Geometría
Triángulos, círculos, geometría analítica y demostraciones.
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points q and r are midpoints of the sides of triangle abc. what is aq? …
20 units
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question 11: if y(1, 3) and a(5, 7), calculate ya in simplest radical f…
\(4\sqrt{2}\)
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ng the pencil, plot the reflection of point a across the y-axis.
The reflection of point A across the y - axis is at the point with coordinates $(5,3)$ (and should be plotted at that location on the graph).
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what is the conclusion in this conditional statement? given that two li…
the two lines do not intersect
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7. which is longer, 4000 ft or 1 kilometer? solve each proportion.
\( 4000 \) ft is longer than \( 1 \) kilometer.
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lesson 2: leap frog ready, set, go ready in each problem, there will be…
To solve these problems, we analyze each image relative to the pre - image by recalling the definitions of rotation and reflection: ### Problem 1 - **Pre - image**: A rectangle wi…
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using the pencil, plot the reflection of point a across the x-axis.
The reflection of point A across the x - axis is the point with coordinates \((0,-6)\), which should be plotted on the graph at the position \((0, - 6)\).
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what is the hypothesis in this conditional statement? if a right triang…
the right triangle has sides with lengths 3 and 4
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which best explains whether or not all isosceles triangles are similar?…
C. All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.
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what is the conclusion in this conditional statement? if it is the holi…
the post office is crowded
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perímetro. el perímetro del triángulo de stephanie es la mitad del perí…
\(\frac{5 + 8 + 12}{2}\)
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drag the right word to its synonyms manner, system, way method hypothes…
Drag "method" to the blue circle containing "manner, system, way".
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solve for x and graph the solution on the number line below. -5x ≤ -20 …
Inequality Notation: \(x \geq 4\) For the number line: Place a closed circle at 4 (since the inequality is "greater than or equal to") and draw an arrow to the right to represent …
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in the experiment, neither the experimenter nor the subjects knew which…
double - blind
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solve for x and graph the solution on the number line below. -7x ≥ 63 a…
Inequality Notation: \(x \leq -9\) For the number line: Plot a closed circle at \(-9\) (since the inequality is "less than or equal to") and draw an arrow to the left (indicating …
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triangle abc will be dilated according to the rule ( d_{f, 0.25}(x,y) )…
D. (1, 0)
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question solve for ( x ) and graph the solution on the number line belo…
Inequality Notation: \( x \geq -2 \) For the number line: We would place a closed circle (since the inequality is "greater than or equal to") at \( -2 \) and shade the line to the…
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2. if ( mangle 9 = 97^circ ) and ( mangle 12 = 114^circ ), find each me…
To solve for the measures of the angles, we use properties of vertical angles, linear pairs, and corresponding angles (assuming parallel lines and transversals, though the diagram…
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what is the length of $overline{mn}$? $\bigcirc$ 58 cm $\bigcirc$ 75 cm…
58 cm
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solve for x and graph the solution on the number line below. -4 > 2x an…
Inequality Notation: \( x < - 2 \) For the number line: We draw an open circle at \( x=-2 \) (because the inequality is strict, \( x eq - 2 \)) and shade the region to the left o…
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the statements below can be used to prove that the triangles are simila…
$\boldsymbol{\frac{BC}{YZ}=\frac{6}{3}}$ (the third option)
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solve for x and graph the solution on the number line below. -40 ≥ 4x a…
Inequality Notation: \( x\leq - 10 \) For the number line graph: We draw a closed circle at \( x = - 10 \) (because the inequality is "less than or equal to") and shade the line t…
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ellipse, rect, and three grid sections with black dot (ellipse) and bla…
For the first grid: $\text{ellipse}(4, 1, 1, 1)$, $\text{rect}(3, 2, 1, 1)$ (coordinates are approximate based on grid analysis)
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which transformations could have taken place to map △abc to △abc? ○ a r…
a translation and a dilation (the third option: "a translation and a dilation")
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solve for x and graph the solution on the number line below. 4x ≥ -32 a…
Inequality Notation: \( x \geq -8 \) (For the number line: Place a closed circle at -8 and draw an arrow to the right, indicating all numbers greater than or equal to -8.)
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solve for ( x ) and graph the solution on the number line below. ( 0 < …
Inequality Notation: \(x > 0\) For the number line: We draw an open circle at 0 (because \(x\) is not equal to 0) and shade the region to the right of 0 to represent all values of…
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use a geometric model to factor ( 3x^2 + 4x + 1 ) by following these st…
\((3x + 1)(x + 1)\) (corresponding to the option: \((3x + 1)(x + 1)\))
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15. can you find a counterexample for the following statement? see exam…
A rectangle (or a square, or a right trapezoid with two right angles) is a counterexample. For example, a rectangle is a trapezoid (with two pairs of parallel sides) and has four …
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line rs intersects triangle bcd at two points and is parallel to segmen…
\( \triangle BCD \) is similar to \( \triangle BSR \), \( \frac{BR}{RD}=\frac{BS}{SC} \), \( (BR)(SC)=(RD)(BS) \) (i.e., the first, second, and fourth options).
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ellipse( , ); rect( , ); ellipse( , ); rect( , ); ellipse( , ); rect( ,…
To solve for the coordinates of the shapes (ellipse as a circle, rect as a square) in each grid, we analyze the grid positions: ### First Grid (Top) - **Ellipse (Circle)**: Let’s …
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solve for x and graph the solution on the number line below. 9x > 45 an…
Inequality Notation: \(x > 5\) For the number line: We draw an open circle at 5 (because the inequality is \(>\) and not \(\geq\)) and shade the region to the right of 5 to repres…
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solve for x and graph the solution on the number line below. ( x - 9 le…
Inequality Notation: \( x \leq 5 \) For the number line: We would draw a closed circle at 5 (since the inequality is "less than or equal to") and shade to the left of 5 to represe…
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solve for ( x ) and graph the solution on the number line below. ( 10 +…
Inequality Notation: \( x > - 7 \) For the number line graph: We draw an open circle at \( - 7 \) (because the inequality is \( > \), not \( \geq \)) and then draw an arrow to the…
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-3.22 ÷ -5 options: -64.4, -0.644, 0.644, 64.4 (each with a selection c…
\(0.644\) (corresponding to the option with \(0.644\))
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to prove that δaed ~ δacb by sas, jose shows that (\frac{ae}{ac} = \fra…
$\boldsymbol{\angle A=\angle A}$ (the first option: $\boldsymbol{\angle A=\angle A}$)
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solve for ( x ) and graph the solution on the number line below. ( 3 ge…
Inequality Notation: \(x \leq 8\) For the number line: We would draw a closed circle at 8 (since the inequality is "less than or equal to") and shade to the left of 8 to represent…
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** this is a 2-page document! ** use the diagram below to answer questi…
\( 37 \) ### Question 2: If \( LN = 54 \) and \( LM = 31 \), find \( MN \).
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1. if m∠... find each measure. give your reasoning. 2. if m∠9 = 97° and…
To solve these angle - measure problems, we will use the properties of angles formed by intersecting lines (such as vertical angles, linear pairs, and corresponding angles). Let's…
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in the diagram, (\frac{vz}{yz} = \frac{wz}{xz}) diagram with points v, …
\(\boldsymbol{\angle VZW \cong \angle YZX}\) (the third option: \(\boldsymbol{\angle VZW \cong \angle YZX}\))
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given, ∠1 ≅ ∠2, transitive property of angle congruence, ∠2 ≅ ∠3, ∠1 ≅ …
To prove $\angle 1 \cong \angle 3$: 1. **Given**: $\angle 1 \cong \angle 2$ and $\angle 2 \cong \angle 3$. 2. **Transitive Property of Angle Congruence**: If $\angle A \cong \angl…
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12 find the value of y.
\(y = 27\)
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complete the two - column proof. given ∠1 ≅ ∠2 prove ∠1 ≅ ∠3 statements…
The completed two - column proof is as shown above, and we have proven that $\boldsymbol{\angle 1 \cong \angle 3}$ using the given information, the Vertical Angles Theorem, and th…
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-3.22 ÷ -5 options: -64.4, -0.644, 0.644, 64.4 (each with a selection c…
\(64.4\) (the option with 64.4)
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avery is hanging three picture frames above her couch. each picture fra…
322 square inches
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solve the inequality and graph the solution on the line provided. -8 - …
Inequality Notation: \( x < 2 \) For the number line: We draw an open circle at 2 (since \( x \) is not equal to 2) and shade the region to the left of 2 to represent all values o…
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solve the inequality and graph the solution on the line provided. -7 + …
Inequality Notation: \( x \geq 7 \) For the number line: We place a closed circle at 7 (since the inequality is "greater than or equal to") and shade to the right of 7 to represen…
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \( x < 1 \) For the number line: Draw an open circle at 1 (since \( x \) is not equal to 1) and shade the region to the left of 1 to represent all values of \…
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solve the inequality and graph the solution on the line provided. (7 + …
Inequality Notation: \( x > -2 \) For the number line: Draw an open circle at -2 (since the inequality is "greater than" and not "greater than or equal to") and shade the region t…
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factoring a polynomial using a geometric model try it use a geometric m…
The factored form of \(3x^{2}+4x + 1\) is \((3x + 1)(x + 1)\)
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determine the length of the diameter, in simplest radical form, of ⊙m w…
The length of the diameter is \(4\).
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5. which pair of angles are vertical angles? diagram of intersecting li…
D. $\angle2$ and $\angle4$
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3. in the figure below, ba is perpendicular to line ( l ). what is the …
A. \( 53^\circ \) ### Question 4
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1. a ray and a line intersect to form $\\angle 1$ and $\\angle 2$ as sh…
A. \( 112^\circ \) ### Problem 2
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solve the inequality and graph the solution on the line provided. $-16 …
Inequality Notation: \(x < -2\) For the number line: We would draw an open circle at \(-2\) (since the inequality is strict, \(x\) is not equal to \(-2\)) and shade the region to …
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6. find the value of x. diagram: two intersecting lines, one angle labe…
C. 16
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solve the inequality and graph the solution on the line provided. 3x - …
Inequality Notation: \( x < -4 \) For the number line: We would draw an open circle at -4 (since the inequality is strict, \( < \), not \( \leq \)) and shade the line to the left …
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graph the interval represented in interval notation on the number line.…
To graph \((-\infty, 6)\cup(11, \infty)\) on the number line: 1. For the interval \((-\infty, 6)\): Place an open circle at \(x = 6\) (because 6 is not included in the interval) a…
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \( x > -7 \) For the number line: We would draw an open circle at \(-7\) (since the inequality is \( > \), not \( \geq \)) and shade the line to the right of …
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1. complete the proof. given: ( hi = 8 ), ( ij = 8 ), ( overline{ij} co…
1. Reason: Given 2. Reason: Given 3. Reason: Transitive Property of Equality 4. Reason: Definition of Congruent Segments 5. Reason: Given 6. Reason: Transitive Property of Congrue…
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practice 1 * 1. complete the proof. statements reasons 1. ( hi = 8 ) 1.…
1. Reason for \( HI = 8 \): given 2. Reason for \( IJ = 8 \): given 3. Reason for \( HI = IJ \): transitive property of equality (or substitution) 4. Reason for \( \overline{HI} \…
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solve the inequality and graph the solution on the line provided. 2x - …
Inequality Notation: \(x > -4\) For the number line: We draw an open circle at \(-4\) (since the inequality is \(>\) and not \(\geq\)) and shade the region to the right of \(-4\) …
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activity 4 1) draw the image of region a after each of the following tr…
### Part (a) #### Explanation: To translate a figure 2 units right and 3 units up, we apply the translation rule \((x,y)\to(x + 2,y + 3)\) to each vertex of region \(A\). 1. Ident…
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circle the answer: 1. paulo, who/whom is a fan of superhero comics, wan…
Circle "who" ### Question 2:
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rotations on the coordinate plane use the figure to answer the question…
To solve these rotation problems, we first need the coordinates of points \( A \), \( B \), \( C \), and \( D \) from the graph. Let's assume the coordinates (by analyzing the gri…
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9. v = bh v = 36 in³ b = 6 in² (image of a hexagonal prism)
The height \( h \) is \( 6\space\text{inches} \).
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give a reason for each statement. f r a n given: $overline{fr} \\cong \…
### Step-by-Step Explanation for Each Statement: #### Statement 1: $\overline{FR} \cong \overline{AN}$ ## Step 1: Identify the Reason This is given in the problem statement. Reaso…
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graph the interval represented in interval notation on the number line.…
To graph the interval \((-6, 5)\) on the number line: 1. Place an open circle (or a parenthesis) at \(-6\) (indicating \(-6\) is not included). 2. Place an open circle (or a paren…
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c) translating shapes sometimes you are asked to translate a shape on a…
(Drawing Instructions): - **Part (a) (B):** Translate each vertex of A 2 right, 3 up. Plot and connect. - **Part (b) (C):** Translate each vertex of A 5 right, 0 up/down. Plot and…
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reflect the figure shown over the x-axis. record the coordinates of the…
To solve the problem of reflecting the figure over the \( x \)-axis, we first need to identify the coordinates of the original points \( J \), \( K \), and \( L \) from the graph.…
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a side of the triangle below has been extended to form an exterior angl…
\(x = 59\)
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graph the interval represented in interval notation on the number line.…
To graph the interval \((-1, 8)\) on the number line: 1. Place an open circle at \(-1\) (because \(-1\) is not included in the interval). 2. Place an open circle at \(8\) (because…
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9. reflect the figure shown over the y-axis. record the coordinates of …
\(M'(8,2)\), \(A'(7,6)\), \(T'(2,6)\), \(H'(2,2)\)
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solve for x and graph the solution on the number line below. ( x + 10 l…
Inequality Notation: \( x\leq5 \) For the number line: We draw a closed circle at 5 (because the inequality is "less than or equal to") and shade the line to the left of 5 to repr…
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build a model to show (\frac{4}{9} \times 2).
To model $\frac{4}{9} \times 2$: - **Area Model**: Draw two identical rectangles, each divided into 9 equal parts (columns). Shade 4 parts in each rectangle. Combining the shaded …
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6 find the value of y. 9x + 42 = 15x -9x -9x 42 = 6x 6 6 x = 7 (15x)° (…
\(y = 22\)
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8. a figure is reflected from quadrant iv to quadrant iii.
The figure is reflected over the \(y\)-axis.
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divides his land into square fields that are \\(\\frac{1}{4}\\) mile lo…
9
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solve for ( x ) and graph the solution on the number line below. ( x - …
Inequality Notation: \( x>12 \) For the number line: We draw an open circle at 12 (because the inequality is \(>\) and not \(\geq\)) and then draw an arrow to the right of 12 to r…
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activity 4 (continued) 2) each of these triangles is labelled with a le…
To solve the translation problems, we analyze the horizontal (x - direction) and vertical (y - direction) shifts between the triangles. Let's assume each grid square represents 1 …
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question solve for x and graph the solution on the number line below. 9…
Inequality Notation: \( x < 12 \) For the number line: We draw an open circle at 12 (since the inequality is \( < \), not \( \leq \)) and shade the line to the left of 12 to repre…
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1/2 mile, 1 mile, 1/2 mile, 1 mile (geometric figure with dashed lines …
$\frac{1}{4}$ square miles (if the problem was about the area of a small rectangle; adjust based on actual question, but this is a common interpretation).
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2) a square with side length 1 inch (marked “1 in” on the bottom and ri…
The area of the square is \( 1 \) square inch.
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solve for ( x ) and graph the solution on the number line below. ( x + …
Inequality Notation: \( x\leq4 \) Number Line: Draw a closed circle at 4 on the number line and an arrow pointing to the left (towards negative infinity) to represent all real num…
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graph the interval represented in interval notation on the number line.…
To graph \((-\infty, 1)\cup(10, \infty)\) on the number line: 1. At \(x = 1\), draw an open circle (since \(1\) is not in the interval) and draw a ray (line with an arrow) extendi…
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24. 11 - p 28. -54 = -9g 29. (\frac{x}{5} = 6) in exercises 32–34, use …
\(g = 6\) ### Problem 29: \(\frac{x}{5}=6\)
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solve for ( x ) and graph the solution on the number line below. ( x + …
Inequality Notation: \( x < 6 \) For the number line: We draw an open circle at 6 (because the inequality is \( < \), not \( \leq \)) and draw a line to the left of 6 to represent…
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1. if ( mangle 8 = 23^circ ), find each measure. give your reasoning. a…
s: a. \( m\angle1 = 157^\circ \) b. \( m\angle2 = 23^\circ \) c. \( m\angle3 = 157^\circ \) d. \( m\angle4 = 23^\circ \) e. \( m\angle5 = 157^\circ \) f. \( m\angle6 = 23^\circ \)…
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solve for ( x ) and graph the solution on the number line below. ( 11 <…
Inequality Notation: \(x > 6\) For the number line: We draw an open circle at 6 (because the inequality is strict, \(x\) is not equal to 6) and then draw an arrow to the right of …
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6.9 in, 2.4 in (dimensions of a rectangular - shaped figure with square…
The perimeter of the figure is \(18.6\) inches.
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a geometric figure (likely a parallelogram) with a base labeled 5.9 in …
The area of the parallelogram is \( 23.6 \) square inches.
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plot the inequality on the number line. -6 < x ≤ 5 choose the proper to…
To plot \(-6 < x\leq5\) on the number line: 1. Place an open circle at \(-6\) (because \(x\) is greater than, not equal to, \(-6\)). 2. Place a closed circle at \(5\) (because \(x…
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1.5 yd, 4 yd (diagram of a geometric figure with these dimensions)
The area of the parallelogram is \( 6 \) square yards.
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question 18: if m(2, -7) and z(6, 3), calculate the coordinates of poin…
The coordinates of point \( F \) are \( (3,-\frac{9}{2}) \) or \( (3, - 4.5) \)
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7) 6 yd 18.7 yd 18.7 yd
The perimeter of the shape is \( 49.4 \) yards.
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a side of the triangle below has been extended to form an exterior angl…
To solve for \( x \), we use the property that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. The triangle is a right - triangle, s…
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8) diagram of a parallelogram with top base 6 m, left side 5.8 m, heigh…
The area of the parallelogram is \( 30 \) square meters.
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a side of the triangle below has been extended to form an exterior angl…
To find the value of \( x \), we use the property that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. First, we find the adjacent i…
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for #16-18, determine what type of angle pair is shown and find the val…
Angle Relationship: Corresponding Angles \(x = 18\) ### Problem 17
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6. complete a table of values for the width and length of a rectangle w…
As the width of the rectangle increases, the length decreases (and vice versa) because their product (the area) remains constant at 12 square inches. They have an inverse relation…
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use the area model to multiply 3(25k + 10). first, find the partial pro…
\(75k + 30\)