幾何
三角形、圓、解析幾何與證明題。
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part b indicate whether each point is a reflection of ( p(3, 4) ) acros…
To solve this, we use the rules for reflecting a point \((x, y)\) across the axes: - Reflection across the \(y\)-axis: \((-x, y)\) - Reflection across the \(x\)-axis: \((x, -y)\) …
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complete the tables in part a and part b. part a indicate whether each …
### Part A Explanation (for each point, we use the rule of quadrants: Quadrant I: (+, +); Quadrant II: (-, +); Quadrant III: (-, -); Quadrant IV: (+, -); points on axes are "None"…
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4. ray o is perpendicular to line p in the diagram shown. determine the…
$x = 20^\circ$
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use the image to answer the question. mike draws a triangle and dilates…
75
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6. mai says that angles a and b are vertical angles and complementary a…
Tyler is correct. Mai is wrong because angles $a$ and $b$ are complementary (they form a $90^\circ$ angle) not vertical angles. Tyler is correct because angles $c$ and $d$ are bot…
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similar figures and area quick check determine how dilation affects the…
The area decreases more rapidly than the lengths of the sides decrease.
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similar figures and area quick check kierra draws a triangle with a bas…
27 cm²
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similar figures and area quick check use the image to answer the questi…
A. \( 2\frac{1}{4} \)
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use the image to answer the question a triangle has a base of 8 cm and …
The original triangle has an area of $12 \, cm^2$ and the dilated triangle has an area of $108 \, cm^2$; therefore, the dilated triangle has an area 9 times the size of the origin…
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solve for x and graph the solution on the number line below. -12 < 3x -…
Inequality Notation: \( -2 < x \leq 1 \) For the number line: Plot an open circle at -2 (since \( x > -2 \), not including -2) and a closed circle at 1 (since \( x \leq 1 \), incl…
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5. line segments ad, be, and cf are all diameters of the circle. the me…
$\boldsymbol{20^\circ}$
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part 3 of 4 label the center and the radius r. (h, k) = (6, 2) and r = …
$(x-6)^2 + (y-2)^2 = 25$
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solve for x and graph the solution on the number line below. -x - 5 ≥ 1…
Inequality Notation: \(x \leq -6\) or \(x > 3\) For the number line: - For \(x \leq -6\), draw a closed circle at \(-6\) and shade to the left. - For \(x > 3\), draw an open circl…
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4. determine whether the statements about the relationships between the…
a. True b. False c. True d. True e. False f. False
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$\\overline{ts}$ is the midsegment of trapezoid $hjkl$. if $kl = 17$ an…
\( 13 \)
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3. select all the equations that represent a true relationship between …
A. $x = 25$ B. $w = 90$ C. $y = 65$
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ts is the midsegment of trapezoid hjkl. if lk = 19 and ts = 15, find hj…
\(HJ = 11\)
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given that $\\angle 1$ and $\\angle 2$ are supplementary, $\\angle 2$ a…
$\boldsymbol{\angle 1 \cong \angle 3}$ is proven using the transitive and subtraction properties of equality, along with definitions of supplementary and congruent angles.
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given: ∠1 and ∠2 are supplementary m∠1 = 53° prove: m∠2 = 127° steps re…
| Step | Steps | Reasons | |------|-------|---------| | 1 | $\angle 1$ and $\angle 2$ are supplementary | Given | | 2 | $m\angle 1 + m\angle 2 = 180^\circ$ | Definition of Supplem…
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four lines intersect to form a square. the equations of three of the li…
# Explanation: ## Step1: Analyze slopes of parallel lines In a square, opposite sides are parallel, so their slopes are equal. Also, adjacent sides are perpendicular, so the produ…
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given ▶ $m\\angle 1 = m\\angle 3$ prove ▶ $m\\angle eba = m\\angle dbc$…
1. Reason: Given 2. Reason: Angle Addition Postulate 3. Reason: Substitution property of = 4. Reason: Angle Addition Postulate 5. Reason: Transitive Property of =
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finding area of the campsite name all the shapes you can make from the …
1. Rectangle 2. Right Triangle 3. Irregular Polygon (the full shape) 4. Square (a subset of the rectangular section)
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find the distance from point a to bd. round your answer to two decimal …
\( 3.12 \)
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given: $\\angle 4 \\cong \\angle 3$ and $c \\parallel d$ prove: $\\angl…
2. Parallel lines cut by a transversal - Corresponding angles are congruent 3. Vertical angles are congruent 4. substitution
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given: $angle 4 cong angle 3$ and $c parallel d$ prove: $angle 4 cong a…
| STATEMENTS | REASONS | |------------|---------| | 1. ∠4 ≅ ∠3 and \(c \parallel d\) | 1. given | | 2. ∠3 ≅ ∠1 | 2. Alternate Interior Angles Theorem | | 3. ∠1 ≅ ∠2 | 3. Vertical …
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complete the proof that \\(\\overleftrightarrow{gi} \\perp \\overleftri…
1) Given 2) Angles forming a linear pair sum to 180 3) Substitution 4) Algebra 5) Definition of perpendicular lines
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determine the center and radius of the circle. $(x - 4)^2 + (y + 1)^2 =…
Part 1: The center is $(4, -1)$ Part 2: The radius is $r=8$
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determine the value of ( x ) in the isosceles triangle. enter the answe…
\( x = 13 \)
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find the midpoint of points a(6, -7) and b(10, -1) graphically. you may…
The midpoint of points \( A(6, -7) \) and \( B(10, -1) \) is \( (8, -4) \).
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determine the value of ( x ) in the isosceles triangle. enter the answe…
\(32\)
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1 what are the x and y coordinates for point h on the graph shown? a. (…
b. \((0, 1)\) ### Question 2
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four lines intersect to form a square. the equations of three of the li…
# Explanation: ## Step1: Analyze slope of parallel lines In a square, opposite sides are parallel. So, the fourth line should be parallel to \( y = -\frac{4}{3}x \) (since \( y=\f…
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math worksheet #2 measuring in inches (there are several rulers with re…
To solve the problem of measuring the lengths of the red bars in inches, we analyze each bar by looking at the ruler markings (assuming each major tick is 1 inch and minor ticks a…
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find the slope of the line graphed below.
\(-\frac{5}{2}\) (or -2.5)
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period: answer to the nea
\( \approx5.6 \)
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the figure is made up of a rectangle and a semicircle. note: not drawn …
$54 + 4.5\pi$ square feet (or approximately $68.14$ square feet if using $\pi \approx 3.14$)
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example 1: use the pythagore 1.)
\( \sqrt{115} \) (or approximately \( 10.72 \))
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use the graph to fill in the missing parts. the y - intercept is ______…
The y-intercept is $(0, -1)$ The axis of symmetry is $x=0$ The vertex is $(0, -2)$
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find the area of the trapezoid below.
80 square feet
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find the area of the triangle below. 15 in 4 in (triangle with base 15 …
30 square inches
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3 find the measure of the arc or angle indicated by the ? mark. assume …
C. \( 286^\circ \)
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2 find ( moverarc{pr} ) ( -7 + 6x ) ( -2 + 11x )
130
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the equation of the line is $y = \\frac{4}{3}x + 7$. there is a coordin…
The intersection point of the two lines is $(-3, 3)$
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a bumper pool table is shaped like a regular octagon. find the measure …
Each interior angle measures \(135^\circ\), and each exterior angle measures \(45^\circ\).
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in which case... and \\(\\frac{qr}{de} = \\frac{qs}{df} = \\frac{rs}{ef…
a rotation of 45° clockwise about vertex $A$ followed by a dilation by a scale factor of 0.95 about the origin
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find the value of x.
$84^\circ$
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if triangle ( abc ) is rotated 90 degrees clockwise about the origin fo…
$A'(0, 4); B'(6, 0); C'(-2, -2)$ (matches the last option)
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5. identify the relationship angles a and b share a common side and for…
The angles have a supplementary (or linear pair) relationship (they are adjacent supplementary angles, as they share a common side and form a straight line, meaning their sum is \…
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4. linear pair angles x and y form a linear pair. angle x = 3x + 10 ang…
\( x = 25 \)
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express the trig ratios as fractions in simplest terms. answer attempt …
$\cos K = \frac{39}{65} = \frac{3}{5}$ $\sin L = \frac{39}{65} = \frac{3}{5}$ $\cos K$ and $\sin L$ are equal
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3. vertical angles two vertical angles are formed when two lines inters…
\(47^\circ\)
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q.11 trigonometric ratios: find a side length uzc find gh. write your a…
3.0
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angle relationships – quiz (5 questions) 1. complementary angles two an…
The measure of the other angle is \(55^\circ\).
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44. the measures of two remote interior angles of a triangle are (3x + …
H. 0.9
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2. supplementary angles angle a measures 118° and forms a supplementary…
The measure of Angle B is \(62^\circ\).
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express the trig ratios as fractions in simplest terms. answer attempt …
$\sin K = \frac{\sqrt{31}}{16}$ $\cos L = \frac{\sqrt{31}}{16}$ $\sin K$ and $\cos L$ are equal
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find xy. write your answer as an integer or as a decimal rounded to the…
3.6
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find jk. write your answer as an integer or as a decimal rounded to the…
5.2
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answer attempt 1 out of 8 \\(\\sin r = \\frac{16}{17}\\) \\(\\cos q = \…
$\sin R = \frac{16}{17}$ $\cos Q = \frac{16}{17}$ $\sin R$ and $\cos Q$ are equal because $\overline{PQ}$ is **opposite** $\angle R$ and **adjacent** $\angle Q$.
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find gh. write your answer as an integer or as a decimal rounded to the…
\( 3.6 \)
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1 find the scale factor that was used to dilate figure i to create figu…
The scale factor is \(\frac{2}{3}\), and the dilation is a reduction.
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3. find the scale factor that was used to dilate figure a to create fig…
Scale factor: \(\frac{3}{5}\) (or 0.6); Dilation: reduction
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6. what formula does the video give for each exterior angle of a regula…
B. \( 360 \div n \) ### Question 7
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solve for ( x ). round to the nearest tenth, if necessary.
\( x\approx39.1 \)
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1. which of the following is the ratio for sina? a. $\frac{15}{17}$ b. …
a. $\boldsymbol{\frac{15}{17}}$ ### Question 2:
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10. complete the following, identify the scale factor original size is:…
Original Size is: 4 units wide × 5 units tall New Size is: 4 units wide × 5 units tall Scale Factor: $1$
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solve for ( x ). round to the nearest tenth, if necessary. answer attem…
\( x \approx 39.1 \)
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solve for x.
$x = 18$
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1. what formula does the video give for the sum of interior angles of a…
B. \( 180\times(n - 2) \) ### Question 2
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solve for x.
$x=6$
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1. what of the following is the ratio for - (partially obscured) a. (8/…
The appropriate setup is \( \tan 75^\circ = \frac{x}{7} \) (option b), and the value of \( x \) is approximately \( 26.12 \) (or \( 7(2 + \sqrt{3}) \approx 26.12 \)).
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find the arc measure where the ? is
$180^\circ$
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find the measure of the angle where the ? is
$115^\circ$
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what is the equation of the line that contains the point (9, 2) and has…
C. $x = 9$
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find the measure of the angle where the ? is
$114^\circ$
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rotation 270° counterclockwise about the origin. find the coordinates. …
- \(C'(4, -1)\) - \(D'(6, -1)\) - \(E'(6, -3)\) - \(F'(5, -5)\) - \(G'(3, -5)\) - \(H'(2, -3)\)
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algebra 2 cp translations of shapes graph the image of the figure using…
1. Translated vertices: $V'(1,0)$, $Q'(3,0)$, $D'(2,-3)$, $U'(1,-1)$ (plot and connect these points) 2. Translated vertices: $T'(-3,-1)$, $R'(0,-1)$, $I'(-3,-3)$ (plot and connect…
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geometry exam - unit 7 name: 1. quadrilateral abcd is a rectangle. ae =…
\( AC = 30 \), \( BD = 30 \), \( BE = 15 \), \( AB = 27 \), \( BC\approx13.1 \) ### Problem 2: Rhombus RSTU
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use the image to answer the question. a right triangle with base and he…
36
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26. given ( overline{ac} cong overline{df} ), what additional informati…
A. \( \overline{AB}\cong\overline{DE} \) or \( \overline{BC}\cong\overline{EF} \)
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mark the following statements as true or false. the most common place f…
True (select the circle under "True" for this statement) ### 2. Statement: "The three - dimensional security ribbon on the $100 bill was introduced in 2013."
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part 1 of 2 use the diagram. find the measure of $\\angle jek$. then cl…
$m\angle JEK = 90^\circ$ The angle is a right angle.
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select the correct location on the map. which location was the focus of…
The location (red circle) on the African continent.
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the solution of the system that has coinciding lines.
The system has infinitely many solutions, consisting of all points on the coinciding line.
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use the number line below to find the lengths of \\( \\overline{mn} \\)…
$MN=8$ $PQ=7$
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which of the following describes the transformation from the preimage t…
A reflection over the x - axis
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use the number line below to find the lengths of ln and mq. ln = \\boxe…
$LN=10$ $MQ=10$
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a system of three equations is shown on the graph below. what is the so…
A. $(2, -1)$
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which of the following describes the transformation from the preimage t…
A reflection over the y - axis
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a triangle has sides of length 11 m, 12 m, and 16 m. what is the measur…
88°
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the area, a, of an ellipse can be determined using the formula ( a = pi…
$y = a \div (\pi x)$ (the fourth option, assuming a formatting error in the original)
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question 1 (1 point) length of arc de = ______ yd question 2 (1 point) …
\(\frac{64\pi}{9}\) (or approximately \(22.34\))
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question 9 (1 point) a fan blade rotates through a 150° angle. the blad…
\( 135\pi \) (or approximately \( 424.12 \)) ### Question 10
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question 6 (1 point) a circular ride has a radius of 12 m. one section …
\( 12\pi \) (or approximately \( 37.7 \)) ### Question 7
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a clock has a radius of 8 cm. from 12 oclock to 2 oclock, the minute ha…
\( 7.5\pi \) (or approximately \( 23.55 \)) ### Question 5
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question 1 (1 point) a pizza has a radius of 14 cm. one slice makes a 4…
\( 76.93 \) (or \( \frac{49\pi}{2} \approx 76.93 \)) ### Question 2
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step three: complete the same processes as practiced in steps one and t…
9) $x \approx 28.3$ 10) $x \approx 13.1$
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12. which expression represents the value of k? the diagram is not to s…
B. \(180 - 93\) ### Question 13
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step two: complete the same process as practiced in step one. then, hig…
5. TOA 6. SOH 7. TOA 8. TOA
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question 2 of 10 which sentence is an example of characterization throu…
A. The clenching of her toes inside her shoes was her only movement as she waited for the police officer to appear.