Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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1. use the given information about $\\triangle abc$ with right angle $b…
a. \( c \approx 23.18, a \approx 6.21 \)
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4. an angle of a parallelogram measures 30°. list the measures of the o…
The other angles are $30^\circ$, $150^\circ$, and $150^\circ$.
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graph y = 3
A horizontal straight line passing through the point $(0, 3)$ (parallel to the x-axis, where every point on the line has a y-coordinate of 3)
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4. find the circumference. 22 cm
$22\pi$ cm (or approximately 69.14 cm, or $\frac{484}{7}$ cm)
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question graph the line that passes through the points (8, -4) and (-8,…
The equation of the line is \( y =-\frac{3}{4}x + 2 \). To graph the line, plot the points \((8,-4)\) and \((-8,8)\) and draw a straight line through them.
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graph the image of rectangle pqrs after a reflection over the line y = …
The image of rectangle \( PQRS \) after reflection over \( y = 1 \) has vertices \( P'(-9, 9) \), \( Q'(-8, 9) \), \( R'(-8, 3) \), \( S'(-9, 3) \). (To graph, plot these points a…
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find the volume of this triangular prism. be sure to include the correc…
\( 270 \text{ in}^3 \)
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5. the bakery makes square 2-layer cakes for $45. each layer measures 1…
216 cubic inches
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directions: find the value of each variable. 5. 4. 7. 8. 9. 10. 11. if …
5. $x=4$ 6. $x=\frac{205}{29} \approx 7.07$ 7. $x=16$ 8. $x=20.5$ 9. $x=27$ 10. $x=\frac{123}{11} \approx 11.18$ 11. $m\angle 1=43^\circ$, $m\angle 2=17^\circ$, $m\angle 3=120^\ci…
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3. e f g triangle, angle at e is 25°, angle at g is 25°, side gf is 18 …
For $\triangle EFG$: $EF = 18$ m $m\angle F = 134^\circ$ For $\triangle PQR$: $m\angle P = 60^\circ$ $m\angle Q = 60^\circ$ $m\angle R = 60^\circ$
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graph the image of kite pqrs after a reflection over the y - axis.
The image of kite \( PQRS \) after reflection over the \( y \)-axis has vertices at \( P'(6, -1) \), \( Q'(4, 0) \), \( R'(6, 5) \), and \( S'(8, 0) \). (Graphing these points and…
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question find the length of side ( x ) to the nearest tenth. answer att…
\(5.8\)
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find the length of side ( x ) to the nearest tenth.
\(1.7\)
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question find the length of side ( x ) to the nearest tenth. answer att…
\(10.4\)
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regularity find each measure. 20. ( mangle cad ) 21. ( mangle acd ) 22.…
\( 44^\circ \) ### Problem 21: \( m\angle ACD \)
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the triangle below is equilateral. find the length of side ( x ) to the…
\(1.0\)
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10. triangle lmn is on a coordinate plane with its vertices located at …
24
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find the area of a circle with a radius of 4 cm.
The area of the circle is \( 16\pi\space\text{cm}^2 \) (or approximately \( 50.24\space\text{cm}^2 \)).
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george has a conical scoop with height 12 cm and radius 1.5 cm and a cy…
C) 96
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ellie is painting the ceiling of a circular gazebo. the diameter of the…
A) 143 square meters
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a segmental paver is installing a circular patio that has a radius of 1…
B) 75.4 feet
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(a) write an expression to find the volume of the prism using its lengt…
\( 7 \times 5 \times 9 = 315 \) cubic units ### Part (b)
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find the area of a circle with a diameter of 2 cm.
The area of the circle is \( \pi \) square centimeters (or approximately \( 3.14 \) square centimeters).
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do you know how? 5. write an equivalent expression for (7^{12}div7^{4})…
$7^{8}$ ### Question 6
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pythagorean theorem - missing sides scavenger hunt directions: start in…
$A ightarrow F ightarrow C ightarrow H ightarrow E ightarrow B ightarrow D ightarrow G ightarrow A$
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9) $-18n > -144$
The solution to the inequality \(-18n > -144\) is \(n < 8\). On the number line, this would be represented by an open circle at 8 (since \(n\) is not equal to 8) and an arrow poin…
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9. if the area of square 1 is 289 units² and the area of square 3 is 64…
$120$ units$^2$ --- ### Problem 10
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2. which of the following statements is not a true statement? a. the le…
D. The hypotenuse is always the shortest side length.
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8) $-2a \\leq 8$
The solution to the inequality \(-2a \leq 8\) is \(a \geq -4\), which would be represented on the number line by a closed circle at \(-4\) and an arrow pointing to the right (towa…
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find ( mangle e ) in parallelogram ( efgh ). ( mangle e = square^circ )
$\frac{299}{3}$ or approximately $99.67$
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find rs in rectangle qrst. rs = \\square
12
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select all the statements that are true for $\\triangle abc$. a $\\over…
A. $\overline{AH}$ is an altitude
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in chet’s example of debt repayment, he forgot a medical debt of $3,500…
His personal loan (the option with the yellow - filled circle, labeled "His personal loan")
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use the coordinates j(7, 8), k(1, 2) and l(5, 2) for △jkl. the orthocen…
\( \boxed{6.3} \) (corresponding to option D)
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what is the relationship between a scalene triangle and the location of…
A. The centroid will always be inside the scalene triangle, since the centroid is always inside any type of triangle.
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a formal garden at the biltmore estate has a large, circular fish pool …
C) 452.2 ft
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are $\\triangle wxy$ and $\\triangle qrs$ congruent? yes no
no
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a segmental paver is installing a circular patio that has a radius of 1…
B) 75.4 feet
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estimating perimeter and area estimate the perimeter and the area of th…
To solve these problems, we'll use the grid method for estimating perimeter (by counting the length of the outer edges) and area (by counting the number of full and partial grid s…
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find the area of a circle with a diameter of 2 cm.
The area of the circle is \( \pi \) square centimeters (or approximately \( 3.14 \) square centimeters).
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find the length of the diagonal of a rhombus (the rhombus is shown in t…
$8\sqrt{74}$
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use the figure below to answer the question that follows. p is the cent…
\( 110^\circ \) (assuming the options include this, but based on the calculation, the measure of angle \( MPN \) is \( 110^\circ \))
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lección 9: pongamos en práctica el área de los círculos hallemos áreas …
• 502,656 m²
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find the area of a circle with a radius of 3 cm.
The area of the circle is \( 9\pi\space\text{cm}^2 \) (or approximately \( 28.26\space\text{cm}^2 \)).
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5) 10 in 7 in 11 in 9 in area =
# Explanation: ## Step1: Divide the shape into two rectangles We can split the T - shaped figure into a vertical rectangle and a horizontal rectangle. The vertical rectangle has a…
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10. find the surface area of the following figure. round to the nearest…
$393.4\ \text{m}^2$
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4) 12 ft 11 ft 8 ft 15 ft area =
\( 92 \, \text{square feet} \)
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sheet 1 7 in 4 in 9 in 5 in area = ____________
\(63\) square inches
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the diagram shows $\\triangle abc$ and $\\overrightarrow{bd}$. what is …
\(133^{\circ}\)
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given ( m parallel n ), find the value of ( x ). answer attempt 1 out o…
\( x = 10 \)
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graph $y = 2x + 1$ and $y = x + 1$. how many times do the two graphs in…
1
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given ( m parallel n ), find the value of ( x ).
\( x = 17 \)
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after graphing $y = \\frac{2}{3}x - 2$ and $y = \\frac{2}{3}x + 3$, how…
0
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given $m\\parallel n$, find the value of x. (9x+4)$^\\circ$ (2x-11)$^\\…
\( x = 17 \)
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in circle r with m∠qrs = 150°, find the measure of minor arc qs. answer…
\(150\)
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question the circumference of a circle is 10π ft. what is the area, in …
\( 25\pi \)
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find the area of a circle with a diameter of 16 cm.
The area of the circle is \( 64\pi \text{ cm}^2 \) (or approximately \( 200.96 \text{ cm}^2 \))
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right triangle similarity theorem 1. the corresponding sides of the sim…
- Altitude \( a \): \( 4 \) - Shorter Leg \( s \): \( 2\sqrt{5} \) (or \( \approx 4.47 \)) - Longer Leg \( b \): \( 4\sqrt{5} \) (or \( \approx 8.94 \))
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8. reinforce for each shape described, write an equation to represent t…
a. Length = 17 cm b. Width = 4.5 in (or $\frac{9}{2}$ in) c. Width = $\frac{4}{3}$ m d. Height = 4 ft
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on a blueprint, a wall that is 45 feet long is 6 inches long. how long …
B) 4 inches
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find the volume of the rectangular prism. try again your answer is inco…
343 yd³
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find the area of each parallelogram. 1) area = 2) area = 3) area = 4) a…
1) $28.35$ square inches 2) $37.44$ square feet 3) $92.96$ square yards 4) $39.9$ square feet 5) $34$ square yards 6) $18.7$ square inches 7) $30.3$ square yards 8) $32.34$ square…
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15. decide whether enough information is given to prove that $\\triangl…
1. For question 15: Yes, $\triangle LMP \cong \triangle NPM$ by SSS. 2. For question 16: Yes, $\triangle WXZ \cong \triangle YZX$ by HL.
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find the area. 9 cm
The area of the circle is \( 81\pi \, \text{cm}^2 \) (or approximately \( 254.34 \, \text{cm}^2 \)).
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can you determine the answers and type the correct code? please remembe…
EHD I
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puzzle #3 1 can you find the trapezoid’s perimeter? $9x + 4$, $7x + 8$,…
FCAH
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4. el carrusel del national mall tiene 4 anillos de caballos. kiran est…
# Explicación: --- ### Problema 4 ## a. ## Paso 1: Calcular radio de Mai $r_{Mai} = 9 + 8 = 17$ pies ## Paso 2: Calcular circunferencia de Kiran $C_{Kiran} = 2\pi r_{Kiran} = 2\pi…
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14. find the values of x and y in the diagram. chapter 5 chapter review…
$x = 11.25$, $y = 5$
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mackenzi knows that the angle below equals 90 degrees. one angle is 62 …
The measure of angle \( j \) is \( 28^\circ \).
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write the coordinates of the vertices after a translation 6 units left …
$R'(-7, -3)$ $S'(-7, 3)$ $T'(-2, -4)$
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write the coordinates of the vertices after a translation 4 units right…
$S'(-4, -8)$ $T'(-4, -7)$ $U'(-1, -7)$ $V'(-1, -8)$
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write the coordinates of the vertices after a translation 7 units down.…
$Q'(-4, -4)$ $R'(-4, -3)$ $S'(6, -4)$
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14 multiple choice 1 point are the following triangles similar, if so, …
Yes, AA (The correct option is the one with "Yes, AA")
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if each point in the diagram can act as an endpoint, how many distinct …
D. six
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select the correct answer. which best defines a ray? a. two lines that …
B. part of a line that has an endpoint and extends infinitely in one direction
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write the coordinates of the vertices after a translation 8 units left …
$P'(-9, -4)$ $Q'(-1, -4)$ $R'(-7, -7)$
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if \\overleftrightarrow{ab} is parallel to \\overleftrightarrow{cd}, wh…
A. $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ do not intersect.
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multiple choice 1 point are the following triangles similar, if so, sta…
No, the triangles are not similar.
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select the correct answer from each drop - down menu. according to eucl…
First drop-down: 3 Second drop-down: do not lie
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8. given the figure shown, complete the flowchart proof to prove that $…
The flowchart is completed by using the triangle angle - sum theorem, substituting known angles, solving for the unknown angle, identifying congruent corresponding angles, and app…
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the triangle below is isosceles. find the length of side ( x ) in simpl…
$10\sqrt{2}$
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select the correct answer. katherine johnson is best known for her work…
B. the geometry of space flight
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challenge #4 plot four lines. each line should pass through the point o…
\(y=-2-\frac{5}{4}x\) (or other valid equations based on different points, e.g., if we take \((-4,-5)\), \(y=-2+\frac{3}{4}x\); if we take \((2,5)\), \(y=-2+\frac{7}{2}x\); if we …
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find the length of side ( x ) in simplest radical form with a rational …
$2\sqrt{3}$
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4. what is the slope of ( overline{tv} ) if the point ( t ) is ( (2, -3…
4. C. $\frac{1}{3}$ 5. C. $\frac{2}{5}$
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given ( m parallel n ), find the value of ( x ). answer attempt 1 out o…
\( x = 18 \)
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josiah leans a 16-foot ladder against a wall so that it forms an angle …
14.8 feet
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find the length of side ( x ) in simplest radical form with a rational …
$\frac{\sqrt{3}}{3}$
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drag \\(\\sqrt{82}\\) based on your estimate above: to one decimal plac…
9.0 and 9.1
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15. a model of a skyscraper is 1.6 inches long, 2.8 inches wide, and 11…
The actual dimensions of the skyscraper are 50 feet long, 87.5 feet wide, and 350 feet high.
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3. the graph shown is that of ( y = g(x) ). which of the following is t…
B. $g(x)=\frac{3}{4}x - 3$
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given ( m parallel n ), find the value of ( x ). answer attempt 1 out o…
\( x = 98 \)
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are the polygons below similar? (there are two rectangles, the left one…
no
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in δvwx, v = 52 inches, w = 62 inches and x = 75 inches. find the measu…
42.9 degrees
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are the polygons below similar? options: yes, no
no
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in δtuv, t = 150 inches, u = 580 inches and ∠v=105°. find the length of…
627 inches
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14. a scale model of a house is 1 ft long. the actual house is 50 ft lo…
14. $5$ feet 15. Length: $50$ feet, Width: $87.5$ feet, Height: $350$ feet
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yes no complete the similarity statement. efgh ~ find the ratio of a si…
### Part 1: \(EFGH \sim UVWT\) (assuming the correct correspondence, but based on the ratio, the similarity statement is \(EFGH \sim WVTU\) or \(UVWT\); however, the most likely i…
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shannon packages dress shirts to ship to various stores. she chooses th…
D) 8,000 cubic inches
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in $\\triangle nop$, $o = 48$ inches, $n = 47$ inches and $\\angle n = …
# Explanation: ## Step1: Apply the Law of Sines The Law of Sines states that $\frac{\sin N}{n}=\frac{\sin O}{o}$. We know $N = 72^\circ$, $n = 47$ inches, and $o = 48$ inches. Plu…