Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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the figure shows square klmn. which of the following conditions satisfi…
The correct option is the one with \( \overline{LM} \parallel \overline{KN} \) (the last option, assuming the options are listed as: \( \overline{LK} \cong \overline{LN} \), \( \o…
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both circles have the same center. the circumference of the inner circl…
8704.08
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15) identify the error made in the following problem, then solve it cor…
15) Where was the error? Line 2 What was the error? Incorrect combination of like terms (should be \(2x - 3x=-x\), not \(-5x\))
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what is the area of the shaded region? 74 in 44 in 88 in 41 in square i…
4708 square inches
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what is the total area of the figure below?
141 square inches
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how many triangles are contained in the figure? there are □ triangles i…
13
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which is the correct measurement for the location marked by the arrow? …
A) 30.046
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for exercise 8, answer the question. 8. stem connection all snowflakes …
The snowflake has 6 - fold rotational symmetry. The basic triangular design (from the folded paper) is rotated around the center of the snowflake. The angle of each rotation is $\…
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both circles have the same center. the circumference of the inner circl…
6154.4
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what is the area of the shaded region? 70 m 42 m 100 m 21 m square mete…
# Explicación: ## Paso1: Área del rectángulo grande $A_{\text{grande}} = 100 \times 70 = 7000 \, \text{m}^2$ ## Paso2: Área del rectángulo pequeño $A_{\text{pequeño}} = 42 \times …
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the diagram shows a scale drawing of a sports field. the diagram is 5½ …
6,600 square yards
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for exercises 3-7, use the figure to answer the questions. 3. where wil…
The point \( W \) will be at \( Z \) after a \( 90^\circ \) clockwise rotation about \( A \).
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what is the area of the shaded region? 26 km 26 km 60 km 60 km square k…
2924 square kilometers
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what is the area of the shaded region? 86.8 mm 64.4 mm 52.6 mm 70.9 mm …
1383.34
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what is the area of the shaded region? 78 cm 58 cm 49 cm 91 cm square c…
4256
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what is the volume of the rectangular prism? type the answer in the box…
$\frac{15}{4}$
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both circles have the same center. what is the area of the shaded regio…
4024.39
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what is the area of the following circle? either enter an exact answer …
If we use the exact form in terms of \( \pi \), the area is \( \pi \) square units. If we use \( 3.14 \) for \( \pi \), the area is \( 3.14 \) square units.
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find the surface area of the prism using the net. what is the area of t…
48
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find the area of a circle with a circumference of 6.28 units.
\( 3.14 \)
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the image contains four coordinate plane graphs (with x-y axes, grids) …
The graph in the top-right (third graph) represents a function.
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for exercises 3-7, use the figure to answer the questions. 3. where wil…
\( T \) ### Problem 4:
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find the surface area of the pyramid using the net. find the area of th…
- Square base: \( 64 \, \text{cm}^2 \) - Triangular sides: \( 128 \, \text{cm}^2 \) - Total surface area: \( 192 \, \text{cm}^2 \)
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what is the area of the shaded region? diagram of a large triangle (bas…
1664 square yards
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∠q and ∠r are complementary. the measure of ∠q is 26° less than the mea…
\( m\angle Q = 32^\circ \), \( m\angle R = 58^\circ \)
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find the surface area of the pyramid using the net. 10 cm (arrow to tri…
s: Square Base: \( \boldsymbol{36} \, \text{cm}^2 \) Triangular sides: \( \boldsymbol{120} \, \text{cm}^2 \) Total surface area: \( \boldsymbol{156} \, \text{cm}^2 \)
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what is the area of the shaded region? 50 mi 50 mi 30 mi 30 mi square m…
1600 square miles
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the measure of an angle’s supplement is 76° less than the measure of th…
measure of the angle = $128^\circ$, measure of the angle's supplement = $52^\circ$
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find the surface area of the cube using the net. find the area of one s…
One square: $\boldsymbol{81}$ $cm^2$ Surface area: $\boldsymbol{486}$ $cm^2$
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∠e and ∠f are complementary. the measure of ∠e is 54° more than the mea…
\( m\angle F = 18^\circ \), \( m\angle E = 72^\circ \)
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what is the area of the shaded region? image of a larger right triangle…
235
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find the surface area of the prism using the net. find the area of the …
- Triangular bases: \( 42 \) \( cm^2 \) - Side rectangles: \( 252 \) \( cm^2 \) - Total surface area: \( 294 \) \( cm^2 \)
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determine the number of triangles (of any size) in the figure. the tota…
12
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what is the area of the shaded region? 31 m 39 m 19 m 15 m square meters
924 square meters
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find the area of a circle with a circumference of 50.24 units.
\( 200.96 \)
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name practice for exercises 1 and 2, use the figure to answer the quest…
### Problem 1: Rotation 90° Clockwise about \( P \) #### Explanation: To determine the position after a 90° clockwise rotation about point \( P \): 1. **Understand Rotation Rules*…
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what is the area of the following circle? either enter an exact answer …
If using \( \pi = 3.14 \), the area is \( 153.86 \) square units. If using the exact form, the area is \( 49\pi \) square units.
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three hundred yards of fencing... to fence in a rectangular garden. the…
the maximum area that can be enclosed by the fencing
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what is the area of the shaded region? 24.5 mm 11.4 mm 11.4 mm write yo…
470.29
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find the area of a circle with a radius of 8. either enter an exact ans…
If in terms of \( \pi \), the area is \( 64\pi \) square units. If using \( 3.14 \) for \( \pi \), the area is \( 200.96 \) square units.
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which is the equation for a circle with center at $(-2, -4)$ that passe…
\((x + 2)^2 + (y + 4)^2 = 169\) (the first option)
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a line is graphed on a coordinate plane. answer choices: -3, -\\frac{1}…
3 (assuming the last option is 3, as the calculation shows the slope is 3)
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problem 1 simplifying square root expressions got it? what is the simpl…
s: 3. Circle \( \boldsymbol{8\cdot8 = 64} \) 4. \( \boldsymbol{8} \) 5. Number line (top): 20, 25, 30, 34, 36, 40; Square root number line (bottom): \( \sqrt{20} \), \( \sqrt{25}=…
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determine the number of triangles (of any size) in the figure. the tota…
# Explanation: ## Step1: Count smallest triangles The figure has 8 smallest (unit) triangles. ## Step2: Count triangles of 2 units By combining two adjacent small triangles, we ge…
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use the golden rectangles shown to the right to obtain an exact value f…
D. $\boldsymbol{\frac{1}{\Phi - 1}}$ ### Part (b)
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if lm = 7 and ln = 12, which of the following statements must be true? …
C. If points \( L \), \( M \), and \( N \) are collinear, then \( MN \) must be either \( 5 \) or \( 19 \)
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find the measures of two supplementary angles if the difference between…
B) \( 72.5^\circ, 107.5^\circ \)
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review 1. circle the numbers that are perfect squares. 1 12 16 20 100 1…
### Part 1: Circle Perfect Squares A perfect square is a number that is the square of an integer (e.g., \( n^2 \) where \( n \) is an integer). - \( 1 = 1^2 \) → Perfect square. -…
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if m || n and the slope of line m is 3, what is the slope of line n? a.…
D. 3
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graph the compound inequality on the number line. ( x geq 7 ) or ( x < …
# Explanation: ## Step1: Analyze \( x < 5 \) For \( x < 5 \), we use an open circle at \( 5 \) (since \( x \) is not equal to \( 5 \)) and draw an arrow to the left (towards negat…
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what should ∠1 be in order for path c and d to be parallel? path a 110°…
\( 110 \)
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one hundred yards of fencing is being used to fence in a rectangular ga…
The maximum area that can be enclosed by the fencing (assuming this is one of the options, e.g., if the options are labeled, say, B. The maximum area that can be enclosed by the f…
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given the information in the diagram and the table, how long is the wir…
The length of the wire is \(24\) feet.
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a city park has multiple paths around a green space. what should ∠2 be …
\(100\)
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choose the 2d shape created from the cross section. options: triangle, …
Square
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appendix b: extra practice multiplying binomials and factoring trinomia…
Let's solve question 13 step by step: ### Step 1: Recall the formula for the area of a rectangle The area \( A \) of a rectangle is given by the product of its length \( l \) and …
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graph the compound inequality on the number line. ( x > 0 ) and ( x < 3…
To graph \(0 < x < 3\) on the number line: 1. Place an open circle at \(0\) (since \(x eq0\)). 2. Place an open circle at \(3\) (since \(x eq3\)). 3. Shade the line segment betw…
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choose the 2d shape created from the cross section. rhombus rectangle s…
Rectangle
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choose the 2d shape created from the cross section. pentagon circle hex…
B. Circle
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choose the 2d shape created from the cross section. triangle hexagon re…
Rectangle
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use the figure shown. if ( mangle 4 = 96 ) and ( mangle 5 = 138 ), what…
B. 54
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choose the 2d shape created from the cross section. rectangle pentagon …
Hexagon
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when reflecting a figure across the y-axis, which coordinate(s) remain …
C. y-coordinates
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use the figure shown. if ( mangle 2 = 42 ) and ( mangle 6 = 126 ), what…
C. 96
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the point (4,1) is reflected in the y-axis. what are the coordinates of…
B. (-4,1)
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use the figure. what is the value of x? a. 38 b. 59 c. 83 d. 96
B. 59
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use the figure. figure: two intersecting triangles. left triangle has a…
D. 97
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shwanda draws a triangle on the coordinate grid and shifts it 2 units t…
D. \( f(x) = x + 2 \)
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if $overrightarrow{bd}$ bisects $angle abc$ and $mangle 3 = 80$, what i…
\( 50^\circ \)
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translate quadrilateral abcd by 2 units to the right and 4 units up. wh…
A'(7,7), B'(9,9), C'(11,7), D'(9,5)
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which polynomial represents the area of a rectangle with sides 3x and x…
c. \( 3x^3 + 6x^2 + 3x \)
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circle k has a diameter of 6 feet. what is the length of (overarc{jl})?…
\( \frac{3\pi}{4} \)
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the student says both x and y are 65. why is he incorrect? use the drop…
The student is incorrect because \(x\) and \(y\) \(\boldsymbol{\text{are not equal}}\). The angles with measures \(x^{\circ}\) and \(40^{\circ}\) are \(\boldsymbol{\text{complemen…
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expanding binomials using pascal’s triangle which row of pascal’s trian…
row 15
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identifying nets which net represents this shape?
The first net (with one rectangle and two circles, one on top and one on bottom of the rectangle)
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identifying nets which solid figure is made from this net?
The third solid figure (the blue cube - shaped one) is made from this net.
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which solid figure is made from this net?
The third solid figure (the purple triangular prism - shaped one)
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complete the paragraph to describe a rotation ( x^circ ) counterclockwi…
First blank: \( PA = PA' \) Second blank: \( x^\circ \)
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in all, eulers legacy included the introduction of the concept of funct…
- the notation for the imaginary unit - the idea of a functional relationship - the formalization of function notation - the notation for the base of the natural logarithm
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the behavior itself - the automatic action you take in response to the …
False
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identifying nets which solid figure is made from this net?
The third figure (the yellow cylinder)
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how many of each shape make a cylinder? enter the total number of shape…
3
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how many of each shape make a cylinder? enter the number of rectangles …
1
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does the point ((-1, sqrt{15})) lie on the circle centered at the origi…
Yes, because the equation for the circle is \(x^{2}+y^{2}=16\) and \((-1)^{2}+(\sqrt{15})^{2}=16\).
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(9x+14), (7x+84)°, 8x+17, 17x+3, (x+20), x°, (210-3x), (9x-14)°, (5x+86…
Let's solve each geometric problem one by one. ### 1. Vertical Angles (Top - Left) Vertical angles are equal. So we set \(9x + 14=7x + 84\) ## Step 1: Subtract \(7x\) from both si…
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exercise #1: classify each angle as acute, obtuse, right or straight. 1…
s: 1) Acute 2) Obtuse 3) Acute
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level 4 25) the average speed of marlons bike ride through the park can…
The total number of miles Marlon biked is \( \boldsymbol{10.75} \) miles (or \( \boldsymbol{10.8} \) miles if rounding for sig figs in addition, but likely just the sum here). ###…
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solve the inequality and graph the solution on the line provided. (15 +…
Inequality Notation: \( x < -6 \) For the number line: Place an open circle at -6 (since the inequality is strict, \( x \) is not equal to -6) and draw an arrow to the left of -6 …
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5 connecting concepts in exercises 45–48, find 45. diagram: parallelogr…
The height \( h \) is \( 4 \) feet.
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select the transversal connecting ∠5 and ∠15. then classify the relatio…
Transversal: \( d \); Relationship: corresponding angles
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determine the angle of rotation. choose 1 answer: a $-105^circ$ b $-75^…
B. \(-75^\circ\)
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triangle △a′b′c′ is the image of △abc under a rotation about the origin…
90 degrees (clockwise) or 270 degrees (counterclockwise), but typically 90 degrees is the answer here.
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determine whether each number is rational or irrational. chart with col…
- $-\frac{3}{7}$: Rational (select the circle under "Rational" for $-\frac{3}{7}$) - $\frac{\sqrt{99}}{3}$: Irrational (select the circle under "Irrational" for $\frac{\sqrt{99}}{…
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multiple choice 10 points which algebraic rule best represents the tran…
\((x - 1, y + 4)\) (the last option)
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warm-up: sequences of transformations five congruent figures are shown …
### First Row (Preimage: Figure P) #### Step 1: Reflect over the \( y \)-axis The reflection over the \( y \)-axis transforms a point \((x, y)\) to \((-x, y)\). Let's assume a ver…
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fill in the blank 45 points given △abc with points a(-2, 3), b(1, 0), a…
\(A'(-3, 6)\) \(B'(0, 3)\) \(C'(-4, 4)\)
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determine whether each number is rational or irrational. rational irrat…
- \( 0.\overline{6} \): Rational (circle the "Rational" option for \( 0.\overline{6} \)) - \( \frac{\sqrt{36}}{3} \): Rational (circle the "Rational" option for \( \frac{\sqrt{36}…
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given △abc with points a(-2, 3), b(1, 0), and c(3, 1), graph it, and it…
\(A'(-5, 3)\), \(B'(-2, 0)\), \(C'(0, 1)\)
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fill in the blank 25 points given △jkl with points j(1, -2), k(4, -1), …
\(J'(1, 4)\) \(K'(4, 3)\) \(L'(3, 5)\)
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classify each triangle as acute, right, or obtuse. also, classify each …
s: 1. Top - Left Triangle: Right, Isosceles 2. Top - Middle Triangle: Obtuse, Isosceles 3. Top - Right Triangle: Acute, Equilateral (or Acute, Equilateral (Isosceles)) 4. Bottom -…