Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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1. in right triangle abc, altitude cd is drawn to its hypotenuse. selec…
A, B, C, D, E, F ### Problem 2
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a male mountain lion has a rectangular territory with an area of 96 squ…
12
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a square has an area of 49 square centimeters. what is the length of on…
7
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use the area formula to find the unknown measure. area = 54 sq m 6 m n …
9
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the number line shows two unknown numbers, p and q. is q - p positive o…
negative
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which of the following is the graph of $4x + 3y = 15$? (images of two g…
The graph that represents \( 4x + 3y = 15 \) is the one with y - intercept 5 and x - intercept \( \frac{15}{4}=3.75 \). Based on the analysis, the correct graph is (assuming the f…
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use the perimeter formula to find the unknown measure. perimeter = 32 y…
8
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the perimeter of a vegetable garden is 48 feet. the width of the garden…
14
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the area of a window is 63 square feet. the height of the window is 7 f…
9
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write the equation of the line in fully simplified slope-intercept form…
\(y =-\frac{2}{3}x-2\)
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write the equation of the line in fully simplified slope-intercept form…
$y = -\frac{1}{2}x - 8$
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graph the line containing the following intercept and ordered pair. y-i…
To graph the line, first plot \((0,3)\) (on the y - axis, 3 units up from the origin) and \((2,5)\) (2 units to the right on the x - axis and 5 units up on the y - axis). Then dra…
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graph the line $y = -6$ on the axes shown below. type of line: choose o…
El tipo de línea es horizontal, y la gráfica de \( y = -6 \) es una línea horizontal que pasa por \( y = -6 \) en el eje \( y \), extendiéndose a lo largo del eje \( x \) (para to…
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name 1 match each equation with the slope and y - intercept of the line…
For \(y=\frac{1}{2}x - 2\): \(m=\frac{1}{2}\), \(b=-2\) For \(y = 3x+2\): \(m = 3\), \(b = 2\)
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write the equation of the line graphed below in simplest form. answer a…
\( x = - 7 \)
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28. geometry the length of a rectangle is 3 cm greater than its width. …
The width of the rectangle is \( 4.5 \) cm (or \( \frac{9}{2} \) cm) and the length is \( 7.5 \) cm (or \( \frac{15}{2} \) cm). Wait, but maybe the problem expects in decimal or f…
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graph the inequality in the coordinate plane. x < -5
To graph \( x < - 5 \): 1. Draw a dashed vertical line at \( x=-5 \) (since \( x=-5 \) is not included in the solution set). 2. Shade the region to the left of the line \( x = - 5…
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give a pair of alternate exterior angles, a pair of corresponding angle…
(a) Alternate exterior angles: $\angle 2$ and $\angle 7$ (or $\angle 1$ and $\angle 6$) (b) Corresponding angles: $\angle 3$ and $\angle 7$ (or other valid pairs like $\angle 2$ a…
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which side of figure jklm corresponds with \\(\\overline{ab}\\)? (optio…
$\angle L$
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which side of figure jklm corresponds with \\(\\overline{ab}\\)? option…
$\overline{JK}$
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give a pair of corresponding angles, a pair of alternate exterior angle…
(a) Corresponding angles: $\angle1$ and $\angle3$ (or other valid pairs like $\angle5$ and $\angle7$, $\angle6$ and $\angle8$, $\angle2$ and $\angle4$) (b) Alternate exterior angl…
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which angle of figure wxyz corresponds with ∠r? ∠w ∠x ∠y ∠z
$\angle Y$
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figure jklm is reflected to form figure pqrs. which angle of figure pqr…
$\angle P$
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give a pair of alternate interior angles, a pair of corresponding angle…
(a) Alternate interior angles: \(\angle3\) and \(\angle6\) (or \(\angle4\) and \(\angle5\)) (b) Corresponding angles: \(\angle1\) and \(\angle5\) (or other valid corresponding ang…
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the figure that results from a transformation is called the image. figu…
\( \overline{AB} \) and \( \overline{DC} \) are parallel. \( \overline{EF} \) and \( \overline{HG} \) are parallel. The transformation maps parallel sides onto parallel sides. (Fo…
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draw a line representing the ise\ and a line representing the un\ of th…
\(-5\)
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there are several statements in the table below. for each, determine wh…
- For "I am not drawing a rectangle": No - For "It is not the case that I am drawing a rectangle": No - For "It is not the case that I am drawing a triangle": Yes - For "I am draw…
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draw the line of reflection that reflects △abc onto △abc.
The line of reflection is the horizontal line \( y = 1 \) (or as per the graph, the horizontal line through the midpoints, which is \( y = 1 \)). Wait, no, looking at the graph, t…
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given the figure below, find the values of x and z. (12x + 77)° (7x + 4…
\(x = 3\), \(z = 67\)
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given the figure below, find the values of x and z. (11x - 41)° z° (14x…
\(x = 10\), \(z = 111\)
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86. a slide 4.1 meters long makes an angle of 35° with the ground. to t…
s: 86. d. 2.4 m 87. c. \( \sin A = \frac{24}{26},\cos A = \frac{10}{26} \) 88. a. \( \sin = \frac{\sqrt{3}}{2} \) 89. b. \( \cos = \frac{1}{2} \)
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match the part of the expression with its corresponding vocabulary word…
- First part (\(17x\) and \(5\) circled): b. term - Second part (\(5\) circled): a. constant term - Third part (\(17\) circled): c. coefficient
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answer the questions below. (a) the perimeter of a rectangular garden i…
(a) Length of the garden: \( 95 \) m (b) Width of the window: \( 84 \) cm
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applying the angle addition postulate if ( mangle bgf = 152^circ ), wha…
$64^\circ$
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solve problems 10 - 13 using the graph of houses a, b, and c 10. (p) as…
Figure B is not a translation of Figure A. A translation preserves the shape, size, and orientation of a figure. Figure A has a height of 6 cm and width of 4 cm, while Figure B ha…
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sketch the angle in standard position. 83. $35^circ$ a. image of coordi…
c (the graph in option c) ### Question 84
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find the measure of the angle. 82. image of a coordinate plane with an …
a. \(155^\circ\)
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ethan says these shapes each have two pairs of parallel sides and four …
Ethan is incorrect about shape C because it has two pairs of parallel sides but does not have four square corners (its angles are not right angles). (If the correct shape is A, th…
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answer the questions below. (a) the area of a rectangular parking lot i…
63 ### Part (b)
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solve the system of equations graphed on the coordinate axes below. y =…
The solution is \( (0, 8) \)
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answer the questions below. (a) the perimeter of a rectangular field is…
(a): \( 51 \) ### Part (b)
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consider the line $y = x + 2$. what is the slope of a line parallel to …
Slope of a parallel line: \( 1 \) Slope of a perpendicular line: \( - 1 \)
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consider the line $y = \\frac{1}{5}x$. what is the slope of a line perp…
Slope of a perpendicular line: \(-5\) Slope of a parallel line: \(\frac{1}{5}\)
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which are vertical angles? \ $\\angle afe$ and $\\angle bfd$ \ $\\angle…
∠AFE and ∠CFD (the third option, assuming the options are ordered left to right as 1 to 4, the correct one is the third rectangle with ∠AFE and ∠CFD)
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problems 1-4 1. translate figure a using the rule (x, y) → (x + 1, y - …
The translation rule from Figure B to Figure D is \(\boldsymbol{(x, y) \to (x - 6, y + 6)}\) (exact coordinates may vary slightly based on graph interpretation, but the direction …
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consider the line $y = 5x - 1$. what is the slope of a line parallel to…
Slope of a parallel line: \( 5 \) Slope of a perpendicular line: \( -\frac{1}{5} \)
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which angle is a vertical angle with ∠efd? ∠dfb ∠bfc ∠ced ∠afb
$\angle AFB$ (the option with $\angle AFB$)
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the figures in the oval on the left are parallelograms. the figures in …
section C
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explore translations use the graph to answer problems 1–4. 1. translate…
To translate Figure A using \((x, y) \to (x + 1, y - 4)\), find each vertex of A, apply the rule to get new coordinates, then draw the figure with those new vertices. (The actual …
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in which diagram are angles 1 and 2 vertical angles?
The Top - Right Diagram
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give the coordinates of the point obtained from each reflection. (a) re…
(a) \((-7,0)\) (b) \((7,0)\)
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1. translate figure a using the rule (x, y) → (x + 1, y − 4). draw the …
The new vertices are \((-4, 6)\), \((-7, 6)\), \((-6, 7)\), \((-7, 8)\), \((-4, 8)\), and \((-5, 7)\).
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give the coordinates of the point obtained from each reflection. (a) re…
(a) \((5,-4)\) (b) \((-5,4)\)
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m∠srw = \\boxed{\\circ}
85
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explore transformations use the graph to answer problems 1–4. 1. transl…
The new coordinates of the vertices of Figure \(F\) after translation are \((-4, 6)\), \((-7, 6)\), \((-6, 7)\), \((-7, 8)\), \((-4, 8)\), and \((-5, 7)\).
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what is the measure of angle c? 20° 97° 83° 43°
43° (assuming the correct calculation leads to 43°, though my steps were confused)
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3 1. determine the measure of angle x in the diagram. be sure to explai…
The measure of angle \( x \) is \( \boldsymbol{12^\circ} \)
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m∠srw = \\boxed{}
# Explanation: ## Step1: Identify Angle Relationship Angles formed by intersecting lines: ∠TRV and ∠SRW are vertical angles? No, wait, ∠TRV (95°) and ∠SRW: Wait, actually, ∠TRV an…
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read the passage. a fairy ring is a circle of mushrooms that grows beca…
the details and history of the fairy ring legend
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in the diagram, which angle is part of a linear pair and part of a vert…
\(\angle GFD\) (the option labeled \(\angle GFD\))
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which shape has at least one pair of perpendicular sides?
The third shape (the square)
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marcus states that angle orp and angle lrp are a linear pair. which bes…
The option "He is incorrect. Angle ORP does not form a linear pair with another angle in the diagram." (the fourth option in the vertical list of options)
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design a problem that could be solved using trigonometry and some of th…
### Designing the Trigonometry Problem Let's consider a right - triangle problem. Suppose we have a right - triangle \(ABC\) with a right angle at \(C\). We know that angle \(A = …
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linear pairs and vertical angles what is the value of m? image of inter…
\(m = 10\)
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explore translations 1. translate figure a using the rule (x, y) → (x +…
The new coordinates of the vertices are \((-4, 6)\), \((-1, 6)\), \((-6, 7)\), \((-7, 8)\), \((-4, 8)\), and \((-5, 7)\).
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what is the distance between points (5, 3) and (-4, -1)? a. \\(\\sqrt{5…
# Explanation: ## Step1: Recall Distance Formula The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)…
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linear pairs and vertical angles what is the value of x? image of inter…
20
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2. a 10 ft. c 6 ft. b b = ____________
\(b = 8\) ft
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which pair of angles are vertical angles?\ \\angle wrs and \\angle vrt\…
A. $\angle WRS$ and $\angle VRT$
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what is the best name for the shape? rectangle square rhombus trapezoid
C. rhombus (assuming the options are labeled A: rectangle, B: square, C: rhombus, D: trapezoid. If the original options have different labels, adjust accordingly. Based on the giv…
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in the diagram, which angles are vertical angles? choose two correct an…
$\angle ABC$ and $\angle EBD$, $\angle ABE$ and $\angle CBD$ (corresponding to the options: the fifth option $\angle ABC$ and $\angle EBD$ and the second option $\angle ABE$ and $…
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what is the area of the arrow shown? diagram of arrow with dimensions: …
44 in²
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find the distance between the points (-5, -7) and (3, -7). distance:
8
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find the distance between the points (-6, 2) and (-6, 5). distance:
3
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find the distance between the points (-5, 6) and (7, 6). distance:
12
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4. détermine la valeur du périmètre si l’aire du trapèze est de 160 cm²…
The perimeter of the trapezoid is \( 56 \, \text{cm} \)
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14. slope (m) = y-intercept (b) = equation:
slope (m) = $\boldsymbol{0}$ y-intercept (b) = $\boldsymbol{3}$ equation: $\boldsymbol{y = 3}$
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which are correct statements regarding proofs? choose three correct ans…
1. A two - column proof consists of a list statements and the reasons the statements are true. 3. In a paragraph proof, statements and their justifications are written in sentence…
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2 circle the pronouns that are used incorrectly, then correct them belo…
In the sentence "Customers can drive up to the window, or you can have your food delivered.", the incorrect pronoun is "you"; the correct pronoun is "they". ### Problem 3:
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given that \\(\\overline{rt} \\cong \\overline{wx}\\), which statement …
The middle - right option (labeled "RT + TW = WX + TW")
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given that d is the midpoint of \\(\\overline{ab}\\) and k is the midpo…
\( \boldsymbol{AK + BK = AC} \) (the option with this statement)
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13. slope (m) = y-intercept (b) = equation: graph of a line on a coordi…
slope (m) = $1$; y - intercept (b) = $1$; equation: $y=x + 1$
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if ( mangle a = mangle b ) and ( mangle a + mangle c = mangle d ), then…
substitution property
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proving the triangle inequality theorem given: abc is a triangle. prove…
The proof shows \( BC + AC > BA \) using the shortest distance theorem (perpendicular segment is shortest) and inequality addition, followed by segment addition postulate for subs…
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which picture shows a translation?
The bottom - left picture (the third picture in the order of top - left, top - right, bottom - left, bottom - right)
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which statement is true about the given information?\ options: bd = \\f…
The option with \( \overline{BD} \cong \overline{CE} \) (the third option in the list, depending on the original order; based on the analysis, the correct statement is \( \overlin…
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segment ab is congruent to segment ab. this statement shows the ______ …
reflexive
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what are oblique triangles? explain with examples. note: use your own w…
Unique triangles are triangles that can be constructed in only one way. For example, a triangle with side lengths 3 cm, 4 cm, and 5 cm is unique. Another example is a triangle wit…
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transformation of figure a. a slide is also called a translation. a tra…
6 units to the left
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name: date: pd: solving equations holiday color by number 10. 4x + 7 = …
s (x-values for equations 10,12,13,11,15; counts for 14): 10. \(x = 4\) 11. \(x = 9\) 12. \(x = 2\) 13. \(x = -7\) 14. Triangles: 4, Circles: 4 (color key dependent) 15. \(x = 15\)
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a change in the location, direction, or size of a figure is called a tr…
Slide
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which statement is true about the diagram? diagram of a line segment wi…
The statement "K is the midpoint of \( \overline{AB} \)" is true. (Assuming the options are presented as: 1. \( AB = KT \); 2. \( B \) is the midpoint of \( \overline{KT} \); 3. \…
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your company is applying sealant to the floors of the 2 rooms shown her…
D. 6
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triangle nop is similar to triangle qrs. find the measure of side qr. r…
\(24.3\)
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identify the two statements that contradict each other in the set: i. (…
I and III (or the statements: I. \( m\angle K + m\angle L=150 \) and III. \( m\angle K = 180 \))
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triangle ghi is similar to triangle jkl. find the measure of side jk. r…
\( 98.5 \)
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question triangle cde is similar to triangle fgh. find the measure of s…
\(93.6\)
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write the first step of an indirect proof for the given statement. ( ma…
A. Assume temporarily that \( m\angle M \) and \( m\angle N \) are not =
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x graphs are shown below. click on the tabs to see them. graph 1 graph …
None of the graphs (specifically, Graph 6 does not represent a function, and assuming others also fail the vertical line test as per the context, the correct option is "None of th…
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date: solving equations holiday color by number directions: solve the e…
s (with solutions for equations): 1. \( x = 1.375 \), Color (depends on table, here solved) 2. \( x = 3 \) (from balance), Color (depends on table) 3. \( x = -7.5 \), Color (depen…