幾何
三角形、圓、解析幾何與證明題。
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given rhombus efgh below. if m∠hie = (-2x + 6)°, solve for x.
$x = -42$
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given rectangle vwxy below, xz = 54. if wz = -3x - 6, solve for x.
$x = -20$
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lines ( l_1 ), and ( l_2 ) are parallel lines. determine the measures o…
$m\angle 1 = 56^\circ$ $m\angle 2 = 56^\circ$ $m\angle 3 = 124^\circ$ $m\angle 4 = 124^\circ$ $m\angle 5 = 56^\circ$ $m\angle 6 = 124^\circ$ $m\angle 7 = 56^\circ$ $m\angle 8 = 12…
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given rhombus uvwx below, m∠vwy = 57°. if m∠xwy = (-x - 2)°, solve for …
$x = -59$
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given rhombus uvwx below, xy = 73. if yv = -3x - 2, solve for x.
$x = -25$
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given rhombus rstu below. if \\(\\text{m}\\angle svt = (x + 1)\\degree\…
$89$
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fill in the sentence below with the description that most specifically …
rhombus, because all four sides are equal in length and both pairs of opposite sides are parallel, with no right angles indicated.
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fill in the sentence below with the description that most specifically …
The quadrilateral is most specifically a **rectangle**, because it has four right angles and its opposite sides are equal in measure.
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if $\\angle bce \\cong \\angle dce$, $be = v + 25$, and $de = 2v$, what…
$25$
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fill in the sentence below with the description that most specifically …
all angles are congruent, because the quadrilateral has four congruent right angles, with opposite sides equal but not all sides equal, fitting this most specific description.
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fill in the sentence below with the description that most specifically …
The quadrilateral is most specifically a square, because all four of its sides are equal in length and all four of its interior angles are right (90°) angles.
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jose caught a fish that is 4.5 feet long. he wants to know its length i…
(a) Double number line: Top line (feet): 0, 4.5 Bottom line (inches): 0, 54 (b) 54 inches
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graph the image of kite tuvw after a rotation 270° counterclockwise aro…
The image of kite \( TUVW \) after a \( 270^{\circ} \) counterclockwise rotation about the origin has vertices at \( W'(-5,0) \), \( T'(-8,-8) \), \( U'(-6,-9) \), and \( V'(-3,-8…
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graph the image of kite pqrs after a rotation 180° counterclockwise aro…
The image of kite \( PQRS \) after a \( 180^\circ \) counterclockwise rotation around the origin has vertices at \( P'(-4, 10) \), \( Q'(-7, 4) \), \( R'(-4, 3) \), and \( S'(-1, …
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answer attempt 1 out of 10 the quadrilateral is most specifically a, be…
isosceles trapezoid; it has one pair of parallel implied sides, and two pairs of congruent adjacent base angles as indicated by the angle markings.
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answer attempt 1 out of 10 the quadrilateral is most specifically a ▼, …
The quadrilateral is most specifically an **isosceles trapezoid**, because it has one pair of congruent base angles (the bottom two angles marked with triple arcs), which is a def…
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transformations and similarity review what is the solution to the syste…
\(\boldsymbol{(-1, -5)}\) (corresponding to the option: \((-1, -5)\))
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find the missing leg if one leg is 4 and the hypotenuse is 8. if needed…
6.9
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b. solve for p in the figure. t s p p t=12 s
\( p = 6\sqrt{2} \) (or approximately \( 8.49 \))
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3. hauteur definition n altitude hauteur dun triangle tout soité qui ha…
Pour identifier la hauteur d'un triangle, on recherche une droite issue d'un sommet et perpendiculaire au côté opposé (ou à sa prolongation) à ce sommet. Dans les figures données,…
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name get out the square tiles below, and construct the following arrays…
1a. Repeated addition: $4 + 4$ 1b. Repeated addition: $2 + 2 + 2 + 2$ 2a. Repeated addition: $2 + 2 + 2$ 2b. Repeated addition: $3 + 3$ 3a. Repeated addition (example): $2 + 2 + 2…
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the right triangle below is dilated by a scale factor of 5. find the pe…
Perimeter of given right triangle: 40 units Perimeter of dilated right triangle: 200 units Area of given right triangle: 60 units² Area of dilated right triangle: 1500 units²
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#1 a square with a side length of 4 units is rotated 30° about 1 vertex…
C. Square
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point a (1, -9) was dilated to a (2, -18). what was the scale factor? (…
2
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what are the coordinates of point c if c(-4, -2) is rotated 270° counte…
\((-2,4)\)
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what are the coordinate points of b if b (-3, 15) is translated right 7…
\((4, 7)\)
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write the translation rule if point a is translated 5 units right and 1…
For the \(x\) - coordinate: Operation: \(+\), Number: \(5\); For the \(y\) - coordinate: Operation: \(+\), Number: \(10\) (The translation rule is \((x,y)\to(x + 5,y + 10)\))
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plot the point c if c (-12, 9) is reflected over the x - axis. your ans…
\((-12, - 9)\)
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reflect △abc over the x - axis. (3 points) a = b = c =
\( A'=(0,-1) \) \( B'=(5,-1) \) \( C'=(0,-4) \)
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given abcd is a parallelogram prove \\(\\overline{ab} \\cong \\overline…
Completed two-column proof: | Statements | Reasons | |------------|---------| | 1. $ABCD$ is a parallelogram | 1. given | | 2. draw $\overline{AC}$ | 2. construction | | 3. $\over…
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Question was provided via image upload.
\( 44 \) ### Problem 12 #### Part (a)
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determine whether the pair of lines are parallel, perpendicular, or nei…
C. Parallel
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determine whether each pair of lines is parallel, perpendicular, or nei…
neither
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wxyz is a quadrilateral. wx = 2x + 16, wz = 8x + 16, xy = 2y - 16, and …
\( x = 2 \), \( y = 24 \)
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find the slope of the line ( y = -8 ). select the correct choice below …
A. The slope is $0$.
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find the slope of the line x = 2. select the correct choice below and, …
B. The slope is undefined.
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for the graph on the right, determine if the slope is positive, negativ…
C. Undefined
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find the length of $overline{ac}$. use that length to find the length o…
10.7 cm (Option C)
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ch equation can be solved to find one of the missing side lengths in th…
A. $\cos(60^\circ) = \frac{12}{a}$
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which equation can be used to solve for b? (there is a right triangle a…
$\boldsymbol{\tan(30^\circ) = \frac{5}{b}}$ (the first option)
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which relationship in the triangle must be true? a c b c b a sin(b) = s…
$\boldsymbol{\sin(B) = \cos(90 - B)}$
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what is the length of (overline{bc})? round to the nearest tenth. 16 cm…
6.8 cm
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kevin was asked to determine the length of side xz. his work is shown. …
He has the side lengths in the wrong place in the cosine ratio.
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solving for measures of right triangles use the diagram to complete the…
The measure of angle L is $\boldsymbol{70}^\circ$. The trigonometric ratio that uses $\angle M$ and $LN$ to solve for $NM$ is $\boldsymbol{\text{tangent (tan)}}$. The length of NM…
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ating unknown lengths of right triangles the measure of angle a is 15°,…
$AC = 29.9$ $AB = 30.9$
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if the width of the rectangular prism is doubled, which of the followin…
The volume is twice as large.
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if the height of the rectangular prisms changes from 5in to 10 in what …
\( 110 \text{ in}^2 \) (corresponding to the option "110 in.²")
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rectangular prism a has a volume of 275 cubic inches. rectangular prism…
825 cu in. (The option is the one with "825 cu in.")
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which statement is not true? doubling the length of a prism will double…
Doubling the length of a prism will double its surface area.
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a cubic box is 12 inches on each side. its height is tripled to create …
The volume is three times as large (the option with this text, e.g., if it's option 2, then "2. The volume is three times as large")
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which statement describes how to derive the equation of a circle in sta…
D. The equation of a circle can be derived using the distance formula
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given right triangle mno, which represents the value of cos(m)? ○ \\(\f…
$\boldsymbol{\frac{MN}{MO}}$ (corresponding to the second option)
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given right triangle mnl, what is the value of cos(m)? $\\frac{3}{5}$ $…
$\boldsymbol{\frac{4}{5}}$ (Option C: $\frac{4}{5}$)
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given right triangle xyz, which correctly describes the locations of th…
a is adjacent, b is opposite, c is the hypotenuse
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given right triangle xyz, what is the value of tan(y)? options: - $\fra…
$\boldsymbol{\frac{\sqrt{3}}{3}}$ (corresponding to the second option)
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which trigonometric ratios are correct for triangle abc? select three o…
$\sin(C) = \frac{\sqrt{3}}{2}$, $\tan(C) = \sqrt{3}$, $\sin(B) = \frac{1}{2}$
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given right triangle gyk, what is the value of tan(g)? ○ \\(\\frac{1}{2…
$\sqrt{3}$ (Option D)
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analyzing the sine ratio explain why the value of the sine ratio for an…
For an acute angle in a right triangle, the sine ratio is defined as $\frac{\text{opposite side}}{\text{hypotenuse}}$. All side lengths are positive, so the ratio is positive. The…
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write the equation in standard form of a circle with center (-7,6), tan…
\((x + 7)^2 + (y - 6)^2 = 49\)
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which triangle is similar to $\\triangle abc$ if $\\sin(a) = \\frac{1}{…
The triangle similar to $\triangle ABC$ is $\triangle XYZ$ (the rightmost triangle with sides $6$, $6\sqrt{15}$, and $24$).
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analyzing co... consider △abc. what are the angles that make the trigon…
$\sin(\boldsymbol{A}) = \cos(B)$ $\sin(B) = \cos(\boldsymbol{A})$
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determining a tangent ratio what is the value of \\(\\tan(60^\\circ)\\)…
$\boldsymbol{\sqrt{3}}$ (Option: $\boldsymbol{\sqrt{3}}$)
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what additional information would be necessary to determine sin(a) with…
The length of BC is needed because it is the side opposite $\angle A$.
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use the diagram and side lengths of triangle rst to determine the angle…
$\sin(\boldsymbol{R}) = \frac{12}{13}$ $\tan(\boldsymbol{T}) = \frac{5}{12}$
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finding the values of trigonometric ratios what are the values of the t…
$\sin(L) = \frac{4}{5}$ $\cos(L) = \frac{3}{5}$ $\tan(L) = \frac{4}{3}$
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identifying equal trigonometric ratios identify the triangle that conta…
The second triangle (right triangle with two 45° angles, marked with equal leg lengths at AC and BC)
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why? the relation fails the vertical line test. there is at least one x…
Yes There is not a vertical line that contains more than one ordered pair from the relation.
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12 use a protractor to estimate the angle.
Approximately $150^\circ$ (acceptable range: $145^\circ$ to $155^\circ$)
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10 the parallelogram below is made from two congruent triangles. one tr…
10 square units
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using the pencil, plot the point (5, 4).
The point is plotted at the intersection of the vertical line through $x=5$ and the horizontal line through $y=4$ on the coordinate grid.
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shade ( a cup b ) on the venn diagram.
Shade three regions: 1. The portion of circle $A$ that does not overlap with circle $B$ 2. The portion of circle $B$ that does not overlap with circle $A$ 3. The area inside the u…
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use the 5 by 5 square lattice shown, with the line segment ab. list all…
a) 2, 12, 22 b) 3, 4, 5, 8, 9, 10, 13, 14, 15, 21, 23, 24, 25 c) 1, 6, 7, 11, 16, 17, 18, 19, 20
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identify the x -intercept. the x -intercept is \\boxed{}.
$0$
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shade $(a cup b) cup (a cap c)$ on the venn diagram.
Shade the entire circle $A$, the entire circle $B$, and the overlapping regions between $A$ and $B$, $A$ and $C$. (This is equivalent to shading all elements in $A$ or $B$.)
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construct a venn diagram illustrating the sets below. $u=\\{a, b, c, d,…
- Region only in circle $W$: $a, b$ - Region only in circle $X$: $h$ - Region only in circle $Z$: $i$ - Region in $W \cap X$ only: $f$ - Region in $W \cap Z$ only: $c$ - Region in…
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shade ( a cup b ) on the venn diagram.
Shade the following regions on the Venn diagram: 1. The entire area inside the universal set box $U$ that is **not inside circle $A$** 2. The entire circle $B$ (including its over…
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25. solve for ( x ). round to the nearest tenth, if necessary.
\(x\approx6.7\)
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use the 5 - by - 5 square lattice shown, with the line segment (overlin…
1, 6, 11, 21
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write an equation of the line below.
\(y =-\frac{1}{3}x + 1\)
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write an equation of the line below.
\(y = -x\)
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use variables to name the figure shown. if more than one symbol is poss…
A. $\overrightarrow{AB}$, E. $\overrightarrow{AC}$
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write an equation of the line below.
\(y = \frac{2}{3}x-3\)
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using the side - splitter theorem, daniel wrote a proportion for the se…
2.4 units
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δxyz was reflected over a vertical line, then dilated by a scale factor…
$\triangle XYZ \sim \triangle X'Y'Z'$ $\angle XZY \cong \angle Y'Z'X'$ $XZ = 2X'Z'$
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what is the value of ( y )? ( 3sqrt{3} ) units ( 6sqrt{3} ) units ( 9sq…
$6\sqrt{3}$ units
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1 unit 1 unit use fractions to complete the sentences. each small tile …
- Each small tile has side lengths $\frac{1}{8}$ units and $\frac{1}{5}$ units. - The area of each small tile is $\frac{1}{40}$ square units. - The area of the shaded rectangle is…
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15. find the length of side ( x ) in simplest radical form with a ratio…
\(\frac{11\sqrt{3}}{2}\)
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1 unit 1 unit use fractions to complete the sentences. each small tile …
Each small tile has side lengths $\frac{1}{8}$ units and $\frac{1}{8}$ units. The area of each small tile is $\frac{1}{64}$ square units. The area of the shaded rectangle is $\fra…
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1 unit 1 unit use fractions to complete the sentences. each small tile …
1. Each small tile has side lengths $\frac{1}{6}$ units and $\frac{1}{4}$ units. 2. The area of each small tile is $\frac{1}{24}$ square units. 3. The area of the shaded rectangle…
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1 unit 1 unit use fractions to complete the sentences. each small tile …
1. Each small tile has side lengths $\boldsymbol{\frac{1}{7}}$ units and $\boldsymbol{\frac{1}{6}}$ units. 2. The area of each small tile is $\boldsymbol{\frac{1}{42}}$ square uni…
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1 unit use fractions to complete the sentences. each small tile has sid…
1. Each small tile has side lengths $\frac{1}{7}$ units and $\frac{1}{8}$ units. 2. The area of each small tile is $\frac{1}{56}$ square units. 3. The area of the shaded rectangle…
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1 unit 1 unit use fractions to complete the sentences. each small tile …
1. Each small tile has side lengths $\frac{1}{4}$ units and $\frac{1}{10}$ units. 2. The area of each small tile is $\frac{1}{40}$ square units. 3. The area of the shaded rectangl…
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1 unit 1 unit use fractions to complete the sentences. each small tile …
Each small tile has side lengths $\frac{1}{8}$ units and $\frac{1}{8}$ units. The area of each small tile is $\frac{1}{64}$ square units. The area of the shaded rectangle is $\fra…
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1 unit 1 unit use fractions to complete the sentences. each small tile …
1. Each small tile has side lengths $\frac{1}{6}$ units and $\frac{1}{5}$ units. 2. The area of each small tile is $\frac{1}{30}$ square units. 3. The area of the shaded rectangle…
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1 unit 1 unit use fractions to complete the sentences. each small tile …
Each small tile has side lengths $\frac{1}{3}$ units and $\frac{1}{10}$ units. The area of each small tile is $\frac{1}{30}$ square units. The area of the shaded rectangle is $\fr…
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1 unit 1 unit use fractions to complete the sentences. each small tile …
1. Each small tile has side lengths $\frac{1}{10}$ units and $\frac{1}{7}$ units. 2. The area of each small tile is $\frac{1}{70}$ square units. 3. The area of the shaded rectangl…
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form a rectangle. use fractions to complete the sentences. each small t…
- Each small tile has side lengths $\frac{1}{9}$ units and $\frac{1}{8}$ units. - The area of each small tile is $\frac{1}{72}$ square units. - The area of the shaded rectangle is…
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1 unit\ 1 unit\ use fractions to complete the sentences.\ each small ti…
- Each small tile has side lengths $\boldsymbol{\frac{1}{4}}$ units and $\boldsymbol{\frac{1}{6}}$ units. - The area of each small tile is $\boldsymbol{\frac{1}{24}}$ square units…
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1 unit 1 unit use fractions to complete the sentences. each small tile …
Each small tile has side lengths $\frac{1}{7}$ units and $\frac{1}{6}$ units. The area of each small tile is $\frac{1}{42}$ square units. The area of the shaded rectangle is $\fra…
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form a rectangle. use fractions to complete the sentences. each small t…
- Each small tile has side lengths $\frac{1}{7}$ units and $\frac{1}{3}$ units. - The area of each small tile is $\frac{1}{21}$ square units. - The area of the shaded rectangle is…