几何
三角形、圆、解析几何与证明题。
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the shorter sides of an acute triangle are x cm and 2x cm. the longest …
7
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determining when to apply the hl congruence property each pair of trian…
Yes ### Part (b)
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the problem is about determining whether the hl (hypotenuse - leg) cong…
To determine if the HL (Hypotenuse - Leg) Congruence Property can be used, we recall that the HL Congruence Theorem applies to right - angled triangles. It states that if the hypo…
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Question was provided via image upload.
\( m\angle1 = \boldsymbol{54^\circ} \), \( m\angle2 = \boldsymbol{42^\circ} \), \( m\angle3 = \boldsymbol{100^\circ} \)
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ella’s geometry teacher asked each student to devise a problem and writ…
Ella's procedure is correct, but her conclusion is incorrect
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which value from the list below when substituted for x, would represent…
14
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plot and label the ordered pairs to create a shape: a (3,4) b (1,2) c (…
Reflected coordinates: $A'(0, -4)$ $B'(1, -2)$ $C'(6, -2)$ (When plotting: Original shape is a triangle with vertices at (0,4), (1,2), (6,2); reflected shape is a triangle with ve…
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plot and label the ordered pairs to create a shape. a (3,4) b (1,2) c (…
The coordinates of the reflected points are \(A'(3,-4)\), \(B'(1,-2)\), \(C'(5,-3)\). To plot them, find the \(x\) - coordinate on the \(x\) - axis and the negative \(y\) - coordi…
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extra practice level up your skills! multiple choice find the value of …
\( m\angle1 = 54^\circ \) \( m\angle2 = 42^\circ \) \( m\angle3 = 100^\circ \) ### Exit Ticket - Problem 2 (Find \( m\angle1 \), \( m\angle2 \), \( m\angle3 \))
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extra practice level up your skills! multi-select in △pqr, ∠q is a righ…
A. \(\angle P\) and \(\angle R\) are complementary., D. \(\angle P\) and \(\angle R\) are acute.
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extra practice level up your skills! multiple choice find the value of …
B. 12
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example 1 check your turn! use the triangle angle sum theorem ex find t…
\( m\angle1 = \boldsymbol{63^\circ} \), \( m\angle2 = \boldsymbol{63^\circ} \), \( m\angle3 = \boldsymbol{38^\circ} \)
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what is the value of c? (with an angle diagram showing 46.2° and angle …
$133.8^\circ$
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what is the value of q? (with a diagram of intersecting lines showing a…
$80.2^\circ$
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lesson 2 wrap-up part i. ask yourself. directions check your understand…
### Part I: True - False Questions 1. **“Sexual orientation” and “gender identity” mean the same thing.** - Brief Explanations: Sexual orientation refers to a person's romantic or…
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describe the dilation that occurs when transforming the graph $y = x^2$…
Compress vertically
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describe the dilation that occurs when transforming the graph $y = x^2$…
Stretch vertically
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find the volume of the given irregular pentagonal pyramid.
The volume of the irregular pentagonal pyramid is \( 80\space cm^{3}\)
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draw the image of $\\triangle abc$ under a dilation whose center is $p$…
The image $\triangle A'B'C'$ is a smaller triangle, with each vertex lying halfway between point $P$ and the corresponding vertex of $\triangle ABC$, and side lengths half of $\tr…
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Question was provided via image upload.
### Third Angles Theorem Blank: $\angle C \cong \angle Z$ ### Proof Completion: | Statements | Reasons | |------------|---------| | 1) $\angle A \cong \angle X, \angle B \cong \an…
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the points p (3, 1) and r (-2, 1). draw the line pr. is the line you dr…
Horizontal #### 2. Choose three more points on line PR
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2) in the diagram below of circle o, go=8, and m∠goj=60°. what is the a…
(4) $\frac{160\pi}{3}$
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example 3 find the volume of the given irregular pentagonal pyramid. st…
The volume of the irregular pentagonal pyramid is \(\frac{1568}{3}\approx522.67\) cubic centimeters (or if the base area calculation is different, the answer will change. But base…
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26)which is the measure of an angle in standard position that is coterm…
A. -278°
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17) the figure shows a can of three tennis balls. the can is just large…
3.87
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(a) triangle ghi and triangle jkl with markings. options: not necessari…
Not Necessarily Congruent ### Part (b)
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you can prove that two circles are similar to each other because the ra…
dilation
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for the triangles shown, determine if they are congruent or not necessa…
Left Pair: Congruent (ΔABC ≅ ΔDEF by SSS or SAS, assuming equal sides and included angle) Right Pair: Not Necessarily Congruent (Note: Due to image clarity, the exact congruence c…
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∠baq = ∠qac ∠bcp = ∠pca aq = 9 cp = 8√2 ac = ?
# Explanation: ## Step1: Identify the Angle Bisectors We know that \( \angle BAQ=\angle QAC \) (so \( AQ \) is the angle bisector of \( \angle BAC \)) and \( \angle BCP = \angle P…
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quadrilateral pqrs is inscribed in circle o. opposite angles p and r me…
40°
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draw the following diagram: quadrilateral (abcd) inscribed in circle (e…
$\boldsymbol{m\angle B = 95.5^\circ}$
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9. $y = -x + 7$ $y = x + 1$
The intersection point of \( y = -x + 7 \) and \( y = x + 1 \) is \( (3, 4) \). To graph, plot the intercepts for each line and draw them, showing their intersection at \( (3, 4) …
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7. $x - y = 4$ $4x + y = 1$ graph of two lines intersecting on a coordi…
The solution of the system of equations is \(x = 1,y=-3\)
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date: prisms and cylinders 1-6: find the volume of each cylinder rounde…
\( 3562.6 \) cubic inches ### Problem 2: Cylinder with diameter 12 m (so radius \( r = \frac{12}{2} = 6 \) m) and height 11 m
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h pair of points. 12) (-3, 20), (-5, 4)
The slope between the two points is \(\boldsymbol{8}\)
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find the slope of the line through each pa\ 11) (-9, -16), (5, -17)
\( \frac{-1}{14} \)
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find the slope of the line through each pair of points. 11) (-9, -16), …
\(-\frac{1}{14}\) ### Problem 12: $(-3, 20), (-5, 4)$
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solve. 19. write an expression for the missing dimension of the shaded …
Missing dimension: $x - 1$ cm; Area expression: $12(x - 1)$; Simplified area: $12x - 12$ cm²
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9-12: find the area of the quadrilaterals with the given vertices! 9. p…
\( 110 \) ### Problem 10: Triangle with vertices \( E(-1, 5) \), \( F(4, -5) \), \( G(4, 7) \)
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is the following statement true or false? a line segment has two endpoi…
true
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is the following statement true or false? the intersection of three pla…
true
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is the following statement true or false? perpendicular lines form a 45…
false
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is the following statement true or false? the intersection of a plane a…
true
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is the following statement true or false? parallel lines intersect in t…
false
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is the following statement true or false? a point is one - dimensional.…
false
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is the following statement true or false? the intersection of three pla…
false
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9. write the equation for the parabola with vertex (0, 6) and focus (0,…
The equation of the parabola is \(x^{2}=-12(y - 6)\) (or \(x^{2}+12y - 72 = 0\)) ### Problem 10: Given the equation \((y - 6)^{2}=-8(x - 6)\) ## Part (a): Coordinates of vertex an…
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consider the following sets. u = {all triangles} e = {x|x ∈ u and x is …
E
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lesson practice 8.4.03 problems 5–6: barneil and diego are each trying …
### Problem 5 (Assuming the original equation is \(6x + 6=5x - 8\)) # Explanation: ## Step1: Analyze the result Barnell's first step result is \(-x + 6=-8\). To get this from \(6x…
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3. in the diagram shown, ( x ) represents the weight of each triangle, …
(Question 3): The correct options are B, C, E. Wait, but let's confirm again. If the diagram is left: 1 triangle, 3 squares (3*3=9), right: 3 triangles, 1 square (3), then B (x + …
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what is its circumference? use 3.14 for π, and do not round your answer…
25.12 ft
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lesson practice 8.4.03 problems 1-2: in this balanced hanger diagram, (…
$x + 3y = 4x + y$ ### Problem 2
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the diameter of a circle measures 24 mm. what is the circumference of t…
75.36 mm
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given: m∠3 = 37° given: m∠11 = 106° (image of angle diagram with labele…
Since the problem is not fully stated (e.g., what angle to find is not specified), we can't provide a solution yet. But if we assume we need to find angles like vertical angles, s…
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consider the diagram. diagram of two parallel lines p and q cut by a tr…
B. Alternate Exterior Angles Converse Theorem
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cubist artists were interested in: ○ making art that did not show objec…
1. showing objects from multiple angles simultaneously 2. False
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enter the answer in each space provided. use numbers instead of words. …
First blank: 6 (or the corresponding angle to 2) Second blank: 6 Third blank: 2 Fourth blank: 2 Fifth blank: 6 Sixth blank: 6 (Note: The angle numbers may vary depending on the sp…
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use the diagram to prove the same - side exterior angles theorem. compl…
$\angle1$ and $\angle4$ are supplementary because $\angle1$ and $\angle2$ are supplementary (linear pair), $\angle2 = \angle4$ (corresponding angles, $a \parallel b$), so substitu…
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which of the following statements is not true concerning angle measure?…
A. The angle in standard position formed by rotating the terminal side of angle one complete counterclockwise rotation has a radian measure of \( \pi \) radians.
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which of the following statements is not true concerning radian measure…
C. An angle in standard position having a radian measure of \(\theta = -\frac{11\pi}{6}\) has a terminal side that lies in Quadrant IV.
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which of the following statements best describes two coterminal angles?…
D. Two angles in standard position are coterminal if they have the same terminal side.
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which of the following statements best describes an angle that is in st…
D. An angle is in standard position if the vertex is at the origin of a rectangular coordinate system and the initial side lies along the positive x - axis.
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6. the parent graph y = x was transformed. write a new equation to repr…
6. a. $y = x - 8$ b. $y = -2x$ c. $y = \frac{1}{2}(x-8)$ 7. $y = |x+3| - 2$
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statements reasons 1. \\overleftrightarrow{jl} \\parallel \\overleftrig…
To solve this proof, we analyze each step based on the given information and geometric theorems: ### Step 1: Understand the Given We know \( \overleftrightarrow{JL} \parallel \ove…
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move a statement or reason to each space provided. statements\treasons …
Statement 5: \( m\angle AFE + m\angle AFG = 180^\circ \) Reason 5: Linear Pair Postulate (or "If two angles form a linear pair, then they are supplementary")
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what is the area of this figure? 2 ft 5 ft 2 ft 3 ft 16 ft 4 ft 8 ft sq…
80 square feet
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in the diagram below, \\(\\overline{ts}\\) is parallel to \\(\\overline…
14.40 units
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eleonore wants to prove that if a line divides two sides in a triangle …
B. In $\triangle ABC$, if $\frac{AE}{EC} = \frac{AD}{DB}$, then $\overleftrightarrow{ED} \parallel \overline{CB}$.
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which coordinate for points a and b would help prove that lines ab and …
B. A': (p, m) and B': (z, -w)
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which points could be on the line that is parallel to \\(\\overleftrigh…
(-3, 5), (3, 2), (5, 1)
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1. 4 m, 26 m² (with a rectangular prism image)
The volume of the rectangular prism is \(104\space m^{3}\)
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find the value of x. (there is a diagram with point f, rays fb (left), …
$86$
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find the length of the missing sides of the right triangle in the below…
B. Height: 35, Base: 12
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the figure contains several triangles with marked equal sides (indicate…
To solve for the unknown angles or sides, we analyze the given diagram: ### Step 1: Identify Congruent Triangles - Triangle \( d \) and \( f \): The marked sides (two tick marks) …
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read the following passage, which is modeled after an encyclopedia entr…
to inform audiences about the production and types of tortillas
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calculate the volume of liquid in the tank sketched below. give your an…
\( 2.5 \)
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3. find x. 4. find mn 5. find cd. 6. find jl. 7. if \\(\\overline{qt}\\…
\( x = 18 \) ### Problem 4: Find \( MN \)
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in the given triangle with angles 41°, 115° and side related to angle x…
If finding \( x \), the answer is \( 24^\circ \); if finding \( y \), the answer is \( 156^\circ \)
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find the distance between the points (3, 3) and (10, 3). graphic of coo…
7 units
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find the distance between the points (5, 10) and (5, 2).
8 units
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select one: a. (1,2) b. (-2,-1) c. (2,-1) d. (2,1)
D. $(2,1)$
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5 find the equation of the line that is perpendicular to the line $y = …
직선의 방정식은 \( \boldsymbol{y = -\frac{5}{2}x + 13} \) (또는 \( \boldsymbol{5x + 2y = 26} \)) ### 문제 6 해결
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2. solve graphically: developing $y = x - 4$ $y = -\\dfrac{2}{3}x + 1$
The solution is the point $(3, -1)$
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5 determine whether the lines $x + 2y - 4 = 0$ and $2x - y - 4 = 0$ are…
The lines \(x + 2y - 4=0\) and \(2x - y - 4 = 0\) are not parallel. ### Question 6
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triangle xyz, with vertices x(-7,-7), y(-4,-5), and z(-6,-4), is drawn …
The length of side XY is \(\sqrt{13}\) units.
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triangle tuv, with vertices t(6,-9), u(7,-2), and v(2,-4), is drawn ins…
The area of triangle TUV is \( \boldsymbol{16.5} \) (or \( \boldsymbol{\frac{33}{2}} \)) square units.
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which graph matches this direct variation equation? $y = -\frac{3}{4}x$
The third graph (the one with the line passing through the origin and having a negative slope, decreasing from left to right)
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which graph matches this direct variation equation? y = -4x
The middle graph (the second graph among the three) matches the equation \( y=-4x \).
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graph each equation. 9) \\(\frac{x^2}{4} + \frac{y^2}{9} = 1\\) graph w…
To graph \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\): 1. Recognize it as an ellipse centered at the origin with a vertical major axis. 2. Identify vertices \((0,\pm3)\) and co - vertice…
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given the following unit circle, rotate the green dot to the appropriat…
\( -\frac{\sqrt{2}}{2} \)
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constructed response graph each equation. clearly mark at least three p…
1. Plotted points: $(-1,2)$, $(0,-1)$, $(1,-4)$; line connects these points 2. Plotted points: $(0,2)$, $(4,-1)$, $(-4,5)$; line connects these points 3. Plotted points: $(4,-2)$,…
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9 calculate the height ah of the trapezoid below. my calculations
The height \( AH \) of the trapezoid is \( 4 \).
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graph this line using intercepts: 10x - 60y = -6,000 click to select po…
To graph the line \( 10x - 60y = -6000 \), plot the x-intercept \( \boldsymbol{(-600, 0)} \) and the y-intercept \( \boldsymbol{(0, 100)} \), then draw a straight line through the…
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graph the points and find the distance between each set of points. when…
1. Distance between $(0,-3)$ and $(3,4)$: $\approx7.6$ 2. Distance between $(-2,1)$ and $(6,-5)$: $10$
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graph this line using intercepts: 6x - 6y = -120 click to select points…
To graph the line \( 6x - 6y = -120 \) using intercepts, plot the x-intercept \(\boldsymbol{(-20, 0)}\) and the y-intercept \(\boldsymbol{(0, 20)}\), then draw a straight line thr…
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graph this line using intercepts: 5x + 4y = 40 click to select points o…
The x-intercept is \( (8, 0) \) and y-intercept is \( (0, 10) \). Plot these points and draw the line.
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graph this line using intercepts: 7x + 7y = 350 click to select points …
To graph the line \( 7x + 7y = 350 \) using intercepts, plot the points \( (50, 0) \) (x - intercept) and \( (0, 50) \) (y - intercept), then draw a line through them.
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graph this line using intercepts: 8x + y = -8 click to select points on…
x-intercept: \((-1, 0)\), y-intercept: \((0, -8)\) (plot these points to graph the line)
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part ii - constructed response find the value of x in each right triang…
1. $4$ 2. $10$ 3. $8$ feet 4. $2.2$ miles 5. $18$ inches
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7 calculate the altitude ah in the triangle below. graph of triangle wi…
s: 7. \( \boldsymbol{\frac{18}{5} = 3.6} \) 8. \( \boldsymbol{\frac{21}{\sqrt{41}} \approx 3.28} \) (or rationalized \( \frac{21\sqrt{41}}{41} \)) 9. \( \boldsymbol{4} \) 10. \( \…