Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
1. Plot the vertices at $(0, 3)$ and $(0, -3)$, and co-vertices at $(2, 0)$ and $(-2, 0)$ on the provided coordinate grid. 2. Draw a smooth, symmetric ellipse passing through all …
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1. given ( lm = 30 ), ( mn = 40 ), ( ln = 50 ), ( pq = 15 ), ( qr = 20 …
1. **Statement 1**: \( LM = 30 \), \( MN = 40 \), \( LN = 50 \), \( PQ = 15 \), \( QR = 20 \), \( PR = 25 \) 2. **Reason for Statement 2**: To check for SSS similarity, set up rat…
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10. use the law of syllogism to write a new conditional statement that …
If a triangle has three equal angles, then the triangle has three equal sides
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8. consider the statement \if a triangle has three equal sides, then it…
### For Question 8: The hypothesis is: a triangle has three equal sides The conclusion is: it is an equilateral triangle ### For Question 9: Condition statement: If a shape is a t…
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6. write the property that justifies each step. solve $4x - 10 = 5x + 1…
Justifications (in order): Given equation, Subtraction Property of Equality, Addition Property of Equality, Division Property of Equality; $x=-27$ --- ### Problem 7
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
1. Plot the points $(0, 3)$, $(0, -3)$, $(2, 0)$, and $(-2, 0)$ on the coordinate grid. 2. Draw a smooth, symmetric oval (ellipse) that passes through all four points, with its lo…
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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5 figurën e dhënë e zhvendosim paralelisht në drejtimin e përcaktuar me…
Coordinates of translated vertices: $A'(2, 3)$ $B'(2, -1)$ $C'(8, -6)$ $D'(8, -2)$ (To complete the figure, plot these points and connect them in order $A'\to B'\to C'\to D'\to A'…
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graph each equation. 9) \\(\frac{x^2}{4} + \frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
The ellipse has vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$. A smooth, closed curve connecting these points is the graph of $\frac{x^2}{4} + \frac{y^2}{…
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graph each equation. 9) \\(\frac{x^2}{4} + \frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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shkruajmë koordinatat e kulmeve të figurës së dhënë. e zhvendosim atë p…
Original coordinates: $B(2, 3)$, $C(3, 3)$, $D(3, 4)$, $E(4, 4)$, $F(4, 2)$, $G(3, 2)$, $H(3, 6)$ Translated coordinates: $B'(2, -2)$, $C'(3, -2)$, $D'(3, -1)$, $E'(4, -1)$, $F'(4…
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evaluate independent practice lesson 9.2 homework complete problems 5, …
1. Problem 5: Pattern: Backward alphabetical order. Next two letters: U, T 2. Problem 7: Pattern: Shapes increase by 1 side each. Next two shapes: A hexagon (6 sides), a heptagon …
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teacher voice - as long as the conclusion of one conditional statement …
4) If it is raining today, then you can go to the mall after school. 5) You cannot use the Law of Syllogism to write a new conditional statement.
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graph $y = \\frac{4}{5}x - 7$.
The graph of \( y = \frac{4}{5}x-7 \) has a y - intercept at \( (0, - 7) \) and a slope of \( \frac{4}{5} \). Two points on the line can be \( (0,-7) \) and \( (5,-3) \), and a st…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
To graph \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\): 1. Recognize it as an ellipse with major axis along the \(y\)-axis, \(a = 3\), \(b = 2\). 2. Plot vertices \((0,3)\), \((0, - 3)\) …
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
To graph \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\): 1. Recognize it as a vertical ellipse centered at \((0,0)\) with \(a = 3\) (along \(y\) - axis) and \(b = 2\) (along \(x\) - axis).…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
To graph \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) (an ellipse): 1. Identify it as an ellipse with vertical major axis (since \(a^{2}=9\) and \(b^{2}=4\), \(a > b\)), centered at \((0…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin with vertices at \((0, \pm3)\) and co - vertices at \((\pm2, 0)\). To draw it, plot the points \((0,3)\), \((0, - 3)\), \((2,0)\), \…
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graph each equation. 9) \\(dfrac{x^2}{4} + dfrac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin \((0,0)\) with vertices at \((0, 3)\), \((0,-3)\) and co - vertices at \((2,0)\), \((-2,0)\). The ellipse is drawn by connecting the…
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin \((0,0)\) with vertices at \((0, 3)\), \((0,-3)\) and co - vertices at \((2,0)\), \((-2,0)\), and the ellipse is drawn passing throu…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse with vertices at \((0,\pm3)\) and co - vertices at \((\pm2,0)\), symmetric about the \(x\) and \(y\) axes, passing through the points \((0,3)\), \((0, - 3)…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
To graph \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\): 1. Recognize it as an ellipse centered at \((0,0)\) with major axis along the \(y\)-axis, \(a = 3\), \(b = 2\). 2. Plot the vertice…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse with vertices at \((0,\pm3)\) and co - vertices at \((\pm2,0)\), plotted and connected as described above. (The actual graph is an ellipse centered at the …
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removed from one arm, so each star has one more unshaded arm than in th…
To sketch the fifth figure: 1. Draw a horizontal row of 5 connected squares (the base). 2. Draw a vertical column of 5 connected squares, where the bottom square of the column is …
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graph each equation. 9) \\(dfrac{x^2}{4} + dfrac{y^2}{9} = 1\\) coordin…
The graph is an ellipse centered at the origin with vertices at \((0, \pm 3)\) and co - vertices at \((\pm 2, 0)\), and the ellipse is drawn through these points on the given coor…
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
To graph \(\frac{x^2}{4}+\frac{y^2}{9}=1\): 1. Recognize it as a vertical ellipse with center \((0,0)\). 2. Plot vertices \((0, 3)\), \((0, - 3)\) and co - vertices \((2,0)\), \((…
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graph each equation. 9) \\(\frac{x^2}{4} + \frac{y^2}{9} = 1\\)
The graph is an ellipse with vertical vertices at $(0, 3)$ and $(0, -3)$, horizontal co-vertices at $(2, 0)$ and $(-2, 0)$, forming a smooth, symmetric oval centered at the origin…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval passing throu…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$, with vertices at $(2, 0)$, $(-2, 0)$, $(0, 3)$, and $(0, -3)$, forming a vertical elongated oval shape passing through thes…
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graph $y = \\frac{4}{5}x - 7$.
The graph is a straight line passing through the points $(0, -7)$ and $(5, -3)$, following the equation $y=\frac{4}{5}x-7$.
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retrieval solve each proportion. show your work and check your solution…
1. $x = 8$ 2. $b = 42$ 3. $x = 10$ 4. Three equivalent ratios: $\frac{2}{4}$, $\frac{3}{6}$, $\frac{x}{5}$ (all simplify to $\frac{1}{2}$)
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is a vertical ellipse centered at the origin, passing through the points $(2,0)$, $(-2,0)$, $(0,3)$, and $(0,-3)$, with a smooth curve connecting these points.
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing through…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(2, 0)$, $(-2, 0)$, $(0, 3)$, and $(0, -3)$, forming a vertical elongated oval shape passing through these…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is a vertical ellipse with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, drawn as a smooth closed curve through these points on the provided co…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval centered at the origin $(0,0)$.
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval centered at the origin.
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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graph each equation. 9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, drawn as a smooth curve connecting these points.
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go for each pair of similar polygons, give three ratios that would be e…
20. $\boldsymbol{\frac{3}{1.5}}$, $\boldsymbol{\frac{5}{3}}$, $\boldsymbol{\frac{c}{a}}$ (or simplified: $\boldsymbol{2}$, $\boldsymbol{\frac{5}{3}}$, $\boldsymbol{\frac{c}{a}}$) …
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19. determine whether or not the pairs of triangles are similar and exp…
a. The triangles are similar. Two pairs of corresponding angles are congruent, satisfying the AA similarity criterion. b. The triangles are not similar. The ratios of correspondin…
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find the volume of this square based pyramid. v = ? cm³
\( 4 \)
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18. one definition of similar triangles is based on transformations. ho…
1. **AA (Angle-Angle) Similarity**: If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. 2. **SAS (Side-Angle-Side) Similarity…
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given the circle below with chords \\( \\overline{uv} \\) and \\( \\ove…
11.1
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given the circle below with chords \\(\\overline{qr}\\) and \\(\\overli…
4.7
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given the circle below with chords \\( \\overline{qr} \\) and \\( \\ove…
4.7
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circle s, m∠utv = 51°. solve for x if muv = (5x + 23)°. if necessary, r…
$x=15.8$
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in circle q, m∠orp = 52°. solve for x if mop = (4x + 39)°. if necessary…
16.3
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in circle v, mtw = 118°. solve for x if m∠utw = (3x + 22)°. if necessar…
$x = 17.3$
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in circle v, muw = 118°. solve for x if m∠utw = (3x + 22)°. if necessar…
$x = 14.7$
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question in circle j, mih = 142°. solve for x if m∠igh = (10x + 36)°. i…
$3.5$
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in circle p, mqo = 131°. solve for x if m∠qpo = (6x + 26)°. if necessar…
$x = 17.5$
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in circle n, m∠onp = 48°. solve for x if mop = (4x - 48)°. if necessary…
$x=36.0$
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given the circle below with chords \\(\\overline{tu}\\) and \\(\\overli…
16.6
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given the circle below with chords \\( \\overline{cd} \\) and \\( \\ove…
20.9
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6. calculate the surface area of the right regular pentagonal pyramid. …
$84$ $\text{m}^2$
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1. consider a right triangular prism. a. the cross section is parallel …
a. Triangle b. Rectangle
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4. consider the following right triangular prism. a. sketch the shape o…
a. A right triangle (congruent to the prism's bases) b. A rectangle
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5. find the surface area of the solid shown. it is composed of a cube a…
264 square inches
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8 practice 8 (from unit 4, lesson 1) here are two triangles, each with …
\( x = 4 \) units \( y = 15 \) units
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7 practice 7 (from unit 4, lesson 6) technology required. this diagram …
3.9
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here is triangle abc. select all the true equations. a (sin(27)=\frac{y…
B. \(\cos(63)=\frac{y}{15}\), C. \(\tan(27)=\frac{y}{x}\), D. \(\sin(63)=\frac{x}{15}\)
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technology required. abc, shown here, is a right triangle. find the unk…
\(BC\approx\boxed{40.82}\) units Measure of \(\angle C\approx\boxed{30.96}\)° (or 31°) Measure of \(\angle B\approx\boxed{59.04}\)° (or 59°) (Note: Depending on rounding, the answ…
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shawn creates a circular garden with a radius of 9.5 feet. part a: shaw…
Part A: 59.66 feet Part B: 207.24 square feet
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find e. write your answer as an integer or as a decimal rounded to the …
\(e \approx 5.1\)
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find d. write your answer as an integer or as a decimal d =
\( d\approx15.1 \) (or 15 if integer is preferred, but more accurately ~15.1)
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consider the map of a maze at a park. the maze has three circular walki…
- Outermost path: Path B - Middle path: Path C - Innermost path: Path A
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find g. write your answer as an integer or as a decimal rounded to the …
\( 14.9 \)
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find p. write your answer as an integer or as a decimal rounded to the …
\(5.2\)
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9. solve for x (and y). a. b. c. d. $\\triangle cde \\sim \\triangle cv…
### Part a #### Step 1: Check Triangle Similarity (AA Criterion) First triangle angles: \(40^\circ\), \(80^\circ\), so third angle \(180 - 40 - 80 = 60^\circ\). Second triangle an…
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in triangle t r s, side t s is 14, angle at r is 77°, angle at s is 58°…
\(12.2\)
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin \((0,0)\) with vertices at \((0,3)\), \((0, - 3)\) and co - vertices at \((2,0)\), \((-2,0)\). The ellipse is symmetric about the \(…
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graph the line that has a slope of $-\frac{2}{3}$ and includes the poin…
To graph the line: 1. Plot the point $(3,2)$ (given point). 2. Use the slope $-\frac{2}{3}$: from $(3,2)$, move 3 units to the right (increase $x$ by 3) and 2 units down (decrease…
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graph the line that has a slope of \\(\\frac{1}{10}\\) and includes the…
To graph the line: 1. Plot the point \((0, 4)\) (since the line passes through this point as it is the y - intercept). 2. Use the slope \(\frac{1}{10}\): from the point \((0, 4)\)…
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question given \\(\\sin a = \\frac{5}{\\sqrt{29}}\\) and that angle \\(…
$\frac{5}{2}$
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question convert the following angle from degrees to radians. express y…
$\frac{10\pi}{3}$
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question convert the angle \\( \\frac{7\\pi}{3} \\) radians to degrees.…
$420^\circ$
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question the terminal ray of some angle \\(\\theta\\) in standard posit…
$\sin(\theta) = \frac{-q}{5}$ because sine is the ratio of Point D's vertical displacement from the x-axis to its distance from the origin
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question find an angle \\( \\theta \\) coterminal to \\( \\frac{35\\pi}…
$\frac{11\pi}{6}$
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2.3.3 quiz: geometric constructions with lines and angles mastery test …
D. the distance from B to E
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question find an angle \\( \\theta \\) coterminal to \\( \\frac{19\\pi}…
$\frac{7\pi}{6}$
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question find an angle \\( \\theta \\) coterminal to \\( \\frac{17\\pi}…
$\frac{5\pi}{3}$
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2.2.3 quiz: parallel and perpendicular lines what is the equation of a …
A. $y = \frac{3}{4}x - 11$
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9. what is the measure of angle abe?
\(40^\circ\)
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question 3 of 5 \\overleftrightarrow{ab} and \\overleftrightarrow{bc} f…
A. $x + 3y = 16$
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question 2 of 5 line m has a y-intercept of c and a slope of \\(\\frac{…
B. $-\frac{q}{p}$
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find the value of x using the figure to the right. x = \\square (simpli…
$\frac{16}{3}$
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Question was provided via image upload.
The two figures **are** congruent because **rigid transformations (translation)** are used to map Figure 1 onto Figure 2. Side corresponding to side $\overline{ON}$: $\boldsymbol{…
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figure 1 and figure 2 below are congruent. which side corresponds to si…
$\overline{FE}$
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find a point on the line and the lines slope, $y - 5 = \\frac{4}{3}(x -…
point on the line: $(4, 5)$ slope: $\frac{4}{3}$
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find the lines slope and a point on the line. y - 3 = -3(x + 2)
slope: $-3$ point on the line: $(-2, 3)$
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solve the absolute value inequality. other than \\( \\varnothing \\), u…
A. $(-\infty, -5) \cup (-5, \infty)$ (With the corresponding number line that has an open circle at $-5$ and shaded lines extending to both the left and right)
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question 10 10 pts what is the area of a triangle with vertices at (0,0…
B. 6 square units