Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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how was figure a transformed to become figure a? 1. dilate 2. ? reflect…
Rotate
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given that △abc is isosceles with vertex angle b, and bd bisects ∠abc, …
C. 4, 3, 5, 1, 2, 6
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how was figure a transformed to become figure a\? 1. ? 2. dilate transl…
1. Dilate 2. None (as no second - step transformation is required to answer the question based on the given options)
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given that △abc is isosceles with vertex angle b, and bd bisects ∠abc, …
1. First, start with the given information. We know that $\triangle ABC$ is isosceles with vertex - angle $B$ (Statement 3). This is the starting - point as it gives the overall p…
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given that ef || hj and ef = hj, prove that △egf ≅ △jgh. statement reas…
6, 3, 7, 5, 2, 1, 4
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dilate △abc with a scale factor of 3. enter the new coordinates. a(1,2)…
$A'=(3,6)$ $B'=(9,-3)$ $C'=(-12,-6)$
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given that △abc is isosceles with vertex angle b, and bd bisects ∠abc, …
C. 3, 1, 4, 5, 2, 6
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given that $overline{ad}=overline{cb}$, and $overline{dc}=overline{ba}$…
D. 1, 3, 4, 2
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dilate △abc with a scale factor of 5. enter the new coordinates. a(-1,1…
$A'=(-5,5)$ $B'=(20,0)$ $C'=(5,-15)$
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given that ef || hj and ef≠hj, prove that △egf ~ △jgh. statement reason…
6, 7, 1, 2, 5, 3, 4
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δabc ~ δdef find the value of x. a 8 ft d x ft e 3 ft f b 6 ft c x = ?
$x = 4$
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given that ef || hj and ef = hj, prove that △egf ≅ △jgh. statement reas…
2, 5, 6, 7, 1, 3, 4
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△abc ~ △def find the value of x. a d 15 ft 5 ft e x ft f b 9 ft c x = ?
$3$
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10. solve for the variables a = _____ b = _____ c = _____
\(a = 2.25\), \(b = 4\), \(c = 10\)
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find the area of each parallelogram. encuentra el área de cada paralelo…
# Explicación: ## Paso 1: Identificar base y altura del paralelogramo A Suponiendo que cada celda del gráfico es de 1 unidad, la base del paralelogramo A es de 4 unidades y la alt…
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determine which translations would map figure x onto figure y. press y …
A translation left 6 units and down 7 units.
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which angles are adjacent angles? ∠sro and ∠nor ∠sro and ∠qro ∠pom and …
$\angle{SRO}$ and $\angle{QRO}$
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identify each pair of angles as corresponding, alternate interior, alte…
1) Corresponding 2) Alternate interior 3) Alternate exterior 4) Consecutive interior 5) Vertical 6) Corresponding 7) \(95^{\circ}\) 8) \(99^{\circ}\)
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reflections on the coordinate plane reflections a reflection ______ a f…
1. - a. | PRE - IMAGE | IMAGE | |----|----| | W(2,6) | W'(-2,6) | | X(6,4) | X'(-6,4) | | Y(2,2) | Y'(-2,2) | - b. x - values: Change sign; y - values: Remain the same. - c. (x,y)…
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state if the three side lengths can form a triangle or not. a. 10 m, 3 …
a. Yes b. No c. Yes x = 52°
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what minimum information is sufficient to determine congruency for each…
a) Two adjacent sides of one rectangle are congruent to the corresponding two adjacent sides of the other rectangle. b) B. Two pairs of corresponding sides and one pair of corresp…
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lines ac and bd intersect at e. las rectas ac y bd se intersectan en e.…
# Explicación paso a paso: ## Paso1: Recordar la relación de ángulos adyacentes Los ángulos adyacentes formados por dos rectas que se intersecan suman 180°. El ángulo dado es de 1…
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what type of angle measures 36°? adjacent opposite obtuse acute
D. acute
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what minimum information is sufficient to determine congruency for each…
C. Two pairs of adjacent corresponding sides congruent
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clare created figure a. then she created figure b by translating triang…
# Explicación: ## Paso 1: Recordar la definición de congruencia y traslación Una traslación es una transformación que mueve todas las point de una figura por la misma distancia y …
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a. prove that a quadrilateral whose diagonals are congruent and bisect …
a. See above proof. b. C. Construct two congruent line segments that bisect each other. The endpoints of these line segments will be the vertices of a rectangle. c. C. If the angl…
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how is the square footage of any building area determined? subtract len…
multiply length by width
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a. prove that a quadrilateral whose diagonals are congruent and bisect …
$90$
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a rectangular park had a dirt path across its diagonal that was 100 yar…
$100\cos30^{\circ}+100\sin30^{\circ}\approx137$ yards (the third option)
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what is the value of x to the nearest hundredth? 14 65° x 15.45 33.13 1…
15.45
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17. triangle jkl with vertices j(-6, 4), k(-4, 2), and l(-6, -3): 90° c…
$J'(-1,1)$ $K'(1,3)$ $L'(6,1)$
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a worker lays the floor of a 4 - meter square shed. what is the floors …
A. $16\ m^{2}$
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16. quadrilateral abcd with vertices a(4, 0), b(6, -2), c(8, -7), and d…
$A'(0,-4)$ $B'(-2,-6)$ $C'(-7,-8)$ $D'(-5,0)$
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solve the right triangle shown in the figure. a = 27.8, c = 52.3 a ≈ □°…
$A\approx32.4^{\circ}$ $B\approx57.6^{\circ}$ $b\approx44.30$
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write the standard form of the equation of the circle with the given ce…
A. $x^2+(y + 2)^2=19$
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what are the exact values of a and b? o a = 7/2, b = 7√3 o a = 7/2, b =…
\(a=\frac{7}{2},b = \frac{7\sqrt{3}}{2}\) (the last option)
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14. find jl. jl = ____
$468$
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15. rectangle mnop with vertices m(-7, -2), n(-5, -1), o(-2, -7), and p…
$M'(2,-7)$ $N'(1,-5)$ $O'(7,-2)$ $P'(8,-4)$
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a. identify all pairs of lines which appear to be perpendicular in the …
a. No hay pares de líneas perpendiculares. b. Las líneas \(t\) y \(s\) parecen ser paralelas.
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a. prove that a quadrilateral whose diagonals are congruent and bisect …
A quadrilateral whose diagonals are congruent and bisect each other is a rectangle.
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13. write a rule for each counterclockwise rotation about the origin: 9…
$90^{\circ}:(x,y)\to(-y,x)$ $180^{\circ}:(x,y)\to(-x,-y)$ $270^{\circ}:(x,y)\to(y,-x)$
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find the length of the arc, s, on a circle of radius r intercepted by a…
\(s = 19\pi\) inches \(s\approx59.69\) inches
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the tallest television transmitting tower in the world is in north dako…
2008
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14. triangle xyz with vertices x(4, -1), y(8, -2), and z(1, -8): 180° a…
$X'(-4,1)$ $Y'(-8,2)$ $Z'(-1,8)$
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9. rhombus pqrs with vertices p(-8, 6), q(-4, 8), r(0, 6), and s(-4, 4)…
$P'(-8,-2)$ $Q'(-4,-4)$ $R'(0,-2)$ $S'(-4,0)$
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use the graph to determine the x - and y - intercepts
C. x - intercept - 2, y - intercept 6
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8. triangle ghi with vertices g(4, 1), h(5, -4) and i(2, -5); y = x g(_…
$G'(1,4)$ $H'(-4,5)$ $I'(-5,2)$
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use the graph to determine the x- and y -intercepts.
x - intercept: -2; y - intercept: 4
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what is the circumference of a circle? o the length of a line from the …
the distance around the outside of the circle
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find the distance between the pair of points. (-2, -5) and (-8,3) a. 20…
B. 10
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7. quadrilateral wxyz with vertices w(-1, 1), x(2, -3), y(0, -6), and z…
$W'(-5,1)$ $X'(-8,-3)$ $Y'(-6,-6)$ $Z'(-4,-5)$
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directions: graph and label each figure and its im give the coordinates…
$A'(-3,-2)$ $B'(-1,-7)$ $C'(6,-1)$
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a. prove that a quadrilateral whose diagonals are congruent and bisect …
a. Proved as above. b. Construction steps as above. c. Construction and explanation of non - congruence as above.
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solve the right triangle shown in the figure. a = 31.4, c = 53.9 a ≈ □°…
$A\approx35.4^{\circ}$ $B\approx54.6^{\circ}$ $b\approx43.81$
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let f(x) = 2x - 1, g(x) = x². circle your answers. 1. f( g(-3) ) 2. f(x…
# Explicación: ## Paso1: Encontrar g(-3) Sustituir x = - 3 en g(x)=x². $$g(-3)=(-3)^2 = 9$$ ## Paso2: Encontrar f(g(-3)) Sustituir el valor de g(-3) en f(x). $$f(g(-3))=f(9)$$ Sus…
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let (f(x)=2x - 1,g(x)=x^{2}). circle your answers. 1. (f(g(-3)) 2. (f(x…
# Explicación: ## Paso 1: Calcular g(-3) Sustituimos x = - 3 en g(x)=x². Entonces g(-3)=(-3)² = 9. ## Paso 2: Calcular f(g(-3)) Sustituimos el valor de g(-3) en f(x). Como g(-3) =…
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a. prove that a quadrilateral whose diagonals are congruent and bisect …
a. Proved as above. b. Construction steps as above. c. Construction and reason as above.
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use the unit circle to find the value of tan(7π/4) and periodic propert…
A. $\tan\frac{7\pi}{4}=-1$ A. $\tan\frac{19\pi}{4}=-1$
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a. prove that a quadrilateral whose diagonals are congruent and bisect …
a. See the above - step by - step proof that a quadrilateral with congruent and bisecting diagonals is a rectangle. b. See the above - described construction steps using a compass…
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use the given triangle to evaluate the expression. if necessary, expres…
$0$
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are ∠bad and ∠bcd congruent? explain why or why not. choose the correct…
B. $\angle BAD$ and $\angle BCD$ are congruent because $\triangle ABD\cong\triangle CBD$ by SSS and corresponding parts of congruent triangles are congruent
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matching 2 points match the statements below for the conjectures given.…
# Explicaciones detalladas: Recordando que: - $ eg$ significa negación (no). - $\vee$ significa disyunción (o). - $\wedge$ significa conjunción (y). ## Paso 1: Analizar $p$: Ángu…
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suppose abc is a right triangle with sides a, b, and c and right angle …
The unknown side length \(b\) is \(15\). \(\sin B=\frac{15}{17}\) \(\cos B=\frac{8}{17}\) \(\tan B=\frac{15}{8}\) \(\csc B=\frac{17}{15}\) \(\sec B=\frac{17}{8}\) \(\cot B=\frac{8…
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write this statement as a conditional in if - then form: all triangles …
# Explicación: ## Paso 1: Identificar la estructura condicional Una proposición condicional tiene la forma "si p, entonces q". Aquí, p es la hipótesis y q es la conclusión. ## Pas…
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the angle t is an acute angle and sin t and cos t are given. use identi…
$\tan t=\frac{\sqrt{15}}{15}$ $\csc t = 4$ $\sec t=\frac{4\sqrt{15}}{15}$ $\cot t=\sqrt{15}$
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given circle o with center d and diameter ac in the figure below, find …
m($\angle$1)=30$^{\circ}$ m($\angle$3)=30$^{\circ}$
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find the radian measure of the central angle of a circle of radius 2 ya…
$3$
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use reference angles to find the exact value of the following expressio…
A. $\tan(-\frac{\pi}{4})=-1$
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given circle o with center d and diameter ac in the figure below, find …
\(m(\angle1)=30^{\circ}\) \(m(\angle2)=60^{\circ}\) \(m(\angle3)=30^{\circ}\) \(m(\angle4)=60^{\circ}\) \(m(\angle5)=30^{\circ}\)
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question 6, 12.2.b - 6. given △ with congruent parts as marked, what el…
$\overline{DE}$
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given △abc and △dec with congruent parts as marked, what else is needed…
If \(AC\cong DC\), then there is congruence by ASA. Alternatively, to use AAS, either of the conditions \(BC\cong EC\) or \(AC\cong DC\) is needed.
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will my circle be colored in? 5≥x
Yes
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let θ be an angle in standard position. name the quadrant in which θ li…
C. II
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given △abc and △dec with congruent parts as marked, what else is needed…
If \(AC = DC\), then there is congruence by ASA. Alternatively, to use AAS, either of the conditions \(BC = EC\) or \(AB = DE\) is needed.
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find the reference angle for $\frac{7pi}{12}$. the reference angle is .…
$\frac{5\pi}{12}$
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which quadrilateral is a trapezoid?
The quadrilateral with vertices A, B, C, D is a trapezoid.
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what minimum information is sufficient to determine congruency for each…
a) The lengths of one side of each square must be equal b) The lengths of two perpendicular sides of the rectangles must be equal c) The lengths of two adjacent sides and an inclu…
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what minimum information is sufficient to determine congruency for each…
C. The lengths of one side of each square must be equal
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the diagonals of one kite are congruent to the diagonals of another kit…
D. No, because it is possible for a rhombus and a non - rhombus kite to have diagonals of the same length
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a parallel ruler, shown to the right, can be used to draw parallel line…
When the parallel ruler is open at any setting, the distance \(BC = CB\). It is given that \(AB = DC\) and \(AC = BD\), so \(\triangle ABC\cong\triangle DCB\) by \(SSS\). Hence, \…
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3. which of the following is the contrapositive of the conditional (\if…
\(x=\frac{452}{17},y=\frac{950}{17}\)
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convert the following angle in degrees to radians. 225° 225° = radians …
$\frac{5\pi}{4}$
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a parallel - ruler, shown to the right, can be used to draw parallel li…
When the parallel - ruler is in any setting, the distance \(BC\) is common. It is given that \(AB = DC\) and \(AC = BD\), so \(\triangle ABC\cong\triangle DCB\) by SSS. Hence, \(\…
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determine whether the conditions ∠q≅∠n, ∠p≅∠m, and (overline{pq}congove…
Yes B. AAS
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determine whether the conditions ∠q≅∠n, ∠p≅∠m, and (overline{pq}congove…
Yes
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parallel lines and triangles 1. select all true statements if n || m. a…
1. (No full - solution due to lack of figure details) 2. E. \(m\angle C = 56\) (after calculation as shown above) 3. A. \(m\parallel n\) 4. A. 130 5. B. Acute triangle; \(m\angle …
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#9 click the circle to select the type of each number. select all that …
4: Rational Number, Integer, Whole Number - 5: Rational Number, Integer 0: Rational Number, Integer, Whole Number 3.14: Rational Number - 5.5: Rational Number 5.5: Rational Number…
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1 given: e is the mid - point of df prove: 2de = df statements reasons …
Pour l'exercice 1 : - Statements et Reasons ont été donnés dans l'explication ci - dessus pour prouver $2DE = DF$ Pour l'exercice 2 : - Statements et Reasons ont été donnés dans l…
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for each of the following conditions, is it possible to construct two n…
b. It is not possible, because any two triangles with these conditions are congruent by AAS c. It is possible, because the given conditions determine a unique shape but not size
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9. find the value of x. 10. solve for the variables
$x = 8$ $a = 3$ $b = 6$ $c=\frac{88}{13}$
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for each of the following conditions, is it possible to construct two n…
a. It is not possible, because any two triangles with these conditions are congruent by ASA b. It is not possible, because any two triangles with these conditions are congruent by…
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write the converse, inverse, and contrapositive of the true conditional…
Converse: If two angles are acute, then the angles are complementary. False. Counterexample: Two acute angles with measures 30° and 40° (sum is 70°≠90°). Inverse: If two angles ar…
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for each of the following conditions, is it possible to construct two n…
C. It is not possible, because any two triangles with these conditions are congruent by ASA.
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find a positive angle less than 360° that is coterminal with the given …
255
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7. geometry the length of a rectangle is 2 feet more than its width. fi…
Length = 9 feet, Width = 7 feet
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the endpoints of the directed line - segment nv are n(-14,9) and v(10,-…
# Explicación: ## Paso 1: Usar la fórmula de la seccionación de segmento La fórmula para encontrar las coordenadas de un punto que divide un segmento de línea con extremos $(x_1,y…
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1. to remember your converses, inverses, and contrapositives, learn thi…
a. $m\angle1 = 59^{\circ}$ b. $m\angle2 = 75^{\circ}$ c. $m\angle3 = 121^{\circ}$ d. $m\angle4 = 59^{\circ}$ e. $m\angle5 = 59^{\circ}$ f. $m\angle7 = 121^{\circ}$ g. $m\angle8 = …
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use reference angles to find the exact value of the following expressio…
A. $\sin\frac{4\pi}{3}=-\frac{\sqrt{3}}{2}$
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6. find the value of x. 7. solve for y. 8. find the value of x. 9. solv…
\(x=\frac{16}{3}\), \(y=\frac{250}{7}\)
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part b. a cylinder has a volume of 100 cm³ and a radius r of 5cm. what …
$\frac{4}{\pi}\ cm$