幾何
三角形、圓、解析幾何與證明題。
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on a zip - line course, you are harnessed to a cable that travels throu…
14.1 meters
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find the slope of the line $y = \\frac{2}{3}x - \\frac{3}{4}$. simplify…
$\frac{2}{3}$
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use an algebraic equation to find the measures of the two angles descri…
$3^\circ$
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if these two shapes are similar, what is the measure of the missing len…
13 feet
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which formulas can be used to find the circumference of a circle? choos…
\( C = 2\pi r \), \( C=\pi d \)
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how many sides does a regular polygon have if each interior angle measu…
The regular polygon has 30 sides.
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the equation p = 3s represents the perimeter p of an equilateral triang…
18
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1 find the area of the rectangle
84 square centimeters
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rotating $\triangle abk$ by $90^circ$ counterclockwise about the origin…
### Part (a) To find the lengths \( CA \), \( CA' \), \( CB \), \( CB' \), \( CK \), and \( CK' \), we use the distance formula between a point \((x, y)\) and the origin \((0, 0)\…
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question determine a series of transformations that would map polygon a…
A **dilation by a scale factor of 7 centered at the origin** followed by a **translation (no vertical shift, horizontal shift is inherent to the origin-centered dilation, or alter…
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solve the inequality and graph the solution on the line provided. $15 +…
Inequality Notation: $x \leq -1$ Number Line: Closed circle at $-1$, shaded region to the left of $-1$ (covering all values $\leq -1$)
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which formulas can be used to find the circumference of a circle? choos…
\( C = 2\pi r \), \( C=\pi d \)
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7. determine if the triangles are similar. if similar, state how and co…
The triangles are similar by AA (Angle - Angle) similarity. The similarity statement is \( \triangle LMN \sim \triangle LGH \) (or appropriate labels) by AA. ### Problem 8:
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(a) use the number line to find the distance between -1 and 7. distance…
(a) 8 (b) $-1 -7 = -8$; $7 - (-1) = 8$ (c) $|-1 -7| = 8$; $|7 - (-1)| = 8$
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the three right triangles below are similar. the acute angles ∠f, ∠j, a…
(a) 0.57, 0.57, 0.57 (b) 0.82, 0.57, 1.44 (c) cosine
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1. find the area. use 3.14 for pi and round your answer. 20.5 ft
329.90 square feet (rounded to two decimal places)
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the hypotenuse of a 45°-45°-90° triangle measures 18 cm. what is the le…
\( 9\sqrt{2} \) cm (corresponding to the option with \( 9\sqrt{2} \) cm)
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question determine a series of transformations that would map polygon a…
First: Dilation by a scale factor of 3 with the origin as the center of dilation followed by a: Translation 1 unit left and 3 units up
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each leg of a 45°-45°-90° triangle measures 12 cm. what is the length o…
\( 12\sqrt{2} \) cm (corresponding to the option with \( 12\sqrt{2} \) cm text)
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graph each equation. 9) \\(\frac{x^2}{4} + \frac{y^2}{9} = 1\\) graph w…
This is an ellipse with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, centered at the origin.
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at the end of a set, what circles are drawn on the score sheet? final s…
B. Final score of both teams in the service round box (assuming the second option is labeled B; if the original options had labels like A, B, C, D, adjust the label accordingly ba…
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the figure shows two intersecting lines. write an equation to show how …
$m\angle 1 + m\angle 2 = 180^\circ$
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using a quadratic equation to solve an area problem a rectangular piece…
The true statements are: - The area of the rectangle is 88 square inches. - The equation \( x^{2}-3x - 88 = 0 \) can be used to solve for the length of the rectangle. - The triang…
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solve for x. round to the nearest tenth of a degree, if necessary. (rig…
\(61.6\)
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find the volume of the right cone below in terms of π. (there is an ima…
\( 240\pi \)
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a rectangle has a width that is 7 centimeters less than its length, and…
length = 22 centimeters width = 15 centimeters
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draw a line representing the ise\ and a line representing the un\ of th…
The slope of the line is \(-\frac{1}{3}\)
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draw a line representing the rise and a line representing the run of th…
The slope of the line is \(-3\)
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question convert the angle -2 radians to degrees, rounding to the neare…
\( -114.6^\circ \)
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4 which angle is adjacent to ∠tvs? ∠nvt 4 what is m∠nvs? m∠nvs = (image…
1. $\angle NVT$ 2. $110$
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the wind changes again and the which angle is adjacent to $\\angle tvs$…
$\angle NVT$
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ux bisects ∠vuw. complete the proof that vx ≅ wx. (image of a triangle …
| Statement | Reason | |-----------|--------| | 1. $\overrightarrow{UX}$ bisects $\angle VUW$ | Given | | 2. $\overline{UW} \cong \overline{UV}$ | Given | | 3. $\angle VUX \cong \…
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complete the proof that (overline{tu} cong overline{su}). image of tria…
| Statement | Reason | |-----------|--------| | 1. $\angle S \cong \angle T$ | Given | | 2. $\angle SRU \cong \angle TRU$ | Given | | 3. $\overline{RU} \cong \overline{RU}$ | Refl…
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uv ⊥ tw and ∠v ≅ ∠u. complete the proof that tu ≅ tv. (image of triangl…
| Statement | Reason | |-----------|--------| | 1 $\overline{UV} \perp \overline{TW}$ | Given | | 2 $\angle V \cong \angle U$ | Given | | 3 $\angle TWU \cong \angle TWV$ | All rig…
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z is the midpoint of \\(\\overline{xy}\\) and \\(\\overline{wz} \\perp …
4. Reason: Definition of midpoint 5. Reason: Reflexive Property of Congruence 6. Reason: Side-Angle-Side (SAS) Congruence Postulate
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writing locate $-sqrt{15}$ to the nearest tenth on a number line. use p…
$-3.9$ (located between $-4$ and $-3$, closer to $-4$ on the number line)
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a rectangle has a length that is 5 inches greater than its width, and i…
D. \(x^{2}+5x - 104=0\)
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how can you find m∠nvt? 90° + 20° = 110° 90° − 20° = 70° 20° + 20° = 40…
$90^\circ + 20^\circ = 110^\circ$
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the perimeter of a rectangle is 260 feet. find the length and width if …
Length = \( 20 \) feet Width = \( 110 \) feet
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what combination of transformations is shown below? options: rotation, …
translation, then reflection
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mixed exercises identify the similar triangles. then find each measure.…
9. $AC = 16$ 10. $JL = 28$ 11. $EH = 9$ 12. $VT = 13.5$
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estimate \\(\\sqrt{50}\\) to the nearest tenth. then locate \\(\\sqrt{5…
$\sqrt{50} \approx 7.1$ To locate on a number line: Place a point between 7 and 8, 1 tenth of the way from 7 toward 8.
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$\\angle tsv \\cong \\angle usv$ and $\\overline{tu} \\perp \\overline{…
The missing reason for Statement 5 ($\triangle STV \cong \triangle SUV$) is **ASA Congruence Postulate**. The completed proof is valid, with $\overline{UV} \cong \overline{TV}$ co…
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j is the midpoint of \\(\\overline{hi}\\). complete the proof that \\(\…
The completed proof has the missing reason for statement 5: **Side-Side-Side (SSS) Congruence Postulate** The final proven statement is $\boldsymbol{\angle HGJ \cong \angle IGJ}$
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what combination of transformations is shown below? grid with three lab…
reflection, then rotation
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determine if the two figures below are congruent. use the drop - down m…
The two figures are congruent (via rigid transformations like translation, rotation, or reflection). The angle corresponding to angle \( K \) is \( \angle S \).
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how many degrees did the arrow turn? (there is a coordinate system with…
90
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determine if the two figures below are congruent. use the drop - down m…
\( \angle M \)
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type the correct answer in the box. use numerals instead of words. if n…
9.8
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determine a series of transformations that would map polygon abcde onto…
One possible series of transformations is: Rotate polygon \( ABCDE \) 90 degrees clockwise about the origin, then translate it 4 units to the right and 2 units down (or other vali…
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writing a two-column proof given: ∠abc ≅ ∠def and ∠ghi ≅ ∠def prove: m∠…
3. $\angle ABC \cong \angle GHI$ 3. Transitive Property of Congruence 4. $m\angle ABC = m\angle GHI$ 4. Definition of Congruent Angles
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writing a two-column proof given ∠abc ≅ ∠def and ∠ghi ≅ ∠def prove: m∠a…
2. $\angle GHI \cong \angle DEF$ 2. given 3. $m\angle ABC = m\angle DEF$ 3. definition of congruent angles 4. $m\angle GHI = m\angle DEF$ 4. definition of congruent angles 5. $m\a…
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writing a two-column proof given: ∠abc ≅ ∠def and ∠ghi ≅ ∠def prove: m∠…
**Statements**: 1. $\angle ABC \cong \angle DEF$, $\angle GHI \cong \angle DEF$ 2. $m\angle ABC = m\angle DEF$, $m\angle GHI = m\angle DEF$ 3. $m\angle ABC = m\angle GHI$ **Reason…
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choose the graph of the solution to the inequality $x < -12$.
The correct graph is the third option: <point>81 582</point> (the number line with an open circle at -10, shading leftward to negative infinity)
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to graph x ≥ 2, place a(n) on a number line at , and shade to the . done
1. closed circle 2. 2 3. right
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question in the diagram below, \\(\\overline{ab} \\parallel \\overline{…
$61$
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question in the diagram below, (overline{ad} cong overline{ae}), (overl…
$62$
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finding angles (level 1) question in the diagram below, \\( \\overline{…
$\boldsymbol{56}$
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triangles abc and def have the following characteristics: ∠b and ∠e are…
A. AAS
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two angles and the non - included side of one triangle are congruent to…
A. AAS
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finding angles (level 1) question in the diagram below, \\(\\overline{a…
$56^\circ$
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given: mq = nq; q is the midpoint of lp; lm ≅ pn. which congruence theo…
C. SSS
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given: \\(\\overline{ar}\\) bisects \\(\\angle bac\\); \\(ab = ac\\)\ w…
SAS
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in the diagram below, $overline{ab} \\parallel \\overline{cd}$, $overli…
$56^\circ$
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in the diagram below, \\(\\overline{ab} \\parallel \\overline{cd}\\), \…
$57$
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example 1 determine whether each pair of triangles is similar. explain …
1. $\triangle GFH \sim \triangle KJH$ by AA Similarity (two pairs of congruent angles: $\angle F \cong \angle J$, vertical angles $\angle GHF \cong \angle JHK$) 2. $\triangle STR …
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the figure below is dilated by a factor of 3 centered at the origin. pl…
To plot the dilated image: 1. **Left Vertical Segment**: Plot points \((-27, 0)\) and \((-27, 27)\), then draw a vertical segment between them. 2. **Quadrilateral (RQPON)**: Plot …
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example 1 determine whether each pair of triangles is similar. explain …
1. $\triangle FGH \sim \triangle KJH$; they are similar by the AA Similarity Criterion (one pair of right angles are congruent, and vertical angles $\angle GHF$ and $\angle JHK$ a…
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the figure below is dilated by a factor of 2 centered at the origin. pl…
To solve the dilation of the figure by a factor of 2 centered at the origin, we follow these steps: ### Step 1: Identify the coordinates of the vertices First, we determine the co…
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e triangles below are similar. find the value of x. the image is not to…
54
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name: maileny unit 2: logic & proof date: per: 5 homework 8: segment pr…
### 1-3. Segment Addition Equations: 1. $PQ + QR = PR$ 2. $QR + RS = QS$ 3. $PS + ST = PT$ --- ### 4. Proof Reasons: | Statements | Reasons | |------------|---------| | 1. $X$ is …
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question what is the slope of the line that passes through the points (…
\(\frac{2}{3}\)
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which angle is adjacent to ∠3? ∠5 ∠2 ∠6 ∠1
∠2
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which angle is complementary to $\\angle 6$? image of intersecting line…
\(\angle 1\)
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online bank simulation click this link to access the ngpf online bank s…
s: 1. \$216.04 2. LESS (circled)
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find the missing angle for each irregular polygon. sum of the interior …
Sum of the Interior Angles = \(\boldsymbol{720}\)° \(x=\boldsymbol{45}\) \(m\angle P=\boldsymbol{125}\)° \(m\angle R=\boldsymbol{120}\)° \(m\angle T=\boldsymbol{95}\)°
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amending the constitution - multiple choice questions circle the correc…
d. By adding an amendment to it ### Question 2
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the articles of the constitution - multiple choice questions circle the…
a. The Congress ### Question 2
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questions: how a bill becomes a law circle the correct answer. 1. which…
A. someone has an idea for a law ### Question 2
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$\\overline{jk} \\cong \\overline{gm}$, $\\angle fkg \\cong \\angle hji…
Substitution Property of Equality
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the measure of each interior angle of a regular polygon is 162°. find t…
20
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the measure of each interior angle of a regular polygon is 144°. find t…
10
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the vertices of parallelogram gram are g(-10,3), r(-9,6), a(-5,6), and …
The correct option (assuming the visual analysis based on the translated coordinates) is the one where the translated parallelogram \(G'R'A'M'\) has vertices \((0,4)\), \((1,7)\),…
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the measure of each interior angle of a regular polygon is 140°. find t…
9
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give an example of when youd use a circle map? why would you not want t…
An example of using a Circle Map is when defining the concept of "Climate Change". Put "Climate Change" in the center circle. In the outer circle, write related ideas like "global…
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find the measure of each interior angle and each exterior angle of a re…
Measure of each interior angle \(=\boxed{150}\)° Measure of each exterior angle \(=\boxed{30}\)°
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find the measure of each interior angle and each exterior angle of a re…
Measure of each interior angle = \(162^{\circ}\) Measure of each exterior angle = \(18^{\circ}\)
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the parallelogram ghij is a dilation of the parallelogram ghij. what is…
\( \frac{5}{4} \)
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why government? b. venn diagram. put the number of the word in the righ…
To solve this Venn diagram problem, we analyze each concept and assign it to the correct category (State of Nature, Social Contract, or both) based on the definitions of these pol…
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section 12.1.12.2 cfu integrated math 2 - version d 1. classify the fol…
1. Acute scalene triangle 2. $x = 59$ 3. $x = 37$, $y = 61$
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similar by: aa ~ aixz - aqex similar by: afny - rwt similar by:
\( \triangle FNY \sim \triangle RWY \) por SAS (Lado - Ángulo - Lado)
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13. find the value of x so that ℓ ∥ m. (7x + 15)° ℓ m 25° n
\( x = 20 \)
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lines k, l, m with angles (3x + 10)° and (5x + 18)° as shown in the ima…
If we are to find \( x \), then \( x = 19 \)
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suppose we are given the following. line 1 passes through $(-3, -4)$ an…
Slope of Line 1: \(\frac{2}{3}\) Slope of Line 2: \(\frac{3}{2}\) Slope of Line 3: \(\frac{3}{2}\) ### Part (b)
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11. there is a diagram with three lines: line k (a transversal) interse…
\( x = 7 \)
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suppose we are given the following. line 1 passes through (4, -1) and (…
### Part (a) To find the slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). #### Slope of …
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question 2 math8: chapter 4 test positive negative zero undefined
- positive ↔ top graph (line rising left to right) - negative ↔ second graph (line falling left to right) - zero ↔ bottom graph (horizontal lines) - undefined ↔ third graph (verti…
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10. there is a diagram with two parallel lines ( l ) and ( m ), and a t…
\( x = 2 \)
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in the diagram, lines l, m are parallel, and line k is a transversal. t…
\( x = 20 \)
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amending the constitution - multiple choice questions circle the correc…
1. d. By adding an amendment to it 2. d. Cannot be changed 3. c. Both a. and b. above 4. d. None of the above 5. d. None of the above 6. a. The Bill of Rights