Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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the parade will begin at the intersection of the path that goes from po…
B. point E
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after the president of the united states is sworn into office, the pres…
A. line segment AB
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each rhombus piece has diagonals of 2 inches and 3 inches. what is the …
3 square inches
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question 7 18 ft $9\\frac{1}{4}$ ft find the area of this parallelogram…
166.5 square feet
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solve the following inequality. graph the solution set and write it in …
The solution to the inequality \(13x < 12x + 3\) is \(x < 3\). The interval notation is \((-\infty, 3)\). The graph of the solution set is option A.
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18. what is the scale factor of figure b to figure a? 19. given the sim…
18. $4$ 19. $x = \frac{280}{23}$ or $\approx 12.17$ 20. $EF = 12$ 21. $JK = 14.4$ 22. $10.5$ feet 23. D. $4\frac{8}{9}$ feet 24. A. $\frac{64}{84} = \frac{x}{92}$ 25. $x = \frac{1…
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in exercises 1–4, find the sum of the measures of the interior angles o…
The sum of the interior angles of a nonagon is \( 1260^\circ \). ### Exercise 2: 14 - gon
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the sides of a triangle measure 35 in, 42 in, and 43 in. find its area.…
\( 677.5 \)
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the sides of a triangle measure 18 mm, 29 mm, and 17 mm. find its area.…
\(142.0\)
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the sides of a triangle measure 8 mm, 12 mm, and 18 mm. find its area. …
\(38.3\)
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the sides of a triangle measure 32 m, 36 m, and 37 m. find its area. wr…
\(524.6\)
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what is the value of x? 1) 10 2) 28 3) 32 4) 40 4 in the diagram below,…
1) 27
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what is the value of x? 1) 10 2) 28 3) 32 4) 40 4 in the diagram below,…
# Explanation: ## Step1: Find ∠LMO in isosceles △LMO Since \( LO = MO \),[SSE onError error]
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graph the image of p(4, 7) after a translation along < 1, -9 > and a re…
The image of \(P(4, 7)\) after the given transformations is \((-1, -2)\)
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△lmn is rotated about point p to create the image △lmn. ( mangle lpl = …
$m\angle L'M'N'=\boldsymbol{34}$° $LN=\boldsymbol{2.5}$ cm $m\angle NPN'=\boldsymbol{105}$°
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the point f(-3, 4) is reflected over the line y = x. what are the coord…
$(4, -3)$
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find the area of a circle with radius 8 yd. use the value 3.14 for π, a…
\( 200.96 \) square yards
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kuta software - infinite pre - algebra slope find the slope of each lin…
1) $\frac{-1}{3}$ 2) $3$ 3) $\frac{-2}{3}$ 4) $\frac{3}{2}$ 5) $\frac{5}{3}$ 6) $2$ 7) $-3$ 8) $3$
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the formula for finding the volume of a ________ is $v = \\frac{1}{3}\\…
cone ### Sub - Question 2
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find the value of x. x = \\square
\(x = \frac{3}{2}\) or \(x = 1.5\)
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find the value of x. x = \\square
\(x = 7\)
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17 the coordinates of the vertices of the triangle shown are p(2,13), q…
13
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question travis is 1.85 meters tall. at 2 p.m., he measures the length …
The height of the tree is approximately \(\boldsymbol{2.07}\) meters? Wait, no, wait, I think I messed up the shadow length. Wait, maybe the distance from Travis to the tree is th…
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question to indirectly measure the distance across a lake, jose makes u…
\( 158.66 \) meters
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the diagram shows a convex polygon. what is the value of ( u )? ( u = s…
$u = 6$
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drag the endpoints of the segment below to graph ( y = h^{-1}(x) ).
The endpoints of $y=h^{-1}(x)$ are $(7, 5)$ and $(4, 8)$; plot and connect these two points to graph the inverse segment.
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show what you know graph the solutions to $-3 > -2x + 9$. $-3 > -2x + 9$
The solution to the inequality \( -3 > -2x + 9 \) is \( x > 6 \). The graph should have an open circle at 6 and shading to the right of 6 on the number line.
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note: figure is not drawn to scale. if x = 4 units, y = 6 units, and h …
36 square units
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divide: \\overline{\\begin{array}{r}\\square\\end{array}} r \\square \\…
The quotient is 1 and the remainder is 317, so the answer is \( 1 \) R \( 317 \)
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9) $y = 2(x + 3)^2 - 2$ v: $(-3, -2)$ a.s: -3 follow up questions. para…
To analyze the parabola \( y = 2(x + 3)^2 - 2 \) and sketch it (or confirm its vertex and axis of symmetry): ### Step 1: Identify the Vertex Form The vertex form of a parabola is …
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solve and graph a. solve $25 - 4x < 1$. b. graph the solutions to the i…
\( x > 6 \) ### Part b: Graph the solution \( x > 6 \) To graph \( x > 6 \) on a number line: 1. Locate 6 on the number line. 2. Draw an open circle at 6 (since \( x \) is not equ…
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what is the area of the object shown? (the figure has a blue shape with…
78 cm²
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00 4 5 256 283 28 in 5 in 7 in 17 in 10 in 7 in 11 in 5 in 6 in 16 in t…
283
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text description for graph a. (0, -3) b. (0, -5) c. (5, -5) d. (6, 0)
C. (5, -5)
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Question was provided via image upload.
$x = 40$
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which angles are vertical to ∠6? select all that apply. ∠1 ∠2 ∠3 ∠8
∠8
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a field is shaped like a trapezoid with the dimensions shown. what is t…
56250 square yards
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which angles are vertical to $\\angle 4$? select all that apply. $\\ang…
∠1
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a baseball diamond is a square with corners at home plate, first base, …
D. 900 square yards
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dilate point b by a scale factor of 1/2; (-1.5, 1); (-2, -2); (1.5, -4)…
(-1, -1.5)
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in a dilation what mathematical operation is used with the scale factor…
multiplication
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dilate point b by a scale factor of 3: (12, 12) (0, 12) (12, 0) (4, 3)
(12, 12)
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which term describes the slope of the line below? a. negative b. zero c…
A. Negative
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which of the following best describes the slope of the line below? a. p…
D. Zero
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5. examine the given information in the diagram shown. use the informat…
C. $117^\circ$
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which graph decreases, crosses the y-axis at (0, −7), and then increase…
C. Graph C
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find t. write your answer in simplest radical form. units
\(17\)
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find g. write your answer in simplest radical form. millimeters
\(7\sqrt{3}\)
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5. examine the given information in the diagram shown. use the informat…
A. $146^\circ$
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in exercises 5–8, point ( d ) is the centroid of ( \triangle abc ). fin…
5. $CD=10$, $CE=15$ 6. $CD=22$, $CE=33$ 7. $CD=18$, $CE=27$ 8. $CD=30$, $CE=45$
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2. △efg ~ △_ehg_ by ______
$\triangle EFG \sim \triangle \boldsymbol{EHG}$ by **AA (Angle - Angle) Similarity Criterion** (or ASA, but AA is more appropriate for similarity)
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4. workers at a construction company are building a triangular enclosur…
A. 24 inches, E. 170 inches
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3. examine the given information in the diagram. use the information to…
C. 160°
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sort the words according to the meanings of their shared roots. enclose…
- shut: enclose, closet - angle: polygon, septagon, octagon - place or put: position, pose, dispose
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2. gerald and jessie are deciding which measure to use for the third si…
C. $27 < x < 77$
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Question was provided via image upload.
\( \triangle ABC\cong\triangle \boldsymbol{ADC} \) by \(\boldsymbol{SSS}\) (Side - Side - Side) congruence criterion.
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1. examine the sets of numbers and decide which set are the sides of a …
B. 3 cm, 4 cm, 5 cm D. 5 cm, 6 cm, 9 cm
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20. rotate the coordinate (3, 5) 90° counter - clockwise around the poi…
1. For question 20: $(-12, -6)$ 2. For question 21: $(-4, -7)$
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find the circumference and the area of a circle with diameter 6 m. use …
Circumference: \( 18.84\) meters Area: \( 28.26\) square meters
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rotations about a point (non - origin) whats the process? make your own…
The 3-step process for rotating a shape about a non-origin point $(h,k)$ is: 1. Translate all vertices by subtracting the rotation point coordinates: $(x,y) \to (x-h, y-k)$ 2. App…
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sort the words according to the meanings of their shared roots. cent pe…
- circle: unicycle, recycling, bicycle - hundred: cent, percent, centigrade
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sort the words according to the meanings of their shared roots. subserv…
- Under "serve": subservient, servant, service - Under "circle": encircled, circuit, circus
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sort the words according to the meanings of their shared roots. liberty…
- straight: rectangle, indirectly, direct - free: liberty, liberate, liberal
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in exercises 1–4, point ( p ) is the centroid of ( \triangle lmn ). fin…
1. $QP=3$, $PN=6$ 2. $QP=7$, $PN=14$ 3. $QP=10$, $PN=20$ 4. $QP=14$, $PN=28$
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the vector that translates a(-2, 7) to a(6, 4) is < , >.
\(\langle8, - 3 angle\)
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analyzing a real - world volume problem a carpenter designs two cabinet…
- The cabinets have the same base area. - The cabinets may have the same base dimensions. - The cabinets may have different base dimensions.
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refer to the graph. a translation select choice map $\\triangle abc$ to…
To solve this, we analyze the translation (shift) of triangle \( \triangle ABC \) to \( \triangle EFG \). ### Step 1: Identify Coordinates (Assume Grid Units) Let’s find coordinat…
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a type of cracker, rectangular in shape, is stored in a vertical column…
$\frac{1}{8}$ inch
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which is the image of ( p(-5, 11) ) along the vector ( langle 3, -8 ang…
D) \( P'(-2, 3) \)
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determining missing lengths in the right triangular prism below, \\(\\o…
12
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determining missing values in expressions for volume the figure below i…
$a=2$, $b=3$, $c=6$
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18. the coordinates of two points, and their images, are given below a …
A 90° counterclockwise rotation about the origin. --- ### Problem 19
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finding the volume of an oblique prism an oblique hexagonal prism has a…
168 cubic centimeters
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practice solving for the volume of right and oblique prisms. the figure…
$\frac{1}{2}x^3$
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△abc and △cde are shown below. which statement is true? △abc is similar…
$\triangle ABC$ is similar to $\triangle CDE$.
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solve for x. 34 x° 84° 32 x = ?° law of sines (\frac{sin a}{a}=\frac{si…
\( 69.51 \)
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2. if the triangles are similar, find the length of side f. e = \\frac{…
$\boldsymbol{\frac{5}{12}}$ mi (Option C: $\frac{5}{12}$ mi)
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what is the area of this figure? 3 mm 8 mm 2 mm 2 mm 7 mm 8 mm 2 mm 6 m…
118 square millimeters
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what is the area of this figure? 13 mi 3 mi 7 mi 6 mi 6 mi 6 mi 3 mi 8 …
99 square miles
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1. if the trapezoids are similar, find the length of side w. y = 80 mm,…
112 mm
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13. in the figure below, triangle efg is reflected across the horizonta…
$-1$ --- ### Question 14
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10) use the situation to answer the question. the scale drawing of a re…
$\boldsymbol{\frac{25\ \text{mm}^2}{1\ \text{yd}^2}}$ (corresponding to the second option)
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1. the diagram below shows a parallelogram. image of parallelogram with…
1. D 240 cm 2. A $28\ \text{m}^2$ 3. D 8 ft × 12 ft 4. B 22 in.
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knows the diameters of all the lids in her kitchen. which equation coul…
A. $\frac{60}{\pi}=d$
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8) use the situation to answer the question. the scale drawing of a rec…
Length: 20 yd Width: 50 yd
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the area of a triangular piece of roof siding is 74 square feet. find t…
18.5 feet
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6) find the area of the figure. the area of a parallelogram - shaped ci…
2.3 mm
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variables and algebraic expressions evaluate ( n - 5 ) for each value o…
3 ### Problem 2: Evaluate \( n - 5 \) for \( n = 121 \)
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a large pond takes up 2,700 square meters of land. if the length of the…
45 meters
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4) find the area of the figure. 25 in 125 in² 625 in² 750 in² 165 in²
625 $\text{in}^2$ (Option: 625 $\text{in}^2$)
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3) find the area of the figure. \\(\\frac{16}{3}\\) yd \\(\\frac{3}{4}\…
4 yd²
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2) find the area of the figure. 0.08 m 0.04 m 0.0016 m² 0.0032 m² 0.000…
0.0016 $\text{m}^2$ (Option 1: 0.0016 $\text{m}^2$)
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1) find the area of the figure. 100 cm 55 cm 60 cm 5,500 cm² 4,650 cm² …
4,400 cm²
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1) use the similar triangles for the following problem. use proportions…
b = 6m
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5) the two triangles are similar. set up and solve a proportion to find…
$s = 1\frac{1}{2}$ yd (matches the second option: $\boldsymbol{s = 1\frac{1}{2}}$ yd)
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use a quadratic function to model the area of the rectangle. graph the …
$f(x)=2x^2+8x+6$
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consider the figure below. a) what is the exact perimeter of the figure…
The exact perimeter is \( \boldsymbol{92\pi + 184} \) inches (or \( \boldsymbol{92(\pi + 2)} \) inches, or simplified further as needed). ### Part (b)
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what is the perimeter of the figure below? you may round your answer to…
The perimeter of the figure is approximately $\boxed{185.66}$ feet.
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which rule explains why these triangles are congruent? options: sas, ss…
AAS
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deriving a tangent ratio for special triangles which statements are tru…
- \( \text{NM}=x \) (True) - \( \text{LM}=x\sqrt{2} \) (True) - \( \tan(45^{\circ}) = 1 \) (True)