Geometrie
Dreiecke, Kreise, Koordinatengeometrie und Beweisaufgaben.
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what is the volume of the piece of wood in the figure has a mass? image…
165
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23. model with math what is the width of the rectangle written as an ex…
The width of the rectangle is \( 10^{1}\, \text{m} \) (or \( 10\, \text{m} \)).
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use the figure to the right to find its area in square units. the area …
60
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9. write the equation for the plane with normal $\\vec{n}$ which passes…
### Part (a) #### Step 1: Write the vector form We know that the vector form of the plane equation is \([(x,y,z)-P]\cdot\vec{n} = 0\). Given \(P=(4,5,6)\) and \(\vec{n}=\langle1,2…
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the formula for the area a of a triangle is ( a = \frac{1}{2}bh ). solv…
\( h = \frac{2A}{b} \)
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if \\(\\vec{v} = \\langle 4, -8 \ angle\\) and \\(\\vec{w} = \\langle 5…
\(\vec{v}-\vec{w}=\langle - 1,-10 angle\)
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absolute value: number lines circle the correct description of the numb…
### Part a: Correct Description of Number Line To determine the correct description, recall that the absolute value of a number \(|x|\) is its distance from 0, and the opposite of…
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5 triangle lmn with vertices l(0, 3), m(3, 4), and n(1, 2): a) 180° rot…
### Part (a): 180° Rotation about the Origin To rotate a point \((x, y)\) 180° about the origin, we use the rule: \((x, y) \to (-x, -y)\). #### Step 1: Rotate \( L(0, 3) \) Applyi…
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using exponents, write two equivalent expressions for the area of the r…
(Assuming length \( = x^{2}\), width \( = x^{3}\)) Two equivalent expressions are \( \boldsymbol{x^{2}\times x^{3}} \) and \( \boldsymbol{x^{5}} \) (The answer will vary depending…
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7. a billboard has the given dimensions.
The area of the billboard is \(\boldsymbol{784}\) square feet.
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4) rotation 90° clockwise about the origin
To solve the problem of rotating triangle \( FGH \) \( 90^\circ \) clockwise about the origin, we first need to identify the coordinates of the vertices \( F \), \( G \), and \( H…
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your answer is partially correct. (c) what are the components of the ve…
The components of vector \(\vec{c}\) are \(\langle -2, -5, 0 angle\) m.
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drag over the word that goes best with the image metric system prefix u…
meter (or kilometer, but more likely meter as a base metric unit)
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which angles are complementary to ∠adb? select all that apply. diagram:…
\(\angle BDC\) (or \(\angle CDB\)) (Note: If we consider the diagram's right - angle, \(\angle ADB+\angle BDC = 90^\circ\), so \(\angle BDC\) (same as \(\angle CDB\)) is complemen…
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3. rhombus pqrs with vertices p(-1, -3), q(3, -4), r(4, -8), and s(0, -…
### Part a) Translation along vector \(\langle 4, 10 angle\) To translate a point \((x, y)\) along the vector \(\langle a, b angle\), we use the rule \((x + a, y + b)\). #### Step…
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ve and graph the following compound inequalities 18. ( 4x leq 48 ) or (…
The solution to the compound inequality \(4x \leq 48\) or \(x - 9 \geq 30\) is \(x \leq 12\) or \(x \geq 39\). For graphing, we would have a number line with a closed circle at 12…
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if two lines are parallel, what must be true about their slopes? a. the…
b. They must be the same.
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name the quadrant in which the angle θ lies. sin θ > 0, cos θ < 0 choos…
Quadrant II
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what is an angle that is adjacent to ∠aeb?
$\angle CEB$ (or $\angle DEB$, $\angle HEB$ are also possible, but based on the diagram and the given box, $\angle CEB$ is a valid adjacent angle)
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a circle has a circumference of 7,850 units. what is the radius of the …
1250
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which scenario describes a real-world application of understanding slop…
a. Designing parallel roads in urban planning
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find the values of x and y. (3x)° (2y + 6)° (8y − 102)° (boxes with x =…
\(x = 20.4\), \(y = 27.6\)
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the formula for the area of a triangle is ( a = \frac{bh}{2} ). solve f…
\( b = \frac{2A}{h} \)
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what is the slope of a line perpendicular to a line with a slope of -3?…
b. \(\frac{1}{3}\)
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graph the following function on the axes provided. $f(x) = \\begin{case…
To graph the piece - wise function: 1. For $y=-x - 1, - 4\lt x\lt1$: - It is a line with slope $-1$. The left - hand endpoint (not included) is at $x=-4,y = 3$ (open circle), and …
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a circle has a circumference of 1,133.54 units. what is the diameter of…
361
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a quadrilateral has vertices at a(1,2), b(4,5), c(7,2), and d(4,−1). wh…
d. \( AB \) and \( BC \)
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in a right triangle, the slopes of the two legs are 0 and undefined. wh…
b. Isosceles triangle
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what feature do parallel lines share in a coordinate plane? a. same slo…
a. Same slope
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a circle has a circumference of 50.24 units. what is the radius of the …
8
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erties of the trigonometric functions question 1, r8.1.105 points: 0 of…
B. The triangle is not a right triangle.
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4) rotation 90° clockwise about the origin
To solve the problem of rotating triangle \( FGH \) \( 90^\circ \) clockwise about the origin, we first need to determine the coordinates of the vertices \( F \), \( G \), and \( …
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find the slope of the line graphed below.
\(\frac{3}{2}\)
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suppose the radius of a circle is 3 units. what is its circumference? u…
18.84
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diagram shows points m, j, k, l, n with angles: ∠mj (132°), ∠jk (2x + 4…
\( x = 30 \)
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you can think of the ceiling and floor of a room as parts of horizontal…
No, two horizontal planes cannot intersect because horizontal planes are parallel, and parallel planes do not intersect. ### Question 28a: Can two vertical planes intersect?
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figure a is a scale image of figure b. diagram: figure a (blue) with si…
30
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figure a is a scale image of figure b. figure a (with side ( x )) and f…
2
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a circle has a circumference of 113.04 units. what is the diameter of t…
36
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5. dilate by a scale factor of 0.5 what is the new location of d?
\((1, 1)\)
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figure a is a scale image of figure b. figure a (a blue triangle) has a…
$4.4$
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4. dilate by a scale factor of 3. what is the location of the new point…
The location of the new point \( J' \) is \( (9, 6) \) (assuming the original coordinates of \( J \) were \( (3, 2) \); if the original coordinates were different, the calculation…
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dilate by a scale factor of 3. what is the location of the new point j?
\((9, 6)\)
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unit 1: shape and space /10 name: lesson 1-2 quiz: area and perimeter c…
s: - **Area of Trapezoid**: \( 60\space m^2 \), **Perimeter of Trapezoid**: \( 45\space m \) - **Area of Shaded Region**: \( 27\space cm^2 \)
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a bicycle wheel is 63 centimeters from top to bottom. when the wheel go…
1. First dropdown: diameter 2. Second dropdown: circumference 3. Third dropdown: divide 4. Fourth dropdown: the diameter (63 cm) To estimate \(\pi\), use \( \pi=\frac{\text{circum…
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name: ____________ date: 9/9/2025 directions: use this number to answer…
100,000,000 (hundred - millions place) ### Question 2
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how can zain use his drawing to derive the general equation of a circle…
First drop - down: \(|x - h|\) and \(|y - k|\) (or \((x - h)\) and \((y - k)\)) Second drop - down: Pythagorean theorem The standard form of the circle's equation is \((x - h)^{2}…
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a triangle dfe with a right angle (90°) at f, angles at d labeled (3x +…
\(x = 14\)
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the base of the pyramid in the diagram is a regular hexagon. the length…
\( 187 \, \text{ft}^3 \) (the option: \( 187 \, \text{ft}^3 \))
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a chemist has an empty cylinder with a height of 30 cm and a cone - sha…
10 cm
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devon reseeded a section of lawn that he plans to protect by putting a …
First, solve \(10^2 + x^2 = 26^2\) to find \(x = 24\). Then, the perimeter is \(10 + 24 + 26 = 60\) feet. Devon does not have enough fencing.
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12. quelle est laire dun rectangle dont le périmètre est de 30 cm et do…
L'aire du rectangle est \( 36 \, \text{cm}^2 \).
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in the figure below, ( k parallel l ) and ( m parallel n ). find the va…
\( y = 79 \), \( z = 22 \)
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the length of the base of a triangle is twice its height. if the area o…
15 kilometers
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16. ( 3x + (-9) < -18 ) (with ( +9 ) added to both sides: ( +9 ) below …
\(x < -3\)
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use the drop-down menus to complete the proof of the pythagorean theore…
1. The combined area of the shaded triangles in Figure 1 is \(\boldsymbol{\text{equal to}}\) the combined area of the shaded triangles in Figure 2. 2. The area of the unshaded squ…
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find the measure of the exterior angle shown. 1) triangle with angles 3…
s: 1. The measure of the exterior angle is \(\boldsymbol{146^{\circ}}\) 2. The measure of the exterior angle is \(\boldsymbol{130^{\circ}}\) 3. The measure of the exterior angle i…
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one leg of a right triangle is 1 millimeter shorter than the longer leg…
5
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type the answer in the box.
8
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one leg of a right triangle is 1 millimeter shorter than the longer leg…
3
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what is the area of the triangle? square units
21
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type the answer in the box. surface area
\( 800 \, \text{cm}^2 \)
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one leg of a right triangle is 1 millimeter shorter than the longer leg…
The lengths of the sides are 3 millimeters, 4 millimeters, and 5 millimeters. The length of the longer leg is 4 millimeters.
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2) rotation 90° counterclockwise about the origin (x,y)→(-y,x)
To solve the rotation of the triangle \( UVW \) \( 90^\circ \) counterclockwise about the origin, we first need to identify the coordinates of points \( U \), \( V \), and \( W \)…
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find the measure of the exterior angle shown. 1) triangle with angles 3…
\(146^\circ\) ### Problem 2:
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adair advertising has 2 spherical balloons. one has a radius of 3 feet …
\( 410.3\space\text{ft}^3 \)
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what percentage of the shape is green? write your answer using a percen…
20%
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the circumference of a circular painting is 56.52 feet. what is the rad…
9
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find the value of x.
\(x = 80\)
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click the arrows to choose an answer from each menu. the volume of ice …
The volume of ice in shape 1 is $\boldsymbol{20}$ cubic centimeters. The volume of ice in shape 2 is $\boldsymbol{10}$ cubic centimeters. Shape 1 contains $\boldsymbol{twice\ as\ …
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find the measure of the exterior angle shown. lock 4 (screen will be bl…
146 ### Problem 2:
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the length of a rectangle is 13 centimeters less than six times its wid…
The width is \( 3 \) centimeters and the length is \( 5 \) centimeters.
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for each line, determine whether the slope is positive, negative, zero,…
Zero ### Line 2
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click the arrows to choose an answer from each menu. li choose... corre…
To solve this, we analyze the transformation (likely a translation or scaling, but from the graph, it's a similarity transformation). ### Step 1: Side Lengths For similar figures,…
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expression for surface area of attic: 45 (40 + 25 + 25) + \\frac{1}{2}(…
The surface area of Linda’s attic is 4350 square feet. (For the other "Choose..." parts, more context on the options is needed, but the surface area calculation gives 4350.)
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what percentage of the shape is blue? write your answer using a percent…
100%
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a student is standing 20 feet away from the base of a tree. he looks to…
29 feet
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if a circular railroad crossing sign has an area of 254.34 in.², what i…
18
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what is the slope of the line?
\(\frac{1}{3}\)
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step 1: set the compass width between k and j. draw arc xy through ∠jkl…
First "Choose...": \( YZ \) Second "Choose...": radii of arcs drawn with the same compass width (or "lengths of arcs drawn with equal compass width") Third "Choose...": \( \overli…
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the formula for the volume of a pyramid is ( v = \frac{1}{3}bh ), where…
40
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apply geometry a square floor has a side length of (8x^3y^2) units. a s…
\( 64x^4y^2 \)
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the diagram shows a straight line with points r, t, v, s (r---t---v---s…
\( x = 18 \)
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a company makes japanese-style lunch boxes called bento boxes. each ben…
1. The manager's formula: \( V = l \times w \times h \) 2. Number of bento boxes: \( \frac{729}{8} \) (or 91.125) 3. Multiply by: volume 4. Comparison: equal to (Note: For the dro…
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step 1 set the compass to the length of \\(\\overline{ab}\\) and draw a…
1. \( \overline{AC} \cong \overline{AB} \) because all \(\boldsymbol{\text{radii of a circle}}\) are congruent. 2. \( \overline{AB} \cong \overline{BC} \) because all \(\boldsymbo…
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click the arrows to choose an answer from each menu. the expression cho…
First "Choose...": $2ab + c^{2}$ Second "Choose...": $(a + b)^{2}$ (or $a^{2}+2ab + b^{2}$) Third "Choose...": $2ab$
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circle the word that has the same middle sound as the picture word. shi…
Circle "ship"
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graph c + d with its initial point at the initial point of c.
To graph \( \boldsymbol{c + d} \): 1. Identify the initial point of \( \boldsymbol{c} \): \( (-4, 5) \) (from the graph). 2. The resultant vector \( \boldsymbol{c + d} \) has the …
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circle the correct verb. the mouse cheese. likes liking
likes
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refer to the figure at the right. 17. if ( mangle adb = (6x - 4)^circ )…
\( x = 7 \) ### Question 18
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triangle hij with vertex h, i, j. angle at h is ( x^circ ), angle at i …
\( x = 33 \)
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write the coordinates of the vertices after a reflection over the y-axi…
\( F(5, 1) \), \( G(1, 1) \), \( H(9, -3) \)
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look at this shape; image of a blue triangle on a grid which image show…
A
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convert the following angle from degrees to radians. express your answe…
\( \frac{\pi}{6} \)
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convert the angle 3 radians to degrees, rounding to the nearest 10th.
171.9
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what is the slope of this line? simplify your answer and write it as a …
\(1\)
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question 7 (multiple choice worth 1 points) (04.03 mc) point b on a seg…
D. (2.5, -0.25) To find the coordinates of point \( B \) that partitions the segment \( AC \) with endpoints \( A(2, -1) \) and \( C(4, 2) \) in the ratio \( 1:3 \), we use the se…
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find the maximum value of p = 9x + 8y subject to the following constrai…
The corner points are \((0,0)\), \((6,0)\), \((0,7)\), \((3,4)\). The maximum value of \(P\) is \(59\) (achieved at \((3,4)\)), and the missing \(y\) - value when \(x = 3\) is \(4…
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the diagram shows a triangle. what is the value of x? x = square^circ
\(102\)
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the diagram shows a triangle. what is the value of c? c = \\boxed{}°
\(22\)