Geometrie
Dreiecke, Kreise, Koordinatengeometrie und Beweisaufgaben.
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5. explain why the function a(x) = 36 - x² represents the shaded area i…
The large rectangle has an area of \( 6 \times 6 = 36 \) square feet. The square cut out has an area of \( x^2 \) square feet (since its side length is \( x \)). The shaded area i…
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15. find the values of x and y. (18y + 5)° (10x − 61)° (x + 10)°
\(x = 21\), \(y = 8\)
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4. choose true or false. true or false: an argument that uses written j…
True
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k is the midpoint of (overline{jl}). if (kl = x + 5) and (jl = 7x + 5),…
12
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13. if ( overline{bd} perp overline{ac} ), ( mangle dbe = (2x - 1)^circ…
\( x = 19 \)
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extra practice in exercises 1–3, name three different angles in the dia…
\( 116^\circ \) ### Exercise 5: \( m\angle RSU = 91^\circ \), Find \( m\angle RST \)
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11 find the value of x. (6x + 7)° (8x − 17)°
\(x = 12\)
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what have i learned? doing the problems in this section will help you t…
15 feet ### CL 1-142b
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prove: (overline{ac} cong overline{de}) diagram with points a, b, c (ho…
2. c. $AB = DB, BE = BC$ 4. b. Substitution 6. e. $AC = DE$ 7. d. Def. of $\cong$ line segments
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a. the greatest angle of △abc has a measure of 104°, and the other angl…
\(\angle A\) measures \(104^\circ\). \(\angle B\) measures \(30^\circ\). \(\angle C\) measures \(46^\circ\).
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center: (1, -5) radius: 3
To determine the equation of the circle with center \((1, -5)\) and radius \(3\), we use the standard form of the equation of a circle: \[ (x - h)^2 + (y - k)^2 = r^2 \] where \((…
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prove: ∠1 ≅ ∠4 diagram of angles 1,2,3,4 with arrows statements 1. ∠1 a…
4. c 6. b 7. e 8. d
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8. ∠k and ∠l are complementary angles. if ( mangle k = (3x + 3)^circ ) …
\(m\angle K = 24^\circ\), \(m\angle L = 66^\circ\)
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1) complete the formal geometric proof: given: ( b ) is the midpoint of…
2. a. \( \overline{BC} \cong \overline{AB} \) 3. c. \( \overline{BC} \cong \overline{DE} \)
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6. ∠1 and ∠2 form a linear pair. if m∠1 = (5x + 9)° and m∠2 = (3x + 11)…
\(m\angle1 = 109^\circ\), \(m\angle2 = 71^\circ\)
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statements 1. ( mangle rst = mangle rsu + mangle ust ); ( mangle rsu = …
### Step 1: Analyze Step 2 (Reason) We know the measures of \(\angle RSU\), \(\angle UST\), and \(\angle RST\) from the given information. To get the equation \(6x - 7=(3x - 5)+(x…
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given: $ce = cd + de$; $cd = (7x - 5)$; $de = (2x + 5)$; $ce = (x + 8)$…
### Step 1: Analyze Statement 2 Reason To get \( x + 8=(7x - 5)+(2x + 5) \) from the given \( CE = CD + DE \), \( CD=(7x - 5) \), \( DE=(2x + 5) \), \( CE=(x + 8) \), we substitut…
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19. if mo bisects ∠pmn, m∠pmn = 74° and m∠omn = (2x + 7)°, find the val…
\( x = 15 \)
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15. ∠p and ∠q are supplementary angles. if ( mangle p = (4x + 1)^circ )…
\(123^\circ\)
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writing an inequality in exercises 117 and 118, write an absolute value…
\(|x - 3| < 2\)
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practice quiz: perimeter and circumference line segment __________ is p…
D. QR, QS, Q (assuming the options are labeled A, B, C, D as the first is A, second B, third C, fourth D)
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question 4 (5 points) listen which of these best describes a line? a li…
D. a series of points moving along a straight path
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14. ∠r and ∠s are complementary angles. if ( mangle r = (12x - 3)^circ …
\(57^\circ\)
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practice quiz: perimeter and circumference question 3 (5 points) listen…
6 (corresponding to the option "6")
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22. choose the best answer. which property is illustrated? if $\\delta …
A. Transitive Property of Congruence
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practice quiz: perimeter and circumference look at this figure. figure …
point Y, ray YZ, angle XYZ (the third option: point Y, ray YZ, angle XYZ)
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willhite_k. geometry a_section 1_fall 25/26 / unit 2 - logic and proofs…
C. Reflexive Property of Congruence ### Second Question ((3x)y = 3(xy))
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practice quiz: perimeter and circumference simone drew these two lines.…
\( 35^\circ \) (corresponding to the option with \( 35^\circ \))
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which property of congruence is illustrated? for any geometric figures …
C. Transitive ### Second Question (Bottom One)
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13. if ( mangle deg = (5x - 4)^circ ), ( mangle gef = (7x - 8)^circ ), …
x = 16, y = 11
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for all expressions a, b, and c, if a = b, then a + c = b + c. ○ commut…
C. Addition Property of Equality ### Second Question (About Congruence Property)
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complete the parts below. (a) find the run, rise, and slope given by tr…
To solve this problem, we need to analyze the triangles \(ABC\) and \(DEF\) to find their run, rise, and slope, and then compare the slopes. However, since the image of the triang…
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12. if ( mangle knm = (8x - 5)^circ ) and ( mangle mnj = (4x - 19)^circ…
\( 131^\circ \)
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read the excerpt from chapter 7 of night. when at last a grayish light …
D. It is a nightmarish atmosphere.
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4. choose true or false. true or false: an application of deductive rea…
True ### Question 5
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11. if $\\overleftrightarrow{ab} \\perp \\overleftrightarrow{cd}$, $m\\…
The measure of \( \angle DCE \) is \( 72^\circ \).
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line l is shown below. right triangles abc and def are drawn to measure…
The slope of line \( l \) is \( \boldsymbol{\frac{1}{2}} \).
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the perimeter of any rectangle in which the length is 5 more than three…
B. \( w=\frac{P - 10}{8} \)
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the perimeter of any rectangle in which the length is 5 more than three…
B. \( w=\frac{P - 10}{8} \)
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14. the midpoint of jk is m(...) 15. point m is the midpoint of (overli…
\(40\)
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9. if \\(\\overline{lk} \\cong \\overline{mk}\\), \\(lk = 7x - 10\\), \…
\( 46 \)
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find the value of x in the triangle shown below. (triangle with sides 6…
68
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abs: (a) (x + 2x) (b) x = -2 or -3 in the adjoining figure, ef intersec…
$\angle APR$ and $\angle PRD$ ### Part (b)
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10) is this a valid argument? given: if an angle is acute, then it cann…
Yes. This argument uses the Law of Detachment.
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problem 7 part 2: spiral review here is an unlabeled rectangle and seve…
(Table Completion): | Quadrilateral | Scale Factor | |---------------|--------------| | A | 1 | | B | \( 2 \) | | C | \( 1.5 \) (or \( \frac{3}{2} \)) | | D | 0.5 | | E | 1 | | F …
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7) is this a valid argument? given: if the sum of the measure of two an…
B. Yes. This argument uses the Law of Detachment.
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in the adjoining figure, ef intersects straight lines ab and cd at poin…
∠APR and ∠PRD ### Part (b)
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a law of deductive reasoning that states that if a conditional statemen…
C. Law of Detachment ### Second Question:
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21. choose the best answer. which statement is the contrapositive of th…
The option: If two figures are not congruent, then they do not have the same shape and size.
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identify the quadrant or quadrants for the angles satisfying the follow…
1
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9. if \\(\\overline{lk} \\cong \\overline{mk}\\), \\(lk = 7x - 10\\), \…
\( x = 3 \) ### Problem 11:
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identify the quadrant or quadrants for the angles satisfying the follow…
4
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identify all possible quadrants of an angle θ that satisfies the given …
A. Quadrant IV
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a biconditional statement that is used to describe a geometric object o…
definition ### Second Question (Converse of Conditional Statement)
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16. choose the best answer. the negation of the hypothesis and conclusi…
D. inverse ### Question 17
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14. choose the best answer. the exchange and negation of both the hypot…
B. contrapositive ### Question 15
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use the triangle area formula $a = \\frac{1}{2}bh$ to fill in the chart…
The height of her garden will be 9 feet. ### Question 17
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problem 7 part 2: spiral review here is an unlabeled rectangle and seve…
| Quadrilateral | Scale Factor | | ---- | ---- | | A | 1 | | B | 2 | | C | 1.5 | | D | 0.5 | | E | 1 | | F | 2 | | G | 1 | | H | 2 |
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12. choose the best answer. the part of a conditional statement that ex…
C. conclusion ### Question 13
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simone used this formula to find the height of a triangle. ( a = \frac{…
multiply both sides by 2, divide by \( b \) (corresponding to the third option in the multiple - choice list)
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find the signs of the six trigonometric function values for the given a…
\(\sin 88^\circ\) is positive, \(\cos 88^\circ\) is positive, and \(\tan 88^\circ\) is positive.
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17. without solving, determine whether the solution of \\(\\frac{1}{3}x…
The solution of $\frac{1}{3}x = 21$ is greater than 21 because to solve for $x$, we multiply 21 by 3 (the reciprocal of $\frac{1}{3}$), and multiplying by a number greater than 1 …
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problem 7 part 2: spiral review here is an unlabeled rectangle and seve…
To determine the scale factor for each quadrilateral, we first identify the dimensions of the original rectangle (let's assume the original rectangle, say the blue one, has a leng…
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if n is an integer, n·180° represents an integer multiple of 180° and (…
is undefined.
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read the passage. the importance of japan’s cherry blossoms in the nort…
Americans appreciate the colorful leaves of fall, but the Japanese view the cherry blossoms of spring as part of their culture.
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problem 7 part 1: spiral review here is an unlabeled rectangle and seve…
# Explanation: ## Step1: Analyze the unlabeled rectangle First, we determine the dimensions of the unlabeled rectangle. Let's assume each grid square has a side length of 1 unit. …
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if n is an integer, ( n cdot 180^circ ) represents an integer multiple …
\(=-1\)
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12) part b: select the word(s) in part a that made the statement become…
A. If and only if ### Question 13 (Part A)
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problem 7 part 1: spiral review here is an unlabeled rectangle and seve…
# Explanation: ## Step1: Analyze the unlabeled rectangle First, we determine the dimensions of the unlabeled rectangle. Let's assume each grid square has a side length of 1 unit. …
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use the trigonometric function values of quadrantal angles to evaluate …
$0$
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8) part b: select the word(s) in part a that made the statement become …
If and only if ### Question 9
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use the trigonometric function values of the quadrantal angles to evalu…
8
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6) part b: select the word(s) in part a that made the statement become …
not ### Question 7 (Part A)
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1. circle all of the following numbers are equal to $-\frac{4}{5}$? $\f…
$\frac{-4}{5}$, $-\frac{8}{10}$ ### Question 2 (Assuming each segment between integers is divided into 10 parts for simplicity, adjust based on actual number line divisions. Here,…
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4) the converse form of the statement would be: if a figure is not a sq…
B. If a figure has four equal sides, then it is a square. (Note: Assuming the options are labeled as A, B, C, D with the first option as A, second as B, etc. as per typical multip…
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2) the biconditional form of the statement would be: - if a figure has …
B. A figure is a square if and only if it has four equal sides ### Question 3
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find the indicated function value. if it is undefined, say so. sin (-90…
A. \(\sin(-90^{\circ})=\boxed{-1}\)
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answer the following questions. answer questions 1-4 given the followin…
C. If a figure does not have four equal sides, then it is not a square.
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find the indicated function value. if it is undefined, say so. sec 0° s…
A. $\sec 0^\circ = \boxed{1}$
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8) choose the best answer. conjecture: intersecting lines form only ver…
No, $\angle AEB$ and $\angle BEC$ are a counterexample.
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7) choose the best answer. conjecture: the noncommon rays of all adjace…
No, \(\angle IJK\) is a counterexample.
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14. if $overline{ef}$ bisects $overline{cd}$, $cg = 5x - 1$, $gd = 7x -…
\( EG = 19 \) ### Problem 15
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solve the inequality and graph the solution on the line provided. -7 + …
Inequality Notation: \( x \geq 7 \) For the number line: Place a closed circle (since the inequality is "greater than or equal to") at 7 and draw a line to the right to represent …
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inch-based rule 1. ______ 2. ______ 3. ______ 4. ______ 5. ______ 6. __…
To solve the problem of measuring lengths using the inch - based rule, we analyze the markings on the ruler: ### Step 1: Understand the Ruler's Graduation The ruler has two scales…
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1. choose the best answer. points that lie on the same line are ______.…
B. collinear (assuming the options are labeled as A. postulate, B. collinear, C. segment bisector, D. angle)
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2. choose the best answer. a(n)____ is a statement accepted as true wit…
A. postulate ### Question 3
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inch-based rule 1. ______ 2. ______ 3. ______ 4. ______ 5. ______ 6. __…
$\frac{1}{16}$ inch ### Problem 2 (top mark 2)
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4. choose the best answer. \the points on any line or line segment can …
A. Ruler Postulate ### Question 5
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mathematical connections in exercises 27 and 28, (a) write an equation …
For part (a): \(x + 90 + y = 180\) (or \(x + y = 90\)) For part (b): \(x = 67\), \(y = 23\) ### Problem 28
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using the midpoint and distance formulas, calculate the coordinate of t…
Length of Segment \( \overline{AB} \): b. 4 Coordinates of Midpoint: d. (3, 2)
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** this is a 2 - page document ** use the diagram below to answer quest…
\( LN = 37 \) ### Question 2:
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7. choose the best answer. what is a figure formed by two rays with a c…
D. angle ### Question 8
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mia uses the formula ( pi r^2 ) to find the area of a circle. what is (…
D. a model (assuming the options are labeled A - D with D being "a model"; if original labels differ, adjust to match, e.g., if the last option is labeled as D, then D. a model)
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of a rectangular prism are \\(\\frac{9}{4}\\) feet, \\(3\\frac{2}{3}\\)…
The volume of the rectangular prism is \( \boldsymbol{9} \) cubic feet.
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read the excerpt from clara barton’s childhood. there was, directly in …
C. It was revered when it froze over
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9. choose the best answer. given line ab and point o on that line, any …
D. Protractor Postulate ### Question 10
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11. choose the best answer. the set of points indicated by 10. is the _…
interior
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12. choose the best answer. the set of points indicated by 11. is the _…
A. interior
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solve the inequality and graph the solution on the line provided. (7 + …
Inequality Notation: \( x > -2 \) For the number line: Place an open circle at -2 (since the inequality is \( > \), not \( \geq \)) and draw a line to the right of -2 to represent…
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type the answer in each space provided. use numbers instead of words. c…
| Circle | Radius (in.) | Diameter (in.) | Circumference (in.) | \( \frac{\text{Circumference}}{\text{Diameter}} \) | |--------|--------------|----------------|-------------------…