Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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15. the triangle below is graphed on the coordinate plane. two of its v…
12
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what is the slope of a line that is parallel to the line $y = \\frac{3}…
$\frac{3}{4}$ (corresponding to the option with $\frac{3}{4}$)
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what is the equation of the line that is perpendicular to the line $y =…
\( y =-\frac{5}{3}x + 20 \) (the fourth option: \( y =-\frac{5}{3}x + 20 \))
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what is the slope of a line that is perpendicular to the line $y = 1$? …
undefined
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what is the equation of the line that is parallel to the line $y = -\fr…
\( y = -\frac{1}{3}x + 7 \)
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2. \\( y \\geq 0 \\)\\( y \\leq x - 5 \\)
# Explicación: ## Paso 1: Graficar $y\geq0$ Se traza la recta $y=0$ (el eje x) y se sombrea la región **arriba** de esta recta (incluyendo la recta misma, ya que es $\geq$). ## Pa…
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classify this triangle by its sides. equilateral scalene isosceles but …
isosceles but not equilateral
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find area and perimeter of the equilateral triangle. round to nearest 1…
Area: \(\approx 6.93\), Perimeter: \(12\) (assuming the triangle is equilateral with side length \(4\), correcting the diagram's possible mislabeling of the base) Wait, but if we …
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somewhere there is a comrade... who will not read this, or write. and h…
### Question 4: The poem has a somber, urgent, and indignant tone. The speaker's attitude is compassionate, guilt-stricken, and defiant—they bear witness to the violent oppression…
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identify the translation from the pre - image, triangle jkl, to the ima…
The pre - image moved horizontally: left The pre - image moved horizontally: 3 units The pre - image moved vertically: up The pre - image moved vertically: 2 units (Note: If the d…
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1. is figure abcd a reflection of figure abcd over the x - axis? explai…
1. No. A reflection over the x-axis maps $(x,y)$ to $(x,-y)$, but Figure A'B'C'D' does not follow this rule (it is reflected over a different line, not the x-axis). 2. B. Only the…
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that somewhere there was an arrest. 10 somewhere there was a small harv…
### Question 2: The speaker emphasizes that tragic, violent events are widespread but unobserved, hidden from public view. The repetition of "somewhere" shapes the poem's meaning …
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#1 sketch and identify the shape of the cross section resulting from th…
### Parte A: # Explicación: ## Paso 1: Analizar la pirámide cuadrada recta Una pirámide cuadrada recta tiene una base cuadrada y caras triangulares. Un plano horizontal que corta …
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1. read as you read lines 1–12, begin to collect and cite text evidence…
- Circled words: "Somewhere" (line 1), "Somewhere" (line 5), "Somewhere" (line 8) - Underlined personification: "the shawled sea's weeping" (lines 5-6) - Tone analysis: The person…
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7. technology required. find the perimeter of the figure. ction to a ra…
\(P\approx8 + 10 + 11.64 + 10.64 = 40.28\)
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using the key at the right, type the equation and the solution for each…
Equation: $x + 4=11$; Solution: $x = 7$ ### Part B
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1. how do the points of a figure move in a translation? a same distance…
1. B. Same distance and same direction 2. Yes. Each vertex of ABCD is moved 4 units left and 2 units up to form A'B'C'D', so all points move the same distance and direction, which…
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19. pentagons if ( abcde sim pqrst ), find the scale factor of ( abcde …
Scale factor: $\frac{7}{15}$ Perimeter of $ABCDE$: $75$ Perimeter of $PQRST$: $35$
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for #23-24, use the figure below. 23. identify the similar triangles in…
23. $\triangle ABD \sim \triangle ECD$ 24. $x = \frac{15}{2}$ or $7.5$
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pam was told to draw a triangle with side lengths 3 centimeters, 5 cent…
$3 + 5 < 9$
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square b is a scaled copy of square a. square a has side length 6, squa…
$\frac{1}{2}$
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on each coordinate plane, the parent function f(x) = |x| is represented…
The first graph (the one with the solid line vertex at (0, - 4))
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the ratio of the radii of two circles is 5:2. what is the ratio of thei…
25:4
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b. draw another angle that measures 45 degrees. it should have the same…
There are 3 angles. Two of them measure \(45^\circ\) and one measures \(90^\circ\) (assuming the two \(45^\circ\) angles are adjacent and form a right angle when combined).
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unit 5 lesson 2 practice problems 1. select all figures for which there…
1. C. rectangular prism, D. cube, E. cone, F. cylinder, G. sphere 2. a. Sketch: A curved, elongated oval (parabola/ellipse segment) that tapers toward the base of the cone, not re…
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complete the sentence. if a point lies on the y-axis, then its ______ m…
x - coordinate
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complete the sentence. on the coordinate plane, the number line that ru…
x - axis
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complete the sentence. when graphing a point on the coordinate plane, t…
how far up or down to travel from the origin
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complete the sentence. in an ordered pair, the ______ number is called …
A. first
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complete the sentence. on the coordinate plane, the vertical number lin…
D. y - axis
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read the directions below for plotting a certain point. start at the or…
\((3, 8)\)
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complete the sentence. in an ordered pair, the ______ number is called …
first
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complete the sentence. the x - coordinate tells you the ______ position…
horizontal
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complete the sentence. to graph the point (1, 9) on the coordinate plan…
D. right... up
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complete the sentence. the y - axis is the ______ number line on a coor…
vertical
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complete the sentence. in an ordered pair, the ______ number is called …
second
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complete the sentence. on the coordinate plane, ______ describes the lo…
an ordered pair
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practice! 1. if z is the circumcenter of $\\triangle tuv$, find each mi…
To solve these problems, we use the property of the circumcenter: the circumcenter of a triangle is the intersection of the perpendicular bisectors of the triangle's sides, so it …
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graph the points (4, 8) and (6, 6) on the coordinate plane. click to gr…
The points \((4, 8)\) (4 units right on x - axis, 8 units up on y - axis) and \((6, 6)\) (6 units right on x - axis, 6 units up on y - axis) are graphed on the coordinate plane.
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grade 7 unit 4 georgia’s k-12 mathematics standards 2. use a protractor…
(The answer will be the measured angle value, e.g., if measured as \( 25^\circ \), then the answer is \( 25^\circ \) (actual value depends on protractor measurement)) ### Question…
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fill in the sentence below with the description that most specifically …
The quadrilateral is most specifically a \(\boldsymbol{square}\), because it has four equal - length sides (\(u\)) and four right angles (indicated by the angle marks).
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5) 6) 7) 8)
To solve for the area of a trapezoid, we use the formula for the area of a trapezoid: \( A = \frac{1}{2}(b_1 + b_2)h \), where \( b_1 \) and \( b_2 \) are the lengths of the two p…
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2. find the fraction piece that would cover half the circle. trace the …
The measure of \( 90^\circ \) is \( \frac{1}{4} \) of the circle. ### Question 5:
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1) 2) 3) 4)
(1): \( 6.96 \) square inches ### 2) Trapezoid with \( b_1 = 0.6 \) in, \( b_2 = 2 \) in, \( h = 2 \) in ## Step 1: Identify the formula \( A = \frac{1}{2}(b_1 + b_2)h \) ## Step …
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page 6 5. cd = 24 cm find the circumference of ⊙c. 6. ( overarc{bd} ) =…
\( 150.8 \, \text{cm} \) (or \( 48\pi \, \text{cm} \approx 150.8 \, \text{cm} \)) ### Problem 6: Find \( \theta \) given \( \widehat{BD} = 69.115 \, \text{cm} \)
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△cba ~ △clk find the length of \\(\\overline{al}\\): answer
112
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find the length of each arc (in centimeters!). show work!! 10. \\(\\ove…
To solve the problem of finding the length of each arc, we need to know the radius of the circle and the measure of the central angle corresponding to each arc. The formula for th…
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in the rectangle below, fh = 4x + 2, eg = 5x - 6, and m∠fig = 56°. find…
\( EI = 17 \), \( m\angle IEH = 62^\circ \)
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in the figure above, the two lines appearing parallel are parallel. fin…
63
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consider parallelogram jklm below. use the information given in the fig…
\( x = 3 \), \( m\angle M = 83^\circ \), \( m\angle MJL = 35^\circ \)
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2.d: analogies directions: circle the analogy that best matches the bol…
1. b) cruel : mean 2. d) chaos : peace 3. c) chapter : book 4. a) towel : dry 5. a) friendship : trust 6. b) careless : dedication
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consider parallelogram abcd below. use the information given in the fig…
\( x = 1 \), \( m\angle A = 114^\circ \), \( m\angle ADB = 32^\circ \) So filling in the boxes: \( x = \boxed{1} \) \( m\angle A = \boxed{114} \) \( m\angle ADB = \boxed{32} \)
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what is the length of \\(\\overline{gr}\\)? (the image shows a triangle…
\( 35 \)? No, wait, no, the calculation says 7. Wait, no, I think I messed up the sides. Wait, maybe the triangle is \( \triangle GFH \) with \( R \) on \( GH \) and \( S \) on \(…
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select the correct answer from each drop - down menu. which are the bes…
1. A statement that is assumed to be true without proof is an) **axiom** 2. A statement that has been shown to be true by rigorous application of logic is an) **theorem** 3. A(n) …
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drag and drop each equation to the model that it represents. equations:…
### First, analyze the two models: #### Top Model (with 15 and 36 in a vertical split? Wait, looking at the diagram: The top model has a rectangle with 36 on the right, and 15 on …
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find the length of side ( x ) to the nearest tenth.
$8.0$
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find the length of side ( x ) to the nearest tenth. (image of a right t…
$x = 1.7$
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find the length of side ( x ) to the nearest tenth.
1.5
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find the length of side ( x ) to the nearest tenth. answer attempt 1 ou…
$x \approx 1.7$
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graph $x = -0.5$.
The graph of \( x = - 0.5 \) is a vertical line passing through the point \( (-0.5,y) \) for all real - valued \( y \). On the given grid, it is a vertical line halfway between \(…
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given right triangle abc with altitude \\(\\overline{bd}\\) drawn to hy…
90
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given right triangle abc with altitude \\(\\overline{bd}\\) drawn to hy…
$9$
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find the length of the third side. if necessary, round to the nearest t…
19.5
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translate up (the chart is a coordinate grid with a triangle and some p…
$L(-3, 2)$, $L'(-3, 6)$ $J(2, -3)$, $J'(2, 1)$ $K(-5, -4)$, $K'(-5, 0)$
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find the length of the third side. if necessary, write in simplest radi…
10
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consider a triangle abc like the one below. suppose that a = 76°, c = 3…
\(B = 65^\circ\), \(a\approx83.3\), \(b\approx77.8\)
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what reflection of the parallelogram abcd results in the image abcd? is…
1. The reflection that maps ABCD to A'B'C'D' is across the vertical line $x=-1$. 2. Yes, the image is unique using only one reflection. 3. No, the image is not unique using one re…
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find the length of the third side. if necessary, write in simplest radi…
# Explicación: ## Paso 1: Aplicar el teorema de Pitágoras Sean los catetos $a=2\sqrt{14}$ y $b=9$, y la hipotenusa $c$. La fórmula es $c=\sqrt{a^2 + b^2}$. ## Paso 2: Calcular $a^…
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name: reflect across the x axis rotate 90° counter clockwise translate …
1. Reflected triangle points: \(A'(3, -2)\), \(B'(3, 6)\), \(C'(1, 6)\) 2. Rotated triangle points: \(X'(-3, -2)\), \(Y'(0, -6)\), \(Z'(0, 0)\) 3. Translated triangle points: \(J'…
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find the length of the third side. if necessary, write in simplest radi…
$2\sqrt{21}$
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true/false decide if each statement is true or false, and write \true\ …
true 2.
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click and drag to draw a ray from the yellow dot. to redraw, click and …
\(\frac{1}{2}(m\angle EFG)=m\angle EFH\) (the option with this statement)
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you are shown $\\angle cde$ below whose measure is $114^\\circ$. draw a…
\( \boldsymbol{\text{m}\angle CDE = 2(\text{m}\angle EDF)} \) (the option with this statement)
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you are shown $\\angle ghi$ below whose measure is $64^\\circ$. draw an…
A. \( 2(\text{m}\angle GHJ) = \text{m}\angle GHI \)
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find the cosine of ∠c. simplify your answer and write it as a proper fr…
\( \frac{48}{73} \)
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question triangle bcd is dilated by a scale factor of \\(\\frac{1}{3}\\…
27
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estimate the solution of the system of equations.
\((2,-5)\)
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triangle bcd is dilated by a scale factor of 2 to form triangle bcd. wh…
36
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find the sine of ∠d. simplify your answer and write it as a proper frac…
$\frac{45}{53}$
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quadrilateral ijkl is dilated by a scale factor of \\(\\frac{2}{3}\\) t…
24
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parallelogram qrst is dilated by a scale factor of 2 to form parallelog…
9
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quadrilateral ghij is dilated by a scale factor of \\(\\frac{3}{4}\\) t…
18
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find the tangent of $\\angle d$. $\\sqrt{35}$ $5\\sqrt{2}$ write your a…
\(\frac{\sqrt{21}}{3}\)
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3. find the measure of ( e^circ ). options: ( 159^circ ), ( 60^circ ), …
21° (Option: 21°)
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1. what is the perimeter of kite defg? 9 cm, 65°, 15 cm (description of…
48 cm
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what type of symmetry does each figure have? check all of the boxes tha…
1. Oval: line symmetry rotational symmetry 2. L-shape: no symmetry 3. Smiley face: line symmetry
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find the cosine of ∠x. write your answer in simplified, rationalized fo…
\(\frac{\sqrt{1349}}{71}\)
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calculate the surface area and volume of the rectangular prism. calcula…
s: - Rectangular Prism: Surface Area: \(342\) in² Volume: \(324\) in³ - Cube: Surface Area: \(61.44\) m² Volume: \(32.768\) m³ - Trailer: Volume (Space Inside): \(10710\) ft³
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what is the measure of ∠wzy? w x (23x - 4)° (8x - 1)° z 27° y © gina wi…
$76.5^\circ$
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a circular tablecloth has a diameter of 70 inches. max wants to add a d…
219.8 inches
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the circumference of a circle is $20\\frac{4}{35}$ cm. what is the appr…
$6.4$ cm
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a pizza has a diameter of 16 inches. what is the best approximation for…
50.2 inches (Option C)
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what is the exact circumference of a circle with a radius of 17 mm? 8.5…
C. $34\pi$ mm
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what is the exact circumference of the circle? 2π cm 4π cm 8π cm 16π cm
8π cm
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perimeter measuring 17 feet, 28 feet, and if cayla is laying a brick bo…
The length of the rod is \( 25\frac{7}{8} \) inches (or \( \frac{207}{8} \) inches).
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14. the area of a triangle is 52 square centimeters. if the base of the…
The height of the triangle is 8 centimeters. ### Question 16
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13. a rectangle has an area of 34.2 square meters. if the width of the …
The length of the rectangle is \( 7.6 \) (units as per the inconsistent units, but mathematically the value is \( 7.6 \)). ### Problem 15
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the segment below is dilated by a scale factor of 4 to form \\(\\overli…
10
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$\\overline{ij}$ is dilated by a scale factor of $\\frac{3}{4}$ to form…
30
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a figure containing $\\angle vwx$ is dilated by a scale factor of $\\fr…
\( 120^\circ \)