Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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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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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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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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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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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. \( \…
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graph this line using intercepts: 42x - 60y = -4,200 click to select po…
To graph the line \( 42x - 60y = -4200 \), plot the x-intercept \( (-100, 0) \) and y-intercept \( (0, 70) \), then draw a line through these two points.
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graph this line using intercepts: x - 9y = 9 click to select points on …
To graph the line \( x - 9y = 9 \), plot the x - intercept \( (9, 0) \) and the y - intercept \( (0, -1) \), then draw a straight line through these two points.
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graph this line using intercepts: 7x - y = 7 click to select points on …
The x - intercept is \( (1, 0) \) and the y - intercept is \( (0, - 7) \). The line is graphed by plotting these two points and drawing a line through them.
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graph this line: y + 2 = x + 9 click to select points on the graph.
To graph the line \(y=x + 7\) (derived from \(y + 2=x + 9\)): - Plot the y - intercept at \((0,7)\). - Plot another point, for example, when \(x=-7\), \(y = 0\) (point \((-7,0)\))…
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the two polygons below are similar. complete the similarity statement. …
$EHGF$
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solve the inequality $x + 6 < 10$ $x+6 < 10$ $-6$ $-6$ $x < 4$ subtract…
The solution is $x < 4$. The graph has an open circle at 4 with an arrow extending to the left along the number line.
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graph this line: y + 4 = -5(x + 8) click to select points on the graph.…
To graph the line \( y + 4=-5(x + 8) \), plot the points \( (-8,-4) \) and \( (-9,1) \) (or other points found using the slope - point form or slope - intercept form) and draw a s…
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solve the inequality $y - 8 > -6$. $y - 8 > -6$ $\\underline{\\quad\\qu…
The solved inequality is $\boldsymbol{y > 2}$. For the graph: place an open circle at 2 on the number line, and shade the region to the right of 2. All values greater than 2 are i…
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1 calculate the distance from the point a(-3,2) to the line y = 2x + 1.…
s: 1. \( \boldsymbol{\frac{7\sqrt{5}}{5}} \) 2. \( \boldsymbol{\frac{3\sqrt{2}}{2}} \) 3. \( \boldsymbol{\frac{4}{5}} \) 4. \( \boldsymbol{\sqrt{5}} \) 5. \( \boldsymbol{\frac{6\s…
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1 the cost for an upcoming field trip is $30 per student. the cost of t…
B. 30, D. 90 ### Question 2 The area of a rectangle \( A=l\times w \), given \( A = 24\space cm^{2}\), so the length \( l=\frac{24}{w}\), and the width \( w>0\) (since width of a …
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cyu perimeter and area of composite shapes 1. determine the area and pe…
### Part (a) #### Step 1: Analyze the Composite Shape The shape can be considered as a rectangle formed by combining the given segments. Let's find the length and width. - The hor…
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cyu perimeter and area of composite shapes 1. determine the area and pe…
Perimeter: \(\boldsymbol{48}\) m, Area: \(\boldsymbol{71}\) m² ### Part (b)
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let’s start by looking at angle abc. click the button to display the pr…
\( 80^\circ \)
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lets start by looking at angle abc. click the button to display the pro…
To solve for the measures of the interior angles of triangle \( ABC \) and their sum, we follow these steps: ### Step 1: Measure \( \angle ABC \) Use a protractor to measure \( \a…
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1. what is the value of x? 83 58
58
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answer the following question in the picture. * lesson 8: exit ticket a…
\(\sin(D)=\frac{4}{5}\), \(\cos(D)=\frac{3}{5}\), \(\tan(D)=\frac{4}{3}\)
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use the given information to prove that $\\triangle sqr \\cong \\triang…
The reason for step 3 is "Hypotenuse - Leg (HL) Congruence Theorem (since \(\triangle SQR\) and \(\triangle QSP\) are right triangles, \(\overline{SQ}\cong\overline{SQ}\) (reflexi…
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3x - y = 9 click to select points on the graph.
Plot the points $(3, 0)$, $(0, -9)$, and $(2, -3)$, then draw a straight line through them to graph $3x - y = 9$.
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11. \\begin{cases} y \\leq -\\frac{3}{5}x \\\\ y > -x - 4 \\end{cases}
The solution is the overlapping shaded region: below the solid line $y=-\frac{3}{5}x$ and above the dashed line $y=-x-4$. (On the provided grid, this overlapping area covers point…
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independent practice write and solve an equation to find the measures o…
\(\angle A = 76^\circ\), \(\angle B = 63^\circ\), \(\angle C = 41^\circ\) ### Problem 2:
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6. which angle pairs form complementary angles? diagram with angles at …
The complementary angle pairs are \(\angle ABE\) (25°) and \(\angle EBF\) (65°), and \(\angle DBE\) (50°) and \(\angle FBC\) (40°). (Or in terms of angle labels: \(\angle ABE\) an…
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y - 7 = -\\frac{9}{5}(x + 10) click to select points on the graph. grap…
Plot the points $(-10, 7)$, $(-5, -2)$, and $(0, -11)$, then draw a straight line through them.
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use the given information to prove that $\\triangle def \\cong \\triang…
To prove $\triangle DEF \cong \triangle HGF$, we use the AAS (Angle - Angle - Side) congruence criterion: ### Step 1: Identify Vertical Angles - **Statement**: $\angle DFE \cong \…
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5. $\\angle m$ and $\\angle n$ are supplementary and $m\\angle m = 37^\…
\(37 + 13x = 180\) ### Part b: Solve for \(x\) and \(m\angle N\)
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read the following passage from night. in the passage, elie wiesel and …
C. It highlights Meir Katz’s initial strength so the reader can better understand how dramatically he changes during the journey.
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solve the inequality and graph the solution. $u + 10 < 19$ to draw a ra…
The solution to the inequality \( u + 10<19 \) is \( u<9 \). For graphing, place an open circle at 9 (if the number line is extended to 9) and draw a ray pointing to the left.
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16. the volume of the rectangular prism below is $36x^6y^8$. determine …
### Question 16 (Volume of Rectangular Prism) # Explanation: ## Step 1: Recall Volume Formula The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), …
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solve the inequality and graph the solution. w - 6 ≤ 3 to draw a ray, p…
The solution to the inequality is \( w\leq9 \). For the graph, plot a closed circle at 9 on the number line and draw a ray pointing to the left.
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problem set 1: properties of real numbers identify the property that ju…
Let's solve each problem by identifying the property of equality or congruence: ### Problem 1 - **Statement**: \( m\angle ABC = m\angle XYZ \) - **Property**: Reflexive Property (…
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solve the inequality and graph the solution. \\(\frac{r}{2} > 4\\) to d…
The solution to the inequality is \(r > 8\). To graph it, plot an open circle at 8 (since the inequality is strict, \(r\) is not equal to 8) and draw an arrow to the right on the …
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solve the inequality and graph the solution. $c + 17 \\geq 20$ to draw …
The solution to the inequality is \( c \geq 3 \). To graph it, place a closed circle at 3 on the number line and draw an arrow pointing to the right.
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triangles independent practice write and solve an equation to find the …
\( \angle A = 76^\circ \), \( \angle B = 63^\circ \), \( \angle C = 41^\circ \) ### Problem 2: Triangle DEF
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solve the inequality and graph the solution. q - 2 ≤ 2 to draw a ray, p…
The solution to the inequality \( q - 2\leq2 \) is \( q\leq4 \). To graph it, plot a closed circle at 4 on the number line and draw an arrow pointing to the left.
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use the given information to prove that $\\triangle adb \\cong \\triang…
To prove $\triangle ADB \cong \triangle CDB$: 1. From $\overline{BD} \perp \overline{AC}$, we have $\angle ADB=\angle CDB = 90^{\circ}$ (definition of perpendicular lines). 2. Fro…
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solve the inequality and graph the solution.\\( j + 7 < 10 \\)\ to draw…
The solution to the inequality is \( j < 3 \). For the graph, there is an open circle at 3 and an arrow pointing to the left along the number line.
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solve the inequality and graph the solution. $f - 5 > 2$ to draw a ray,…
The solution to the inequality \( f - 5>2 \) is \( f > 7 \). For the graph, there is an open circle at 7 on the number line and an arrow pointing to the right from 7.
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name problem set 1: properties of real numbers > identify the property …
Reflexive Property of Congruence ### Problem 4: $GH \cong MN$ and $MN \cong OP$, so $GH \cong OP$
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use the given information to prove that $\\triangle def \\cong \\triang…
1. Reason for \(\overline{EF} \cong \overline{GF}\): Given 2. \(\angle EDF \cong \angle \boldsymbol{GHF}\) (Given) 3. Reason for \(\angle DFE \cong \angle HFG\): Vertical angles a…
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a number of squares are connected in a row to form a rectangle. the tab…
- The table can be represented by the equation $y = 4x + 4$. - The relation is a function. - The graph of the function is linear.
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what fraction of the entire 6 × 4 grid is covered with colored tiles? h…
\(\frac{2}{3}\)
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fractions simplifying fractions simplify each fraction by using the cor…
$\frac{1}{2}$ (GCF circled: 16) #### b) $\boldsymbol{\frac{27}{30}}$
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additional example 1 find the sum of the interior angles of the polygon…
The sum of the interior angles of the polygon (quadrilateral) is \( 360^{\circ} \)
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find the area of the figure below by first finding the areas of the rec…
- Area of the rectangle: \( 12 \) square units - Area of the triangle: \( 4 \) square units - Area of the figure: \( 16 \) square units