x in terms of a, b, and c.
\(x=\dfrac{ac}{a + b}\)
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period: 2nd a/b day: a for exercises 1 & 2, the vertices of δxyz are x(…
\(\Delta X'Y'Z'\) with vertices \(X'(-3, -7)\), \(Y'(-6, -4)\), \(Z'(-1, -2)\) ### Problem 2:
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16 square a was transformed to create square b. which of the following …
# Explanation: ## Step1: Analyze horizontal translation Square A is on the left side of the y - axis, and Square B is on the right side. To move from A to B horizontally, we can c…
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transformations - translations try again! at least one of your coordina…
To solve the translation of the triangle, we first identify the coordinates of the original triangle's vertices. Let's assume the original vertices (from the grid) are: - Purple: …
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a hexagon is shown on the coordinate grid. which transformations produc…
The three correct transformations are: \((x, y) \to (-x, y)\), \((x, y) \to (x, -y)\), \((x, y) \to (-x, -y)\)
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assignment #9 name the polygon by the number of sides. tell whether it …
The polygon is a pentagon and it is convex. ### Problem 2:
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14 a circle with center c(-3, 3) is graphed on a coordinate plane. the …
D. Reflection across the \(y\)-axis: \((x, y) \to (-x, y)\)
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13 which rule can be used to represent each transformation? move the co…
- A triangle is translated 1 unit to the left: \((x,y)\to(x - 1,y)\) - A square is reflected across the x - axis: \((x,y)\to(x,-y)\) - A pentagon is rotated \( 270^{\circ} \) cloc…
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12 a figure is graphed on a coordinate grid and then rotated. if (x, y)…
| Transformation | \((-y,x)\) | \((-x,-y)\) | \((y,-x)\) | |----------------|------------|-------------|------------| | \(90^\circ\) counterclockwise rotation about the origin. | …
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find m∠tuv if m∠tuv = x + 135, m∠tuf = 60°, and m∠fuv = 2x + 75.
\( 135^{\circ} \)
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estimate the measure of $\\angle mno$ to the nearest $10^\\circ$.
130 (Wait, no, maybe 140. Wait, maybe I was wrong. Let me check again. The angle between NM and NO: if NO is horizontal right, NM is going up and left. The angle is obtuse. Let's …
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14. if ef bisects cd, cg = 5x - 1, gd = 7x - 13, ef = 6x - 4, and gf = …
\( 19 \)
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a triangle has side lengths of (6v + 3) centimeters, (2v + 5) centimete…
\(8w + 8v + 13\) (corresponding to the option "8w + 8v + 13")
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a triangle has side lengths of (9v − 7w) centimeters, (7v + 10x) centim…
\( 18x - 2w + 16v \) (corresponding to the option "18x − 2w + 16v")
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look at this shape: image of a blue trapezoid on a grid which image sho…
B
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look at this shape: image of a trapezoid on a grid which image shows a …
A. Option A
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name the marked angle in 2 different ways. diagram with points p, q, o …
\( \angle QPO \), \( \angle P \)
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find the value of x for which m || n. (3x - 33)° (2x + 20)° m n the val…
\( 53 \)
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question convert the following angle from degrees to radians. express y…
\( 3\pi \)
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if segment ab is 2 centimeters long, how long is segment ab?
2 centimeters
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convert the following angle from degrees to radians. express your answe…
\( \frac{5\pi}{2} \)
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if cd = 6x, de = 5, and ce = x + 10, what is cd? c d e 6x 5 x + 10 simp…
6
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7. which one does not belong with the other three? explain.
The third figure (with angles ∠3 and ∠4) does not belong. Others have complementary angles (sum 90°), but it has supplementary angles (sum 180°).
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if fg = 7x, gh = x + 1, and fh = 9, what is fg? diagram: points f, g, h…
7
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question convert the angle \\(\\frac{\\pi}{2}\\) radians to degrees.
$90^\circ$
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nd then find the specified lengths. 6x + 11 9x − 13 j ---- m ---- k x=_…
\( x = 8 \), \( JM = 59 \), \( MK = 59 \)
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if bc = 7x, cd = 4, and bd = x + 10, what is bc? simplify your answer a…
7
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if tu = 5 and uv = 6, what is tv? t u v 5 6 write your answer as a deci…
11
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nd then find the specified lengths. 6x + 11 9x - 13 j m k x=____ jm=___…
\(x = 8\), \(JM = 59\), \(MK = 59\)
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the lacrosse player shown passes the ball to a team member who is direc…
50
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if kl = 14 and lm = 6, what is km? write your answer as a decimal or in…
20
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in the given figure, which lines or segments are parallel? justify your…
C. $\overline{EA}\parallel\overline{BC}$ by the Converse of the Same - Side Interior Angles Postulate
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if pq = 11 and pr = 17, what is qr? diagram of line segment with p, q, …
6
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in the given figure, which line or segments are parallel? justify your …
A. \( \overline{IJ} \parallel \overline{GH} \) by the Converse of the Alternate Interior Angles Theorem
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if two rectangles have the same perimeter, will they always be congruen…
No
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in the given figure, which lines are parallel? justify your answer. det…
F. \(\overline{CE}\parallel\overline{HK}\) by the Converse of the Same - Side Interior Angles Theorem
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for problems 1 and 2, graph the solution set on the number line. 1. {g …
### Problem 1: $\{g \mid g > 4\}$ # Explanation: ## Step1: Identify the inequality The solution set is all real numbers $g$ where $g$ is greater than 4. ## Step2: Graph on the num…
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triangle abc and triangle xyz are congruent. which sequence of transfor…
A reflection across the \(y\) - axis, and then a translation 2 units up.
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the interior angles of a regular hexagon are congruent. why are any pai…
First dropdown: (No specific value here, context is about the theorem) Second dropdown: Alternate Interior Angles Theorem Third dropdown: congruent Fourth dropdown: parallel (Note…
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problem 2 determine whether the figures are congruent. yes no
Yes
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pregunta encuentra el volumen de un cono circular recto que tiene una a…
150.0
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look at this diagram: diagram if $overleftrightarrow{pr}$ and $overleft…
\( 136 \)
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look at this diagram: diagram shows two parallel vertical lines ( overl…
\( 129 \)
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which of the following sequences of transformations maps lmno onto abcd…
Sequence A: A translation 6 units to the left and 1 unit up, then a reflection over the horizontal line through point \( A \).
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construct a line through p parallel to l. (hint: copy either ∠pca or ∠p…
The theorem that justifies the construction is the Corresponding Angles Theorem (which states that if two lines are cut by a transversal and the corresponding angles are congruent…
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10. which of the following pictures shows the bisection of an angle? a.…
B. (The option with the correct arc markings for angle bisector construction)
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which of the following sequences of transformations maps △mno onto △abc…
C. Both
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what is the student’s error? given ∠1 ≅ ∠2. by the vertical angles thm.…
B. \( \angle 2 \) and \( \angle 3 \) are not corresponding angles.
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10. which of the following pictures shows the bisection of an angle? a.…
A. The picture in option A shows the bisection of an angle.
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5. ∠p and ∠q are supplementary angles. if the measure of ∠q is 64°, fin…
\(116^\circ\)
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which of the following sequences of transformations maps △xyz onto △abc…
C. Both
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eak, so lets start a new one today. which of the following sequences of…
C. Both
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5. tobys principal wants to put a new fence around the playground. the …
361.56
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break, so lets start a new one today. which of the following sequences …
C. Both
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which of the following sequences of transformations maps △pqr onto △abc…
C. Both
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15. if r is the midpoint of \\(\\overline{qs}\\), \\(rs = 2x - 4\\), \\…
\( 68 \)
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14. rooms a rectangular room is 12½ feet wide and 14 feet long. what is…
The perimeter of the room is 53 feet. ### Question 15
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which of the following sequences of transformations maps △uvw onto △abc…
Sequence A (A 180° rotation about point \( V \), then a translation along the directed line segment \( \overrightarrow{VB} \))
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multiple choice questions circle the correct answer for each of the fol…
c. liability ### Question 2
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write an indirect proof of the converse of the corresponding angles the…
The indirect proof shows that assuming \( l \) is not parallel to \( n \) leads to a contradiction (\( m\angle 3 = 0 \) vs \( m\angle 3>0 \)), so \( l\parallel n \). The key steps…
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11. geometry the area of a rectangle is ( x^3 + 8x^2 + 13x - 12 ) squar…
The length of the rectangle is \( x^{2}+4x - 3 \) units.
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11. geometry the area of a rectangle is ( x^3 + 8x^2 + 13x - 12 ) squar…
The length of the rectangle is \( \boldsymbol{x^{2}+4x - 3} \) units.
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10) determine if the following side lengths form a right triangle: 4, 4…
The side lengths 4, 4, 4 do not form a right triangle.
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what is st? st = \\boxed{} submit
\( 57 \)
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name: mirk... patterns & conjectures 1. how can you prove that a conjec…
By finding a counterexample (a specific case where the conjecture's hypothesis is true but the conclusion is false). ### Question 2 (Sketching the next figure)