幾何
三角形、圓、解析幾何與證明題。
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the area of a rectangle is $56x^{12}y^9$ square yards. if the length is…
Option 4. $8x^{9}y^{6}$
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question determine a series of transformations that would map polygon a…
A series of transformations that maps polygon \(ABCDE\) onto \(A'B'C'D'E'\) is: Rotate \(ABCDE\) 90° counterclockwise about the origin, then translate the rotated polygon 5 units …
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circles try another translation using the circle from the previous prob…
B. $(x-8)^2 + (y+4)^2 = 9$
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circles what is the equation of a circle with center (-3,1) and radius …
D. $(x+3)^2+(y-1)^2=4$
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determine the length of the longest side and the measure of the largest…
Longest side length (example): \( 4.0 \) cm, Largest angle measure (example): \( 80^\circ \) (Replace with actual measurements from the triangle using ruler and protractor.)
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shown below. you must use the ruler and protractor for precise measurem…
To solve this problem, we'll use a ruler to measure the side lengths and a protractor to measure the angles of the triangle. ### Step 1: Measure Side Lengths 1. **Measure \( AB \)…
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determine if triangle fgh and triangle ijk are or are not similar, and,…
The triangles are similar, by the AA (Angle-Angle) similarity criterion (all three corresponding angles are equal, satisfying the condition for similarity).
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commas activity directions the sentences below don’t make sense because…
To solve this, we add a comma to each sentence where it clarifies the meaning, then circle the letter after the comma (assuming each sentence has a lettered option, but since the …
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test prep consider the diagram. (x + 5)° (x - 5)° 120° find the value o…
60
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3 find the measure of angle θ. round your answer to the nearest degree.…
\(43^\circ\)
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rhombus defg is a translation of rhombus defg. write the translation ru…
\( (x, y) \to (x + 12, y + 12) \)
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segment addition / subtraction (algebra) score: 3/4 penalty: 1 off you …
$4$
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segment addition / subtraction (algebra) score: 1/4 penalty: 1 off ques…
7
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3. the surface area of a rectangular prism can be calculated by utilizi…
$474\ \text{cm}^2$
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graph the point (3.5, -2.5) on the coordinate plane.
The point $(3.5, -2.5)$ is plotted 3.5 units to the right of the y-axis and 2.5 units below the x-axis, at the intersection of the vertical line through $x=3.5$ and horizontal lin…
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5. myla wants to wrap a birthday present for her mother, but needs to m…
A. Myla will not have enough paper to wrap the gift. B. Myla still needs 89.6 in.$^2$.
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the hypotenuse of a 45°-45°-90° triangle measures 18 cm. what is the le…
B. $9\sqrt{2}$ cm
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triangle mno is an equilateral triangle with sides measuring $16\\sqrt{…
24 units
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which triangle is a $30^{circ}$-$60^{circ}$-$90^{circ}$ triangle? - fir…
The triangle with side lengths 5, $5\sqrt{3}$, and 10 (the first option)
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consider the incomplete paragraph proof. given: isosceles right triangl…
B. Divide both sides of the equation by two, then determine the principal square root of both sides of the equation.
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each leg of a 45°-45°-90° triangle measures 12 cm. what is the length o…
12$\sqrt{2}$ cm (Option D: $12\sqrt{2}$ cm)
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a person is standing exactly 36 ft from a telephone pole. there is a 30…
B. $12\sqrt{3}$ ft
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consider triangle qrs. the legs each have a length of 10 units. what is…
D. $10\sqrt{2}$ units
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consider triangle pqr. what is the length of side qr? 8 units 8√3 units…
16 units
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applying the 30°-60°-90° and 45°-45°-90° relationships isaiah sketches …
$4\sqrt{2}$ in.
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classify each number below as a rational number or an irrational number…
- For $\pi$: irrational (select the circle in the 'irrational' column for $\pi$) - For $\sqrt{4}$: rational (select the circle in the 'rational' column for $\sqrt{4}$) - For $-27.…
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solving real - world problems with 30° - 60° - 90° triangles from the s…
$\frac{5\sqrt{3}}{3}$ ft
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the roof of a house is the shape of an isosceles right triangle as show…
B. \( 5\sqrt{2} \) ft
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3. name each shape and tell how many sides it has: | shape | number of …
- Top shape: 5 sides, Pentagon - Middle shape: 3 sides, Triangle - Bottom shape: 5 sides, Pentagon
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9 which equation represents a parabola opening to the right with a vert…
$\boldsymbol{x=\frac{1}{36}y^2}$ (la opción más a la izquierda)
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1. draw a rectangle with an area of 18 square units. = 1 unit
A rectangle with length 6 units and width 3 units (or length 9 units and width 2 units, or length 18 units and width 1 unit) can be drawn. For example, using the factor pair \( 3\…
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solve for x and graph the solution on the number line below. -36 < -3x …
## Inequality Notation: $x < 9$ or $x \geq 11$ ## Number Line Graph Instructions: 1. For $x < 9$: Draw an open circle at 9, then draw an arrow pointing left from the circle to cov…
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7 select the equation for a graph that is the set of all points in the …
B. $y = -\frac{1}{32}x^2$
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find the area of the shaded shape. 1 unit 1 unit 11 square units
11 square units
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question using the graph, determine the coordinates of the vertex of th…
(1, - 5)
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in the right triangle, one leg is 11, the acute angle is 30°, and the o…
$x=11\sqrt{3}$ or approximately $19.05$
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in the right triangle with a right angle, one acute angle is 45°, anoth…
$3\sqrt{2}$
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4. select the equation for a graph that is the set of all points in the…
$\boldsymbol{y = \frac{1}{20}x^2}$ (corresponding to the third option)
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for the following right triangle, find the side length x. round your an…
\( 12.21 \)
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find the value of x. triangle with angles 35°, 92°, and x° x = blank
\(x = 53\)
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find the third side in simplest radical form: (an image of a right tria…
\(2\sqrt{17}\) Wait, no, wait I think I made a mistake. Wait the vertical leg: from (0,0) to (0,5) is length 5, horizontal leg from (0,0) to (4,0) is length 4. Then hypotenuse is …
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find the third side in simplest radical form:
\(2\sqrt{3}\)
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unit 1 lesson 6 practice problems 1. quadrilateral abcd is congruent to…
A sequence of rigid motions is: First, translate quadrilateral \(ABCD\) horizontally to map point \(B\) to point \(B'\). Then, rotate the translated quadrilateral \(90^\circ\) clo…
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explore the area of sectors of circles by following these steps. the ar…
\( \frac{1}{4} \) (corresponding to the option "1/4")
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unit 1 lesson 6 practice problems 1. quadrilateral abcd is congruent to…
First, translate quadrilateral \( ABCD \) along the vector \( \overrightarrow{BB'} \) (so \( B \) maps to \( B' \)), then reflect the translated quadrilateral over the line contai…
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explore the area of sectors of circles by following these steps. the ra…
\( \frac{1}{4} \) (corresponding to the option "1/4")
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desmos unit 8.4, lesson 14: equation cards a. \\begin{cases} y = 4 \\\\…
$x=-14$, $y=4$ (or the ordered pair $(-14, 4)$)
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determine whether the slope of each line is positive, negative, zero, o…
To determine the slope type for each line, we analyze the direction of the line: ### First Line (Left Graph): A line that falls from left to right has a **negative slope** (as \( …
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explore the area of sectors of circles by following these steps. 1. wha…
\(\frac{1}{2}\)
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a 12-foot ladder is leaning against a wall. the distance from the base …
The triangle is isosceles. The leg-to-hypotenuse ratio is $1:\frac{\sqrt{2}}{2}$. The nonright angles are congruent. The ladder represents the longest length in the triangle.
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x + y = 2\ y = -2x + 3\ click to select points on the graph.
The solution to the system is $(1, 1)$. To graph: 1. Plot points $(0,2)$ and $(2,0)$, draw a line through them for $x+y=2$. 2. Plot points $(0,3)$ and $(1.5,0)$, draw a line throu…
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which fraction does the point on the number line represent? 0 1 options…
$\frac{3}{4}$ (Note: The initially selected option $\frac{1}{4}$ is incorrect. The correct fraction represented by the point on the number line is $\frac{3}{4}$.)
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which fraction does the point on the number line represent? 0 1 listen
\(\frac{3}{4}\) (corresponding to the option with \(\frac{3}{4}\))
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what is the volume of this cone? round your answer to the nearest hundr…
2654.65 cubic feet
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explore the relationship between the radius and area of a circle by fol…
\((r)(\pi r)\)
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show that the length of the hypotenuse is \\(\\sqrt{2}\\) times as long…
The simplified equation is $\boldsymbol{c = a\sqrt{2}}$, so the first dropdown selects $\boldsymbol{a}$ and the second dropdown selects $\boldsymbol{a}$ (to write the relationship…
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explore the relationship between the radius and area of a circle by fol…
The height of the parallelogram is $r$. So the correct option (from the dropdown) is $r$.
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explore the relationship between the radius and area of a circle by fol…
base × height
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warm-up what is the measure of the central angle? 140° what ratio repre…
s: - Ratio: \(\frac{7}{18}\) - Length of minor arc AB: \(14\pi\) (or if we use decimal, approximately \(43.98\))
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using portions of a circle what is the measure of the central angle? ° …
\( 140^\circ \) ### Second Question: Ratio of central angle to entire circle
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the equation of a line is given below. $7x - 5y = -35$ (a) find the x-i…
(a) x-intercept: $-5$ y-intercept: $7$ (b) 1. Plot the point $(-5, 0)$ on the x-axis. 2. Plot the point $(0, 7)$ on the y-axis. 3. Draw a straight line connecting these two points…
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the equation of a line is given below. x - 4y = 4 (a) find the x-interc…
(a) x-intercept: $4$ y-intercept: $-1$ (b) Graph: Plot points $(4, 0)$ and $(0, -1)$, then connect them with a straight line.
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the equation of a line is given below. $5x + 4y = -20$ (a) find the $x$…
(a) x-intercept: $(-4, 0)$ y-intercept: $(0, -5)$ (b) Graph: Plot the points $(-4, 0)$ and $(0, -5)$, then connect them with a straight line that extends across the coordinate pla…
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6. modeling with mathematics the backboard of the basketball hoop forms…
The distance between the rods where they meet the backboard is approximately \(9.14\) inches.
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m∠bec = m∠abc = 62
\(m\angle BEC = 31^\circ\), \(m\angle ABC = 62^\circ\)
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6. modeling with mathematics the backboard of the basketball hoop forms…
Approximately \(9.14\) inches
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consider a regular hexagon inscribed in circle c with radius r. regular…
slightly greater than \( 6r \)
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m∠bec = m∠abc = (and a diagram with points a, b, c, d, e, f, angles lab…
\( m\angle BEC=\boldsymbol{31^\circ} \) \( m\angle ABC=\boldsymbol{62^\circ} \)
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the points (g, 5) and (-1, -2) fall on a line with a slope of $-\frac{7…
$g=-3$
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a line with a slope of $-\frac{1}{9}$ passes through the points (5, 0) …
$1$
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ordering question click and drag on elements in order place the followi…
1. Choose a reference point. 2. Identify two specific directions. 3. Determine the distance along each direction.
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5. describe and correct the error. (there is a right triangle with hypo…
The error was misidentifying the hypotenuse (used \( x \) as a leg but treated it as a non - hypotenuse, then incorrectly applied Pythagorean theorem). Correct solution: \( x = 24…
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a line that includes the points (c, 4) and (4, 5) has a slope of \\(\fr…
$c=-5$
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consider a regular hexagon inscribed in circle c with radius r. regular…
\(60\) ### Second Sub - Question: Find the length of segment \(AB\)
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4. describe and correct the error. 5. describe and correct the error. 6…
Error (Q4): Incorrectly wrote $x^2=(7+24)^2$ instead of $x^2=7^2+24^2$. Correct answer: $x=25$. Error (Q5): Treated the hypotenuse as a leg; correct formula: $26^2=x^2+10^2$, so $…
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consider circle o below. the length of arc ba is 8.4 cm and the length …
s: ### Part 1: Measure of angle \( BOA \) The measure of angle \( BOA \) is \( \boldsymbol{60^\circ} \) (since \( 8 \times \frac{\pi}{3} \approx 8.4 \) cm, which matches the arc l…
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4 m∠bca = m∠abc = grade 8 • lesson 7 page 1 of us expires on 4/24/2025.
\( m\angle BCA = 14^\circ\) \( m\angle ABC = 83^\circ\)
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the face of a clock is divided into 12 equal parts. the radius of the c…
- The central angle measure when one hand points at 2 and the other points at 4 is 60°. - With one hand at 5 and the other at 10, the minor arc formed by the hands is about 15.7 i…
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multiple select question select all that apply which describe the posit…
A. 5 m north and 7 m east B. 2 blocks west and 4 blocks south E. 10 ft up and 8 ft to the left
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the points (6, -3) and (5, t) fall on a line with a slope of -8. what i…
$5$
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in circle c, sq = 10 cm. which statements about the circle are correct?…
- Arc PQ is congruent to arc SR. - The measure of arc QR is \( 150^\circ \). - Arc PS measures about 13.1 cm. - Arc QS measures about 15.7 cm.
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consider circle c below, where the central angle is measured in radians…
12
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consider circle o, in which arc xy measures $16\\pi$ cm. the length of …
The circumference of the circle is \(64\pi\) cm. ### Second Sub - Question: Ratio of arc length to circumference
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in circle o, central angle aob measures \\(\\frac{\\pi}{3}\\) radians. …
\( 6\pi \) cm (corresponding to the option "6π cm")
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which point is the solution to the system of equations shown on the gra…
\((2,4)\) (assuming the vertical line is \(x = 2\) and the other line intersects it at \(y = 4\))
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8. find the value of x. then determine if the side lengths form a pytha…
The value of \(x\) is \(4\sqrt{2}\) (or approximately \(5.66\)) and the side lengths do not form a Pythagorean triple.
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consider circle c with radius 5 cm and a central angle measure of 60°. …
\( \frac{1}{6} \) ### Second Question: What is the approximate circumference of the circle?
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circle o has a circumference of 88π cm. what is the length of the radiu…
44
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select the angle(s) with measures that are less than $m\\angle 1$. a) $…
B) \( \angle 6 \), E) \( \angle 3 \)
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use the given information to find the segment lengths or value of the e…
\( \boxed{8} \)
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2. is triangle mno a right triangle? explain. n (37 cm)---o | / | / | /…
Yes, triangle MNO is a right triangle. Because when we check the Pythagorean theorem for the side lengths 12 cm, 35 cm, and 37 cm, we find that $12^{2}+35^{2}=37^{2}$ (since $144 …
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in circle o, angle aob measures $\frac{pi}{4}$ radians. what is the len…
\( 4 \)
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Question was provided via image upload.
1. b. Perpendicular #### 2.
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find the perimeter. simplify your answer. diagram of a square with each…
$4p - 8$
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find the perimeter. simplify your answer. w-2 10w-7 w-2 10w-7 submit
$22w - 18$
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explore radian measure by following these steps. and radius? arc length…
\( r\theta \)
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explore radian measure by following these steps. relationship between t…
\(\boldsymbol{\theta}\)
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find the perimeter. simplify your answer. a square with side length 2v …
8v
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1. what is kl? image of a right triangle jkl with right angle at j, jk …
The length of \( KL \) is \( 41\space cm \).
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explore radian measure by following these steps. 1. move point k to set…
arc length = 2 × radius