几何
三角形、圆、解析几何与证明题。
-
5. there are two triangles, triangle pqr with angle at r being 57°, and…
If the question was to find \(\angle T\) in \(\triangle STU\), the answer is \(63^\circ\). If it was to find the third angle in \(\triangle PRQ\) (assuming we need to express it i…
-
amelia builds a cube - shaped flowerpot that is 5 inches on each side. …
\( 5\cdot5\cdot5 \)
-
the diameter, d, of a sphere is 18 cm. calculate the spheres volume, v.…
\( 3052.1 \)
-
the radius, r, of a sphere is 7.2 mm. calculate the sphere’s volume, v.…
1562.7
-
volume is the amount of space inside a three - dimensional figure. you …
27
-
4. in the figure, there are lines and angles: angle at c is 142°, angle…
\(x = 16\)
-
the dilation rule $d_{f,3}(x, y)$ is applied to $\\triangle abc$, where…
The distance in the y - coordinates from \(A(-2,2)\) to \(F(1,1)\) is \(\boldsymbol{1}\) unit(s).
-
pythagorean theorem only applies to right triangles. true or false fals…
True
-
the radius, r, of a sphere is 7.2 mm. calculate the spheres volume, v. …
1562.6
-
13. by inspecting the graph, what can you determine about the solution(…
The system of equations \(20y = 15x + 55\) and \(12y=9x + 33\) has infinitely many solutions because the two lines represented by the equations are coincident (they have the same …
-
14. choose the statement that correctly describes how many solutions th…
C. No solution because the slopes are equal and the \(y\)-intercepts are NOT equal
-
the pythagorean theorem has to do with shapes with more than five sides…
The option "right triangles and the relationship between the sides of right triangles." (the last option)
-
volume is the amount of space inside a three - dimensional figure. you …
\( 3 \cdot 3 \cdot 3 \)
-
amelia is building 3 square garden beds that are all the same size. she…
108
-
1. (options about angle sum: a. 90°, b. 180°, c. 360°, d. congruent mea…
D. Vertical ### Question 3
-
3. which of the following terms best describes the relationship between…
A. Adjacent
-
3 (8x - 34)° (4x + 12)° 80° (6x - 14)° ulum associates, llc copying per…
\(x = 22\)
-
2. what type of relationship to angles m and p have? image of intersect…
D. Vertical
-
10. use patterns and structure for each graph, draw a line to make a sy…
### Part a (No Solution) Draw a line parallel to the given line (same slope, different y - intercept). For example, if the given line is \(y = x\), draw \(y=x + 2\) (or any line w…
-
on circle o below, the measure of \\(\\overarc{fj}\\) is \\(84^\\circ\\…
\( 80 \)
-
amelia is building 3 square garden beds that are all the same size. she…
$3\times6^2$ (or $3\cdot6^2$)
-
amelia is building 3 square garden beds that are all the same size. she…
$3s^2$
-
7. how many solutions does this system have?
Infinitely many
-
2 in the figure, there is a triangle cba with angle at c being 38 degre…
\(x = 9\)
-
name: 1. which of the following is a true statement about supplementary…
B. The sum of their measures is \(180^\circ\)
-
amelia builds a square garden that is 6 feet on each side. which expres…
The correct expression to find the area of a square is \( s \cdot s \) (the first option in the given choices).
-
6. which is the best description of adjacent angles? f. two angles that…
F. Two angles that share a common side and a common vertex
-
use the diagram below for questions 16-18 in which p is the incenter of…
19. \( PO = \boldsymbol{21} \) 20. \( LO = \boldsymbol{27} \) 21. \( PL = \boldsymbol{3\sqrt{130}} \) (or approximately \( \boldsymbol{34.2} \)) 32. \( AC = \boldsymbol{70} \) 33.…
-
which expression represents the area of the garden? 6·6 when the unit y…
36
-
5. which pair of angles below appear to be supplementary? a. c. b. d.
D. \(125^\circ\) and \(55^\circ\)
-
the construction crew for a new store will dig a hole in the shape of a…
\( 13608 \, \text{ft}^3 \) ### (b)
-
4. which pair of angles shown below are vertical angles? a. 1 & 2 c. 2 …
B. 1 & 3
-
amelia builds a square garden that is 6 feet on each side. which expres…
\( 6 \cdot 6 \)
-
which expression represents the area of the garden? 6·6 \t 6·2 6+6+6+6 …
\( 6 \times 6 \) (the first option)
-
a factory makes candles. each candle is in the shape of a triangular pr…
9408
-
1. there is a triangle abc, with angle at b being 80 degrees. there is …
The measure of \( \angle A \) is \( 67^\circ \)
-
a factory makes bottled cologne. each bottle is in the shape of a trian…
30
-
area is the amount of space inside a two - dimensional figure. one way …
16
-
a factory makes aquariums. each aquarium is in the shape of a triangula…
576
-
40. $x - \\frac{1}{5} = -\\frac{4}{5}$ 41. $\\frac{n}{7} = 4.5$ 42. $7t…
\( x = -\frac{3}{5} \) ### Problem 41:
-
area is the amount of space inside a two - dimensional figure. one way …
\( 4 \cdot 4 \) (the last option among \( 2 + 4 \), \( 2 \cdot 4 \), \( 4 + 4 \), \( 4 \cdot 4 \))
-
given: (overline{qs}) bisects (angle tqr), (overline{tq} cong overline{…
1. (First blank) the problem states it (given) 2. (Second blank) \(\angle RQS\) 3. (Third blank) reflexive property (or "itself") 4. (Fourth blank) SAS (Side - Angle - Side) congr…
-
lesson 7 using angles to determine similar trian use the information gi…
If \(\angle ACB = 38^\circ\) (correcting a potential diagram misread), then \(\triangle ABC \sim \triangle XYZ\) by AA similarity (two angles equal: \(\angle A = \angle X = 62^\ci…
-
the dilation $d_{o,3} (x, y) \\to (3x, 3y)$ is performed on the pre-ima…
The true statements are: - $\boldsymbol{\angle A}$ corresponds to $\boldsymbol{\angle A'}$. - $\boldsymbol{\triangle ABC \sim \triangle A'AC'}$. (So the checked boxes should be th…
-
9: circle all of the numbers that are solutions to the following inequa…
B: -16, C: -19, F: -25
-
9. the sail below is in the shape of a triangle. is the sail a right tr…
A. Yes, because \( 15^2 + 36^2 = 39^2 \)
-
a rectangular paperboard measuring 20 in long and 15 in wide has a semi…
78.55 in
-
a training field is formed by joining a rectangle and two semicircles, …
376.4 m
-
jennas family went berry-picking at greenfield berry farm. they picked …
The inequality is \( r > 7 \). For the graph, place an open circle at 7 on the number line and draw an arrow pointing to the right (towards values greater than 7).
-
materials on earth that have an economic value the skills and knowledge…
The option with "Fertile farmland helps crops to grow" (the third option in the list of the question's options, the one with the blue circle indicating it's selected in the image,…
-
the volume of this cone is 3,532.5 cubic feet. what is the radius of th…
15.00
-
14 a circular clock has a minute hand that rotates from the center of t…
The end of the minute hand moves \( 4\pi \) centimeters (or approximately \( 12.56 \) centimeters).
-
a rose garden is formed by joining a rectangle and a semicircle, as sho…
120.54 feet
-
for her science fair experiment, layla is comparing how items float in …
The inequality is \( s < 16 \). For the graph, place an open circle at 16 on the number line and draw an arrow pointing to the left (towards values less than 16).
-
jada is getting ready for her schools pep rally next week. she grabbed …
The inequality is \( r \geq 18 \). For the graph, plot a closed circle at 18 on the number line and draw an arrow to the right.
-
in which figure is $\\angle 1$ congruent to $\\angle 2$?
The top - right figure (the second figure in the top row)
-
6. solve the system of equations by graphing. 7 $y = -x + 7$ $5x + 5y =…
For problem 7 (system $y=-x + 7$ and $5x + 5y = 10$): No solution (parallel lines). For problem 9 (system $y=\frac{3}{2}x - 2$ and $y = 2x - 1$): Solution is $x=-2$, $y=-5$ (or th…
-
find the surface area of a cylinder with a base radius of 2 m and a hei…
\( 87.92 \, \text{m}^2 \)
-
find the surface area of a cylinder with a height of 9 in and a base di…
\( 439.6 \) square inches (or \( 439.6 \text{ in}^2 \))
-
find the surface area of a cylinder with a height of 8 in and a base ra…
\( 301.44 \) square inches (or \( 301.44 \text{ in}^2 \))
-
every year, oakwood community center holds a bike-a-thon to raise money…
The inequality is \( m \geq 28.5 \). For the graph, plot a closed circle at 28.5 and draw an arrow to the right.
-
identifying additional information needed to show that $\\triangle fgh …
2. \(\boldsymbol{\angle G\cong\angle K}\) and \(\boldsymbol{\overline{GH}\cong\overline{KL}}\) 5. \(\boldsymbol{\overline{FH}\cong\overline{JL}}\) and \(\boldsymbol{\overline{HG}\…
-
unit: systems of equations homework 3 name date pd solving systems by g…
1. the same 2. the same 3. different 4. the same 5. different
-
the happy pup pet shop sells homemade dog biscuits. leon is buying 25 b…
The inequality is \( b < 9 \). For the graph, plot an open circle at 9 and draw an arrow pointing to the left (towards numbers less than 9).
-
7. michael is using computer software to design a new logo for his comp…
B. rotation
-
what is the volume of this figure? 2 ft. 4 ft. 2 ft. 6 ft. 4 ft. 3 ft. …
72
-
a surveyor wants to know the length of a tunnel built through a mountai…
\( 359.4 \) meters
-
find the slope 6.
\(-1\)
-
4. find the measure of angle t.
\( 60^\circ \)
-
name the marked angle in 2 different ways.
\( \angle PNO \) and \( \angle ONP \) (or \( \angle MNP \) and \( \angle PNM \), depending on the diagram; but based on the rays, likely \( \angle PNO \) and \( \angle ONP \))
-
a shipping container will be used to transport several 120-kilogram cra…
D. \( 25500 \geq 120x + 7900 \) (assuming the last option is D; if options are labeled as per the circles, the correct one is the fourth option: \( 25500 \geq 120x + 7900 \))
-
square abcd is the final image after the rule $t_{-4,-1} \\circ r_{y, w…
# Explanation: ## Step1: Identify \( A'' \) coordinates From the graph, \( A'' \) has coordinates \( (-3, -4) \). ## Step2: Reverse translation \( T_{-4,-1} \) To reverse \( T_{-4…
-
graph this function. $y = |x|$ click to plot the vertex first.
The vertex of the function \( y = |x| \) is at the point \((0,0)\). To complete the graph, plot additional points such as \((1,1)\), \((-1,1)\), \((2,2)\), \((-2,2)\) and connect …
-
two parallel lines are crossed by a transversal. what is the value of b…
b = 52
-
using the graph, determine the coordinates of the y-intercept of the pa…
The coordinates of the y - intercept of the parabola are \((0, - 4)\) (and the answer type is "One point" as the y - intercept is a single point on the graph).
-
answer the questions below. write your answers in simplest form. (a) a …
(a) \( \boxed{12} \) yd (b) \( \boxed{8} \) ft
-
using transformations to prove congruence is there a rigid transformati…
yes, because a reflection across \(\overline{BA}\) will map \(\triangle ABC\) to \(\triangle ABD\)
-
solve the following inequality and graph the solution set on a number l…
The solution to the inequality \(4 < x + 9 < 6\) is \(-5 < x < - 3\). The graph of the solution set on the number line has open circles at \(-5\) and \(-3\) and the region between…
-
refer to the number line. find the coordinate of point x such that the …
\( 2.5 \) (or \( \frac{5}{2} \))
-
graph the image of δklm after a dilation with a scale factor of 3, cent…
The dilated triangle has vertices at \( K'(-9, 0) \), \( L'(-9, 9) \), \( M'(9, -6) \). (Graph by plotting these points and connecting them.)
-
write the coordinates of the vertices after a dilation with a scale fac…
- \( B'=(0, 3) \) - \( C'=(3, 0) \) - \( D'=(-3, 3) \)
-
the point p(-3, 4) is reflected over the x - axis. what are the coordin…
\((-3,-4)\)
-
for each part below, write an inequality to represent the given stateme…
### Part (a) Inequality: \( 7 < a < 14 \) Graph: Open circles at 7 and 14, shade between them on the number line (1 - 15 with 7, 8, 9, 10, 11, 12, 13 shaded between 7 and 14). ###…
-
what is an equation of the line that passes through the points (-1, -2)…
The equation of the line is \( y = 3x+1 \) (or other equivalent forms like \( 3x - y=-1 \) or \( y+2 = 3(x + 1) \))
-
which rule describes the composition of transformations that maps $\\tr…
# Explanation: ## Step1: Recall Transformation Notation - \( R_{O, 90^\circ}(x, y) \) means a 90° rotation about the origin, with the rule \( (x, y) \to (-y, x) \). - \( T_{a, b}(…
-
question move at least one of the 5 guide points below to complete the …
To graph \( y = x^2 - 2 \) from \( y = x^2 \): 1. Move the blue vertex point (originally at \((0,0)\)) down 2 units to \((0, -2)\). 2. Move each red point down 2 units (e.g., \((1…
-
name the marked angle in 2 different ways. answer attempt 2 out of 2 ∠ …
\( \angle EBC \), \( \angle B \) (or \( \angle CBE \), \( \angle B \))
-
the point s(4, 5) is reflected over the y - axis. what are the coordina…
\((-4,5)\)
-
the equations of three lines are given below. line 1: $4x - 10y = -6$ l…
Line 1 and Line 2: Perpendicular Line 1 and Line 3: Perpendicular Line 2 and Line 3: Parallel
-
a right triangle has side lengths d, e, and f as shown below. use these…
\( \sin x = \boldsymbol{\frac{d}{f}} \) \( \cos x = \boldsymbol{\frac{e}{f}} \) \( \tan x = \boldsymbol{\frac{d}{e}} \)
-
for the right triangles below, find the exact values of the side length…
\( c = 2\sqrt{3} \) \( d = \frac{3\sqrt{2}}{2} \)
-
the graph of the function h(x) is shown. find the function values h(5),…
\( h(5)=\boxed{2} \) \( h(7)=\boxed{6} \) \( h(8)=\boxed{2} \)
-
37. given: \\(\\overline{ab} \\parallel \\overline{cd}, \\overline{bc} …
The completed proof table is as shown above, and the key steps use properties of parallel lines (AIA), reflexive property, ASA congruence, and CPCTC to prove $\overline{AD} \cong …
-
draw a line representing the ise\ and a line representing the un\ of th…
\(-1\)
-
question in \\(\\triangle klm\\), \\(l = 9\\) inches, \\(k = 8.6\\) inc…
First possible angle: \(79.6^{\circ}\), Additional angle: \(100.4^{\circ}\)
-
prove the following statement using the given pieces of information giv…
Reflexive property of \( \cong \)
-
which of these relations are functions? select all that apply.
The top - left graph, the top - right graph, and the bottom - right graph.
-
find ( mangle u ). write your answer as an integer or as a decimal roun…
\( 48.9 \)
-
which of the following transformations carry this regular polygon onto …
- Rotation of \( 90^\circ \) clockwise - Rotation of \( 90^\circ \) counterclockwise - Reflection across \( l \) (Note: The "rotation of \( 30^\circ \) clockwise" is incorrect and…
-
consider the line $y = \\frac{2}{3}x$. what is the slope of a line perp…
Slope of a perpendicular line: \(-\frac{3}{2}\) Slope of a parallel line: \(\frac{2}{3}\)