Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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what is the slope of this line? the line passes through points (-2, 6) …
\(-2\)
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33. analyze and persevere a dog running an agility course has difficult…
The most difficult corner to turn is corner \( B \).
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find the volume of the object by counting the cubic units. assume that …
100
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a farmer is building a fence around the field he just bought. the field…
180
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3. consider the diagram. a. describe the relationship between $\\angle …
$\angle CAB$ and $\angle DAB$ are complementary angles (their sum is $90^\circ$).
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are the triangles below acute, obtuse, or right? triangle a triangle b …
Triangle A: Acute Triangle B: Right Triangle C: Obtuse Triangle D: Acute
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are the triangles below acute, obtuse, or right? triangle a: angles 30°…
- Triangle A: Obtuse - Triangle B: Right - Triangle C: Acute - Triangle D: Acute
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what is the slope of this line? the coordinate grid has a blue vertical…
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for each number below, is it even or odd? 77 131 475 99 38 odd even
- 77: Odd (select the circle under Odd) - 131: Odd (select the circle under Odd) - 475: Odd (select the circle under Odd) - 99: Odd (select the circle under Odd) - 38: Even (selec…
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32. use patterns and structure a stage manager must use tape to outline…
\( SR > RQ > SQ \)
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for problems 7 and 8, write equations by using angle relationships give…
(for Problem 8): \(x = 0\), \(y = 6\) (For Problem 7, if we assume \(11y + 8 = 118\) (supplementary to \(62^\circ\)), then \(y = 10\), and \(5x + 7 = 62\) (corresponding angles), …
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(c) choose the equation that is true. area of sector = \\frac{360^{\\ci…
For part (d), the correct option is "Area of sector \( = \frac{m\overarc{AB}}{360^\circ} \cdot \pi r^2 \)" (the second option in the set of options for part (d)).
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are the triangles below acute, obtuse, or right? triangle a: angles 30°…
Triangle C: Acute Triangle D: Obtuse (For Triangle C, the correct option is "Acute"; for Triangle D, the correct option is "Obtuse")
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question 7 identify which equation does not correspond to the following…
\( 37x - 23y = 99 \) (the first option)
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are the triangles below acute, obtuse, or right? triangle a: angles 50°…
- Triangle A: Acute (all angles < 90°: 50°, 75°, 55°). - Triangle B: Right (has a 90° angle). - Triangle C: Obtuse (has a 110° angle > 90°). - Triangle D: Acute (all angles < 90°:…
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identify which equation corresponds to the following coordinates: (13, …
None of the answers
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2. in the diagram, ∠cab is a straight angle, a. describe the relationsh…
\( \angle CAD \) and \( \angle DAB \) are supplementary (form a linear pair, sum to \( 180^\circ \)). ### Part b
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complete the statements below. give your answers as exact values, not d…
(a) \(\frac{1}{8}\) (b) \(45\)
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what is the slope of this line? (2, 4) (6, 6) options: \\(\frac{1}{2}\\…
\(\frac{1}{2}\)
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6) triangle with angles 88°, 46°, and an exterior angle 3s + 1°. find s…
For problem 6 (assuming a typo and using exterior angle theorem): \( s = 45 \) (if we correct \( 3s + 1 \) to \( 3s-1 \), otherwise there is a mistake). For problem 7: \( e = 130 …
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question 2 2 points given the coordinates of (24, -22) and (-9, -21), w…
\( y =-\frac{1}{33}x-\frac{234}{11} \) (corresponding to the first option: \( y =-\frac{1}{33}x-\frac{234}{11} \))
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question 1 2 points given the coordinates of (24, -22) and (-9, -21), w…
\( x + 33y=-702 \) (the last option: \( x + 33y=-702 \))
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find ( mangle r ). triangle with right angle at t, sides rt = 5.7, st =…
\( 50.5 \)
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what is the slope of this line? (-3, 3) (-3, 1) -8 -7 -6 -5 -4 -3 -2 -1…
undefined
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triangle angle sum solve for the given variable. 1) b = ____ 2) r = ___…
\( b = 9 \) ### Problem 2: Solve for \( r \)
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e figure below shows a circular courtyard. its diameter is 96 m. (a) us…
(a) Circumference: \( 301.44 \, \text{meters} \) Area: \( 7234.56 \, \text{square meters} \) (b) Area (c) Circumference
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question: 9 consider the function below. graph of a parabola opening up…
B. \(y\geq - 4\)
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4. $y = -\frac{1}{2}x + 3$ $y = -\frac{5}{2}x - 1$
The solution is \( x = -2 \), \( y = 4 \) (or the point \((-2, 4)\)).
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find ( mangle f ). write your answer as an integer or as a decimal roun…
\( 44.4 \)
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making comparisons comparative adjectives are used to compare two thing…
shorter, C ### Question 2
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the figure below shows a circular lawn. its radius is 38 ft. (a) use th…
# Explanation: ## Step1: Calcular la circunferencia La fórmula para la circunferencia de un círculo es \( C = 2\pi r \). Dado que \( r = 38 \) ft y \( \pi \approx 3.14 \), entonce…
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find ( mangle f ). triangle def with right angle at e. de = 3.8, ef = 7…
\( 27.8 \)
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1. write the equation of the line that goes through the point (-2,8) an…
- **Point - Slope Form**: \( y - 8=\frac{7}{2}(x + 2) \) - **Slope - Intercept Form**: \( y=\frac{7}{2}x+15 \)
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what is the volume of this figure? 4 m 6 m 4 m 6 m 4 m 6 m 12 m cubic m…
# Explanation: ## Step1: Analyze the figure's structure The figure can be divided into three rectangular prisms. Let's identify their dimensions. - First prism (bottom left): leng…
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e figure below shows a circular park. its diameter is 26 yd. (a) use th…
(a) Área: \( 530.66 \text{ yd}^2 \), Circunferencia: \( 81.64 \text{ yd} \) (b) Área (c) Circunferencia
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what is the volume of this figure? 4 cm 4 cm 8 cm 8 cm 12 cm 4 cm 14 cm…
416
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for the right triangles below, find the values of the side lengths ( b …
(a) \( b \approx 11.3 \) (b) \( a \approx 5.2 \)? Wait, wait, me equivoqué. Wait, en el segundo triángulo, el lado dado es \( 3 \), que es el cateto adyacente al ángulo de \( 60^\…
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find the slope of the line that passes through (7, 4) and (9, 7). simpl…
\(\frac{3}{2}\)
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1. write the equation of the line that goes through the point (-2,8) an…
\( x = -23 \) ### Problem 3:
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24. the length of each side of a regular pentagon is increased by 8 inc…
The original length of each side is 5 inches.
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practice: 1. on a sunny day, sara’s shadow is 5 m long while the shadow…
The height of the tree is \( 2.56 \) m. ### Problem 2:
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in the figure below, j || g. find the values of z and x. z = \\square x…
\( z = 64 \), \( x = 29 \)
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for each number below, is it even or odd? 28 957 66 55 273 odd even
- 28: Even (mark the "Even" circle) - 957: Odd (mark the "Odd" circle) - 66: Even (mark the "Even" circle) - 55: Odd (mark the "Odd" circle) - 273: Odd (mark the "Odd" circle)
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prove $\\triangle aeb \\cong \\triangle dcb$, and then solve for $x$. p…
The height of the tree is \( 2.56 \) m. ### Problem 2: Determine the height of the shed
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in the figure below, m || l. find the values of z and y. z = \\boxed{} …
\( z = 69 \), \( y = 17 \)
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if triangle abc is translated 3 units right, what are the coordinates o…
For the first sub - question (translating \( A \) 3 units right), if the original \( A \) is \( (-1,1) \), the new coordinates are \( (2,1) \). So the answer is \( (2,1) \) (among…
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for each number below, is it even or odd? 58 \todd \teven 75 \todd \tev…
- 58: Even (select the circle under "Even" for 58) - 75: Odd (select the circle under "Odd" for 75) - 963: Odd (select the circle under "Odd" for 963) - 27: Odd (select the circle…
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in the triangle below, ∠b is a right angle. suppose that m∠a=(2x+37)° a…
(a) Ecuación: \( (2x + 37) + (4x - 19) = 90 \) (b) \( m\angle A = 61^\circ \), \( m\angle B = 90^\circ \), \( m\angle C = 29^\circ \)
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for each number below, is it even or odd? 58 75 963 27 389 odd even
- 58: Even (select the circle under "Even" for 58) - 75: Odd (select the circle under "Odd" for 75) - 963: Odd (select the circle under "Odd" for 963) - 27: Odd (select the circle…
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ivan is sitting in a movie theater, 19 meters from the screen. the angl…
\(12.8\)
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in the triangle, suppose that m∠q=(3x - 3)°, m∠r=(7x - 4)°, and m∠s=x°.…
(a) Equation: \( (3x - 3) + (7x - 4) + x = 180 \) (b) \( m\angle Q = 48^\circ \), \( m\angle R = 115^\circ \), \( m\angle S = 17^\circ \)
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16. triangle xyz with sides: xz = 25m, xy = 27m, yz = 24m
Using Heron's formula: First, find the semi - perimeter \(s=\frac{24 + 25+27}{2}=\frac{76}{2} = 38\) m. Then, the area \(A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{38(38 - 24)(38 - 25)…
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1. solve the system of equations graphed on the coordinate axes below $…
The solution is \( (0, 5) \). ### Problem 2: Solve the system \( y = -\frac{3}{2}x + 4 \) and \( y = 5x + 4 \)
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in the triangle, suppose that m∠e=(x+4)°, m∠f=(5x+8)°, and m∠g=(6x)°. (…
(a) Equation: \((x + 4) + (5x + 8) + 6x = 180\) (b) \(m\angle E = 18^\circ\), \(m\angle F = 78^\circ\), \(m\angle G = 84^\circ\)
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which point was translated 2 units down from the point at (-4, 4)?
A (assuming point \(A\) is the one with coordinates \((-4, 2)\) from the translation of \((-4, 4)\) 2 units down)
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which point was translated 2 units down from the point at (-4, 4)?
A (the point labeled A)
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what is the slope of this line? (-2, 3) (2, 3) -8 -7 -6 -5 -4 -3 -2 -1 …
0
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a surveyor wants to know the length of a tunnel built through a mountai…
\( 359.4 \) (rounded to the nearest tenth)
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graph this line using the slope and y-intercept: $y = -\frac{1}{3}x + 8…
Plot the \( y \)-intercept at \( (0, 8) \). From there, use the slope \( -\frac{1}{3} \) (down 1, right 3) to find another point \( (3, 7) \) and draw the line.
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which point was translated 3 units right from the point at (-4, 4)?
The point with x - coordinate - 1 (e.g., the blue point at \(x=-1\) on the grid, corresponding to the calculation of translating \((-4,y)\) 3 units right to \(x=-1\)). (Assuming t…
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a 32-m tall building casts a shadow. the distance from the top of the b…
\( 18.6 \, \text{m} \)
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a 9-ft ladder leans against the side of a house. the bottom of the ladd…
6.7
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triangle 2 find the length of the sides ab, bc, and ef. hint: you might…
# Explanation: ## Step1: Identify Triangle Type Both triangles have a right angle (angle C is right) and a \(28^\circ\) angle, so they are similar (AA similarity). ## Step2: Analy…
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the length of a shadow of a building is 29 m. the distance from the top…
\( 24.6 \) m
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determine whether a triangle with the given side lengths is a right tri…
# Explanation: ## Step1: Analizar (a) 8, 14, 16 Comprobar el teorema de Pitágoras: \(8^2 + 14^2 = 64 + 196 = 260\), \(16^2 = 256\). \(260 eq256\), no es triángulo rectángulo. ## …
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determine whether a triangle with the given side lengths is a right tri…
s: (a) Not a right triangle (b) Not a right triangle (c) Not a right triangle (d) Right triangle
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determine whether a triangle with the given side lengths is a right tri…
(a) 8, 15, 17: Right triangle (b) 4, 7, 8: Not a right triangle (c) 22, 29, 36: Not a right triangle (d) 10, 24, 26: Right triangle
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the equation of line t is ( y = \frac{-9}{7}x + 4 ). the equation of li…
parallel
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a right triangle has side lengths a, b, and c as shown below. use these…
\( \sin x = \boldsymbol{\frac{b}{c}} \), \( \cos x = \boldsymbol{\frac{a}{c}} \), \( \tan x = \boldsymbol{\frac{b}{a}} \)
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find the slope of the graph and the equation. do they have the same slo…
Slope of graph = \(4\) Slope of equation = \(4\) Yes, they have the same shape because their slopes are equal.
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1.08) a. set of equations: b. classification: 1.09) a. set of equations…
a. A. \( y = x + 1 \), \( 2y = 2x + 2 \) b. Coincident (or Dependent, Same Line)
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where is the blue dot on the number line? -6 -6.5 -7
-6.8
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a right triangle has side lengths d, e, and f as shown below. use these…
\( \tan x = \boldsymbol{\frac{e}{f}} \), \( \cos x = \boldsymbol{\frac{f}{d}} \), \( \sin x = \boldsymbol{\frac{e}{d}} \)
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which rule describes the composition of transformations that maps pre -…
\( T_{-6,1} \circ r_{x\text{-axis}}(x,y) \) (the option with this notation, assuming it's one of the four, likely the fourth option in the given choices)
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consider the following figure. (note that the figure is not drawn to sc…
\( FG < DF < DG < GE < DE \)
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what is the final transformation in the composition of transformations …
a 270° rotation about point B' (the option with "a 270° rotation about point B'")
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(a) one triangle has side lengths 10, 26, and 24. compute the sum of th…
### Parte (a) #### Explicación: Para determinar el tipo de triángulo, usamos la relación entre los cuadrados de los lados (Teorema de Pitágoras y sus extensiones). Primero, calcul…
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consider the following figure. (note that the figure is not drawn to sc…
(a) \( m\angle C < m\angle CED < m\angle D \) (b) \( EF < FG < EG \)
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(a) one triangle has side lengths 14, 11, and 12. compute the sum of th…
(a) \(11^2 + 12^2 = 265\), \(14^2 = 196\), Triángulo: Acute triangle (b) \(6^2 + 14^2 = 232\), \(18^2 = 324\), Triángulo: Obtuse triangle
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transform quadrilateral efgh by using the rule $r_{y\\text{-axis}} \\ci…
The transformed vertices are \( E''(-6, -8) \), \( F''(-2, -5) \), \( G''(-3, -2) \), and \( H''(-7, -5) \) (plot these points on the given grid).
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(a) one triangle has side lengths 18, 19, and 10. compute the sum of th…
Acute triangle ### (b)
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venn diagram template | to use this template, first the items being com…
To solve this Venn diagram problem about Shay's Rebellion and the Whiskey Rebellion, we analyze the unique and shared characteristics: ### Unique to Shay’s Rebellion (Top Circle, …
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venn diagram template: to use this template, type five items being comp…
### Shay’s Rebellion (Top Circle) Unique Characteristics: 1. Occurred in Massachusetts. 2. Farmers’ rebellion (debt/tax - related). 3. 1786–1787. 4. Exposed Articles of Confederat…
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consider the following figure. (note that the figure is not drawn to sc…
$HG < FH < FG < EG < EF$ (assuming $HG=HC$, $FG=FC$, $EG=EC$; if labels differ, adjust, but based on angle analysis, the order is $HG$ (or $HC$) < $FH$ < $FC$ (or $FG$) < $EC$ (or…
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volume of a sphere (level 1) score: 4/12 penalty: 1 off question what i…
\( 305907.4 \)
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figure wxyz is transformed using the rule $r_{y-axis} \\circ t_{-4, 2}(…
\( (3,8) \) (the first option: \( (3,8) \))
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(a) one triangle has side lengths 18, 19, and 10. compute the sum of th…
- Sum of squares of shorter sides: \(424\) - Square of longest side: \(361\) - Type of triangle: Acute triangle ### Part (b)
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compositions what is the final transformation in the composition of tra…
a reflection across line \( m \)
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which composition of transformations maps figure efgh to figure efgh? a…
a reflection across line \( k \) followed by a translation down
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(a) one triangle has side lengths 18, 19, and 10. compute the sum of th…
- Suma de cuadrados de lados cortos: \(424\) - Cuadrado del lado largo: \(361\) - Tipo de triángulo: Acute triangle (Acutángulo) ### (b)
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compositions which rule describes the composition of transformations th…
\( \boldsymbol{r_l \circ R_{Q, 180^\circ}} \) (the first option: \( r_l \circ R_{Q, 180^\circ} \))
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(a) one triangle has side lengths 16, 6, and 13. compute the sum of the…
(a) - Suma de cuadrados de lados cortos: \(6^2 + 13^2 = 205\) - Cuadrado del lado largo: \(16^2 = 256\) - Tipo de triángulo: Obtuse triangle (b) - Suma de cuadrados de lados corto…
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use the dropdown menus and answer blanks below to prove the quadrilater…
Quadrilateral ABCD is a rectangle because it is a parallelogram (opposite sides have equal slopes, so parallel) and adjacent sides have slopes whose product is - 1 (so perpendicul…
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find the length x.
$x = 6$
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which rule describes the composition of transformations that maps $\\tr…
\( R_{B', 90^\circ} \circ T_m \) (the second option, assuming the options are labeled as: A. \( T_m \circ R_{B', 90^\circ} \) B. \( R_{B', 90^\circ} \circ T_m \) C. \( R_{B', 180^…
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a composition of transformations maps $\\triangle xyz$ to $\\triangle x…
The first transformation is a reflection across line \(m\) (the option "a reflection across line \(m\)").
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find the length x.
$x = 3$? Wait, no, corregir: $2.5\times4 = 10$, $10\div5 = 2$. Entonces $x = 3$? No, 2.5*4=10, 10/5=2. Entonces x=3? Wait, no, 2.5/5 = x/4? Wait, tal vez la correspondencia es 2.5…
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find the length x.
\(x = 4\)
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find the length x.
\(\frac{7}{2}\) (or 3.5)
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similarity finding angle measures of a triangle given two angles of a s…
\( m\angle J = 25^\circ \), \( m\angle K = 90^\circ \), \( m\angle L = 65^\circ \)