幾何
三角形、円、座標幾何、証明問題。
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look at this diagram; if \\(\\overleftrightarrow{df}\\) and \\(\\overle…
\( 124 \)
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assume that the following graph has the given type of symmetry. x - axi…
To complete the graph with x - axis symmetry, for every point \((x,y)\) on the given upper part of the graph (where \(x\geq5\) and \(y\geq0\)), plot the point \((x, - y)\) below t…
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solve for x: (59 - 2x)° (64 - 3x)° x = submit work it out not feeling r…
\( x = 5 \)
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jl and mo are parallel lines. which angles are corresponding angles? ∠m…
\(\boldsymbol{\angle MNK}\) and \(\boldsymbol{\angle JKN}\)
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solve for x. x = submit
\( x = 6 \)
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ce and fh are parallel lines. which angles are corresponding angles? ∠e…
\(\angle EDB\) and \(\angle HGD\)
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use the algebraic tests to check for symmetry with respect to both axes…
x - axis symmetry
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solve for x, x = submit work it out not feeling ready yet? these can h …
\( 20 \)
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find the measure of $\\angle plj$.
\(\frac{1000}{9}^\circ\) (or approximately \(111.1^\circ\))
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solve for x. x = \\square
\( x = 4 \)
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solve for x. (124 - x)° (8x + 43)° x = submit work it out not feeling r…
\(x = 9\)
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find g. write your answer as an integer or as a decimal rounded to the n
\(10.9\)
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find s. write your answer as an integer or as a decimal rounded to the …
\(13.1\)
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7. graph g r a m; the image of gram after a translation 11 units right …
To graph \( G'R'A'M' \), first find the coordinates of the original vertices \( G, R, A, M \) from the graph: \( G(-8,1) \), \( R(-7,6) \), \( A(-4,6) \), \( M(-4,1) \). Apply the…
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find p. write your answer as an integer or as a decimal rounded to the …
\(12.5\) (or \(13\) if rounded to nearest integer)
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find h. write your answer as an integer or as a decimal rounded to the …
\( \boxed{6.0} \) (or \( 6 \) if integer is preferred)
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find r. write your answer as an integer or as a decimal rounded to
\( \approx 12.9 \) (or 13 if rounded to integer, but more accurately 12.9)
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find s. write your answer as an integer or as a decimal rounded to the …
\( s\approx10.7 \)
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find r. write your answer as an integer or as a decimal rounded to the …
\( 9.0 \)
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1 ) 128° ? angle = ____ 2 ) 95° ? angle = ____ 3 ) ? 97° angle = ____ 4…
1) $52^\circ$ 2) $85^\circ$ 3) $83^\circ$ 4) $145^\circ$ 5) $108^\circ$ 6) $70^\circ$ 7) $33^\circ$ 8) $120^\circ$ 9) $123^\circ$ 10) $115^\circ$
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find the measure of $\\angle fli$. $m\\angle fli = \\square^\\circ$
\( 122 \)
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find the measure of $\\angle bhe$. $m\\angle bhe = \\square^\\circ$
\( 49 \)
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solve for x. (3x + 24)° (5x - 12)° x = submit
\( 18 \)
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solve for x.
\( 25 \)
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solve for x. x = submit work it out not feeling ready yet? these can he…
\(x = 6\)
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3. (a parallelogram with base 7 ft and height 3 ft, likely asking for a…
The area of the parallelogram is \( 21 \) square feet.
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solve for x. x = submit work it out not feeling ready yet? these can he…
\( 11 \)
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solve for x.
\( 21 \)
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（the image shows a trapezoid with a base of 10 yd and a height of 9 yd.…
The area of the figure is 90 square yards.
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what is the equation for the axis of symmetry? options: x=3, x=5, y=3, …
A. x=3
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what is the significance of the point (-3, 18)? select all correct opti…
vertex
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solve the problems below. estimate your final answer to the nearest ten…
3) 8.5 cm 4) 10 blocks 5) 11.6 feet 6) 15 inches
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what is the green dot on the parabola called? zeros minumum maximum roo…
C. maximum
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identify the y - intercept. options: (-4, 0), (-1, 9), (0, -8), (0, 0)
C. (0,-8)
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what is the equation for the axis of symmetry? options: x=5, x=1, y=3, …
B. x=1
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identify the vertex (0,0) (-4,0) (-1,-9) (0,-8)
C. (-1,-9)
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what is the green dashed line called? parabola roots or x - intercepts …
D. axis of symmetry
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define x - intercept where the parabola touches or intersects the y - a…
Where the parabola touches or intersects the x-axis
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question 6 of 10 jake and erica were solving a system of equations. the…
C. Erica is correct. Two lines with equal slopes could be the same line, but only if they have the same y - intercept.
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the graph of $y = f(x)$ is shown below. which point could be used to fi…
Point B (the point with $x$-coordinate $-1$)
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the hypotenuse of the right triangle is 5y inches long. the lengths of …
A) 35
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graph the line that passes through the points (-9, 8) and (-3, 6) and d…
The equation of the line is $\boldsymbol{y=-\frac{1}{3}x + 5}$ (The graph is already correctly plotted with the line passing through $(-9,8)$ and $(-3,6)$, extending in both direc…
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consider the line ( x - 9y = 9 ). what is the slope of a line parallel …
Slope of a parallel line: $\frac{1}{9}$ Slope of a perpendicular line: $- 9$
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andrew constructed a triangle so that $\\angle 1$ and $\\angle 2$ were …
$50^\circ$
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find the equation and slope of a line that is parallel to the line ( x …
Equation: \( x = -7 \) Slope: Undefined
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supplementary angles are two angles that have measures with a sum of 18…
The measure of angle 1 (x) is 50 degrees and the measure of angle 2 (y) is 130 degrees.
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in the diagram, which two angles are adjacent? options: $\\angle deq$ a…
$\angle MKT$ and $\angle NJT$
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9 a flagpole casts a shadow 10 ft long. if a man 6 ft tall casts a shad…
The flagpole is 15 feet tall. ### Problem 10
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12 multiple choice 2 points if the length of one of the legs of a right…
12. D. 26 13. D. (3, -4) 14. A. 29° 15. B. IV
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8 multiple choice 2 points triangle fgh and two of its angle measures a…
1. 8. B. $91^\circ$ 2. 9. C. 29 3. 10. B. 16 4. 11. C. Vertical angles are always congruent.
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4 multiple choice 2 points study $\\triangle rst$ on the grid below. gr…
1. $(-4,-8)$ 2. $2, 3, 4$ 3. $13$ 4. $\{6,9,16\}$
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multiple choice 2 points the diagram shows triangle abc. grid with tria…
$\boldsymbol{\{(-2,2),\ (-3,-2),\ (-1,-1)\}}$
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which set of side measurements could be those of a triangle? 3cm, 4cm, …
B. 5 cm, 7 cm, 11 cm
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the sides of $\\triangle abc$ are 2, 3, and 4. which set of numbers cou…
$\{20, 30, 40\}$
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two triangles are similar. the measure of the shortest side of the firs…
6.25 ### Question 2
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what is an equation of the line that passes through the point (4, 8) an…
$y = 2x$ (or equivalent forms like $2x - y = 0$)
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graph the line that passes through the points (-8,6) and (-6,3) and det…
$y = -\frac{3}{2}x - 6$
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define axis of symmetry a line that divides the graph into two equal pa…
A line that divides the graph into two equal parts. i.e. cuts the graph in half
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define vertex where the parabola touches or intersects the x-axis the h…
B. The highest or lowest point on the graph
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what are the green dots called? y - intercepts rate of change verte x -…
D. x-intercepts
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what is the significance of the ordered pair (2, -4) to the graph? it i…
A. It is the vertex
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what is the vertex of the graph? (2, 4) (3, -1) (0, 8) (4, 2)
B. (3, -1)
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name the x-intercept(s)? options: (0, 0); (2, 4); (0, 0) and (0, 4); (0…
D. (0, 0) and (4, 0)
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• contains the following groups: - dashed box with a circle • consists …
1. First blank (top group): Document Formatting 2. Second blank (under Page group): Background
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a parabola has a vertex at (-3,2). where is the axis of symmetry? y = -…
x = -3
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what is the vertex? options: (4,-4), (2,0), (0,2), (6,0)
(4,-4)
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*21. the perimeter of a square room is 80 feet. the area of the room is…
400 square feet
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refer to the figure below. if the triangle is reflected across the x - …
C. (2, -4)
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refer to the figure below. if the triangle is reflected across the y - …
(4, 3)
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if the triangle is translated so that z becomes z(-2, -3), then x becom…
$X'(2,-2)$
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calculate the area of each right triangle below. note that the figures …
1. $141.96\ \text{cm}^2$ 2. $9.375\ \text{km}^2$ 3. $3.84\ \text{in}^2$ 4. $330\ \text{mm}^2$ 5. $\frac{200}{3}\ \text{ft}^2$ (or $66.67\ \text{ft}^2$)
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10. solve for x. area = 45 un² answer:
$x = 9$
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graph the inequality below on the number line. ( y geq 7 )
To graph \( y\geq7 \) on the number line: 1. Place a closed (filled) circle at the point corresponding to 7 on the number line. 2. Draw an arrow starting from the closed circle at…
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4. you and 4 friends split the total cost of one pizza and one pitcher …
### Pizza & Iced Tea a. Variable: \( x \) = cost of iced tea (in dollars). Expression: $\frac{15 + x}{5}$ b. $\$5.40$ ### Arcade Cost a. Variable: \( g \) = number of games played…
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find the area of the right triangle. area = square units
12 square units
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use pascals triangle to expand ((z + 1)^6). ((z + 1)^6 = square)
$z^6 + 6z^5 + 15z^4 + 20z^3 + 15z^2 + 6z + 1$
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use pascals triangle to expand ((3s + 2)^5). ((3s + 2)^5 = square)
$243s^5 + 810s^4 + 1080s^3 + 720s^2 + 240s + 32$
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in exercises 1 and 2, copy and complete the table. write your answers i…
| $x$ | 5 | 4 | $\sqrt{2}$ | $12\sqrt{2}$ | |-----|---|---|------------|--------------| | $y$ | $5\sqrt{2}$ | $4\sqrt{2}$ | 2 | 24 | --- ### Exercise 2 (30°-60°-90° Triangle)
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use pascals triangle to expand ((m + 4)^4). ((m + 4)^4 = square)
$m^4 + 16m^3 + 96m^2 + 256m + 256$
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the volume of a cube depends on the length of its sides. this can be wr…
D. A cube with side lengths of 3 feet has a volume of 27 cubic feet.
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which pairs of figures below are congruent? (the chart part is omitted …
1. First pair: No 2. Second pair: Yes 3. Third pair: No 4. Fourth pair: Yes
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the function f(r) gives the area of a circle with radius r. it can be w…
A. 28.26
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find the missing side length using the trigonometry functions( sine,cos…
1. $x \approx 8.66$ cm (or $5\sqrt{3}$ cm) 2. $y \approx 42.60$ m 3. $a \approx 15.41$ cm
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complete the proof that $\\triangle wxy \\cong \\triangle vuz$. 1. $\\a…
1. Reason for Statement 4: Additive Property of Length 2. Reason for Statement 6: Substitution Property of Equality 3. Reason for Statement 8: ASA (Angle-Side-Angle) Congruence Po…
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$angle rqv cong angle stu$, $angle qvr cong angle tsu$, and $overline{u…
| Statement | Reason | |-----------|--------| | 1. $\angle RQV \cong \angle STU$ | Given | | 2. $\angle QVR \cong \angle TSU$ | Given | | 3. $\overline{UV} \cong \overline{RS}$ | …
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the triangles below are congruent and their corresponding parts are mar…
(a) $\angle A \cong \angle Z$ $\angle B \cong \angle X$ $\angle C \cong \angle Y$ (b) $\overline{AB} \cong \overline{ZX}$ $\overline{AC} \cong \overline{ZY}$ $\overline{BC} \cong …
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2. read the story a second time. this time, underline the main idea and…
a. Bees are smart creatures that work together to make honey. ### Second Sub - Question (How do you know this is the main idea?)
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the triangles below are congruent and their corresponding parts are mar…
(a) $\angle A \cong \angle Z$, $\angle B \cong \angle Y$, $\angle C \cong \angle X$ (b) $\overline{AB} \cong \overline{ZY}$, $\overline{AC} \cong \overline{ZX}$, $\overline{BC} \c…
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2. read the story a second time. this time, underline the main idea and…
a. Bees are smart creatures that work together to make honey ### 2. How do you know this is the main idea?
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$overline{fh} cong overline{fi}$, $angle j cong angle g$, and $angle gf…
1. $\overline{FH} \cong \overline{FI}$ | Given 2. $\angle J \cong \angle G$ | Given 3. $\angle GFH \cong \angle IFJ$ | Given 4. $m\angle HFJ = m\angle HFI + m\angle IFJ$ | **Addit…
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7. solve. x = 1.5 cm; y = 5.5 cm; find h . options: 8.25 cm, 38.5 cm, 6…
2.9 cm
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△vwz and △xyz are equilateral. complete the proof that △vyz ≅ △wxz. 1\t…
SAS
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the triangles below are congruent and their corresponding parts are mar…
(a) $\angle A \cong \angle Z$ $\angle B \cong \angle Y$ $\angle C \cong \angle X$ (b) $\overline{AB} \cong \overline{ZY}$ $\overline{AC} \cong \overline{ZX}$ $\overline{BC} \cong …
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c = 7 cm; y = 5.5 cm; find ( s_2 ).
6.2 cm
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j is the midpoint of \\(\\overline{fh}\\) and \\(\\overline{gi}\\). com…
SSS
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16. choose the correct answer if jk = 3 cm. use the value ( s_2 = 6.2 )…
$\frac{3}{7} \approx 0.4$
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17. choose the correct answer if jk = 3 cm. use the value $s_2 = 6.2$ f…
$\frac{3}{7} \approx 0.4$
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the formula for the volume of a cone is $v = \\frac{1}{3}bh$. solve $v …
A. \( b = \frac{3V}{h} \)
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18. choose the correct answer if jk = 3 cm. use the value $s_2 = 6.2$ f…
$\frac{6.2}{3} \approx 2.1$
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6.1 properties and attributes of polygons 1. classify the polygon as co…
1. Concave, irregular pentagon 2. $3600^\circ$ 3. $162^\circ$ 4. $\frac{360}{7}^\circ \approx 51.43^\circ$ 5. $x=12$ 6. $x=114$ 7. $x=50$ 8. $x=32$, $(4x-8)^\circ=120^\circ$, $(3x…