幾何
三角形、圓、解析幾何與證明題。
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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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writing trigonometric ratios use the diagram of triangle xyz to answer …
Length of side XY: 10 Value of $\sin(X)$: $\frac{4}{5}$ Value of $\cos(X)$: $\frac{3}{5}$ Value of $\tan(X)$: $\frac{4}{3}$
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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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which graph shows a function?
The top-right parabola graph (opening upwards with vertex below the x-axis) shows a function.
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deriving a tangent ratio for special triangles which statements are tru…
NM = x LM = $x\sqrt{2}$ $\tan(45^\circ) = 1$
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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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consider △lnm. which statements are true for triangle lnm? check all th…
- The side opposite $\angle L$ is $\overline{NM}$. - The side opposite $\angle N$ is $\overline{ML}$. - The hypotenuse is $\overline{LN}$.
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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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is this a function? yes no
Yes
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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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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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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…
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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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1 unit 1 unit use fractions to complete the sentences. each small tile …
Each small tile has side lengths $\frac{1}{9}$ units and $\frac{1}{4}$ units. The area of each small tile is $\frac{1}{36}$ square units. The area of the shaded rectangle is $\fra…
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use fractions to complete the sentences. each small tile has side lengt…
- Each small tile has side lengths $\boldsymbol{\frac{1}{6}}$ units and $\boldsymbol{\frac{1}{7}}$ units. - The area of each small tile is $\boldsymbol{\frac{1}{42}}$ square units…
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6. rectangle tuvw with vertices t(-3, -1), u(0, -2), v(-2, -8), and w(-…
### Problem 6: Rotación de 90° en sentido contrario a las agujas del reloj para el rectángulo TUVW #### Explicación: La fórmula para rotar un punto \((x, y)\) 90° en sentido contr…
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angle $\\theta = 70^{\\circ}$, which of the following is the measure of…
(c) \(-290^\circ\)
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rotate \\(\\triangle xyz\\) \\(270^\\circ\\) about the origin, \\((0,0)…
To solve the problem of rotating \(\triangle XYZ\) \(270^\circ\) about the origin \((0,0)\), we use the rotation rule for a \(270^\circ\) counterclockwise (or \(90^\circ\) clockwi…
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what is the angle of rotation about the origin, (0,0), that maps \\(\\t…
D. \(180^\circ\)
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question 1 respond to the following based on your reading. draw a coord…
To draw the coordinate plane: 1. Draw a horizontal x - axis and a vertical y - axis intersecting at the origin (0,0). 2. Mark values from - 5 to 5 on both axes (e.g., - 5, - 4, - …
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using co-function theorem (complementary angle theorem) to answer the q…
75 ### Second Question (tan(42°) = cot(?)°)
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convert the angle $\\theta = -\\frac{3\\pi}{4}$ to degree measurement. …
a. $-135^\circ$ ### Second Question (Converting $\frac{5\pi}{3}$ to degrees)
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convert angle $\\theta = 225^{\\circ}$ to its radian measurement.\ (a) …
c. \( \frac{5\pi}{4} \) ### Question 2:
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problem 1 the volume of a cone is 30π cubic units. what is the volume o…
$108\pi$ cubic units
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factor to find the dimensions. 1 the area of a rectangle is $4x^2 + 4x …
The dimensions of the rectangle are \(2x + 1\) and \(2x + 1\) (or \((2x + 1)\) by \((2x + 1)\)). ### Problem 2
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the movement of the progress bar may be uneven because questions can be…
120°
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the diagram shows a triangle. what is the value of a? ( a = square^circ…
$a=6$
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the diagram shows a triangle. what is the value of c? c = \\square^\\ci…
$c = 22^\circ$
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look at this diagram: if \\(\\overleftrightarrow{ce}\\) and \\(\\overle…
$40$
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the diagram shows a triangle. what is the value of v? write your answer…
$v \approx 0.8$
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what is the area of this figure? write your answer using decimals, if n…
49 square feet
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select the correct answer from each drop - down menu. given: m is the m…
First dropdown: segment GM is congruent to segment HM Second dropdown: ASA
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△jkl and △mno are shown below. which statement is true? △jkl is similar…
$\triangle JKL$ is not similar to $\triangle MNO$.
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trazar la recta. $y=\\frac{3}{5}x - 1$
To graph \(y = \frac{3}{5}x-1\), plot \((0, - 1)\) (y - intercept) and \((5,2)\) (using slope \(\frac{3}{5}\)), then draw a line through these points.
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7) choose the best answer. nester needs a cover for his circular outdoo…
200.96 m²
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which inequality pairs with ( y leq -2x - 1 ) to complete the system of…
$y>-2x+2$ (Option B)
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6) solve the word problem. pietro is planning a patio using paving ston…
$\square$ 5 circles = 1,570 in² $\square$ 10 semicircles = 1,570 in² $\square$ 100 quarter-circles = 7,850 in² $\square$ total area = 10,990 in²
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5) find the area of the circle. find the solution in terms of \\(\\pi\\…
$A = 0.09\pi \text{ mi}^2$, $A = 0.28 \text{ mi}^2$ (The correct options are $\boldsymbol{\square\ A = 0.09\pi\ \text{mi}^2}$ and $\boldsymbol{\square\ A = 0.28\ \text{mi}^2}$)
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4) find the area of the circle. find the solution in terms of \\(\\pi\\…
In terms of $\pi$: $A = 400\pi \ \text{dm}^2$ Decimal form: $A = 1,256 \ \text{dm}^2$ (The correct options are $\boldsymbol{A = 1,256 \ \text{dm}^2}$ and $\boldsymbol{A = 400\pi \…
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2) find the area of each circle to the nearest hundredth, if needed. \\…
A = 1,962.5 km²
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trazar la recta. $y=\\frac{1}{3}x + 5$
To graph the line \( y=\frac{1}{3}x + 5 \), plot the y - intercept at \( (0,5) \), use the slope \( \frac{1}{3} \) to find another point (e.g., \( (3,6) \) or \( (-3,4) \)), and t…
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the two triangles below are similar. also, ( mangle x = 35^circ ) and (…
$m\angle C = 85^\circ$ $m\angle D = 35^\circ$ $m\angle E = 60^\circ$
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a regular octagon has a side of approximately 6.0 cm and an apothem of …
$172.8$ $\text{cm}^2$
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a regular heptagon has an apothem of approximately 7.3 ft and a perimet…
178.85 ft²
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a circle with center at point o is shown below. quadrilateral abcd is i…
# Brief Explanations: - **Option A**: In $\triangle ABO$, $BO = AO$ (radii), so $\triangle ABO$ is isosceles. If $m\angle ABO = 52^\circ$, then $m\angle BAO = 52^\circ$. In $\tria…
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find the value of each variable. a. ( x = 75^circ ) and ( y = 78^circ )…
B. \(x = 78^\circ\) and \(y = 65^\circ\)
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select the correct answer from each drop - down menu. a ray of light is…
(-2, -8)
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select the correct answer from each drop - down menu. a ray of light is…
The equation of the reflected ray is $\boldsymbol{y + x = 6}$. A point that does not lie on the reflected ray (e.g., $\boldsymbol{(3, 4)}$) (any point not satisfying $y+x=6$ is va…
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triangle def is dilated with respect to the origin by a scale factor of…
D. $\sqrt{5}$ units
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42 point r divides \\(\\overline{pq}\\) in the ratio 1 : 3. if the x - …
C. 5
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type the correct answer in the box. use numerals instead of words. if n…
5
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type the correct answer in each box. complete the statement, and find t…
The quadrilateral shown is a kite. $x = 3$
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if two or more polygons are congruent, which statement must be true abo…
B. A, B, and E
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drag the tiles to the boxes to form correct pairs. not all tiles will b…
- Contrapositive → If a figure is not a polygon, it is not a square. - Converse → If a figure is a polygon, it is a square. - Inverse → If a figure is not a square, it is not a po…
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transversal $overleftrightarrow{ef}$ cuts parallel lines $overleftright…
D. $m\angle5 = 55.1^\circ$, and $m\angle7 = 124.9^\circ$.
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35 type the correct answer in the box. use numerals instead of words. i…
The length of $\overline{DE}$ is $\frac{9}{2}$ units and $m\angle CAB$ is $45$ °.
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select the correct answer. the endpoints of \\(\\overline{wx}\\) are \\…
E. $3\sqrt{2}$
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type the correct answer in the box. write your answer to one decimal pl…
2.7
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the rectangular pyramid and rectangular prism shown below have the same…
(a) $40$ (b) $120$ (c) $\frac{1}{3}$; This equation is true for all rectangular prisms and rectangular pyramids with the same length, same width, and same height.
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△abc is reflected about the line ( y = -x ) to give ( \triangle abc ) w…
B. $A(-1, 1), B(1, 2), C(0, 1)$
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type the correct answer in the box. a flight of stairs is supported by …
8
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select the correct answer. an interior angle of a regular convex polygo…
B. 9
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type the correct answer in the box. use numerals instead of words. squa…
4
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the coordinate plane shows the floor plan for a swimming pool. what is …
C. 80 square meters
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27 which polygons can be mapped onto each other by similarity transform…
C. polygons 1 and 3
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select the correct answer. a parallelogram rotates about its center. at…
C. $180^\circ$