幾何
三角形、圓、解析幾何與證明題。
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determine which graphs are linear and nonlinear.
First graph: Linear Second graph: Linear Third graph: Nonlinear
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in the figure below, m∠4 = 67°. find m∠1, m∠2, and m∠3.
$m\angle1 = 67^{\circ}$, $m\angle2 = 113^{\circ}$, $m\angle3 = 113^{\circ}$
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explore the properties of rotation by following these steps. vertices c…
\(90\)
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in the figure below, m∠4 = 67°. find m∠1, m∠2, and m∠3.
$m\angle1 = 67^{\circ}$ $m\angle2 = 113^{\circ}$ $m\angle3 = 113^{\circ}$
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graph the following function on the axes provided. f(x)=\begin{cases}3x…
The graph consists of a line \(y = 3x+6\) for \(x\in(-4,-1)\) and a line \(y=-2x + 2\) for \(x\in(-1,3)\) with open - circles at the endpoints of each line segment.
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in the figure below, m∠1 = 96°. find m∠2, m∠3, and m∠4.
$m\angle2 = 84^{\circ}$, $m\angle3 = 96^{\circ}$, $m\angle4 = 84^{\circ}$
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if a rectangle has an area of 12 m², then it has sides of length 3 m an…
Hipótesis: Un rectángulo tiene un área de 12 m². Conclusión: Tiene lados de longitud 3 m y 4 m. ### 8.
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3×3 systems applications the interior angles of a triangle sum to 180°.…
$m\angle A = 92^{\circ}$, $m\angle B = 43^{\circ}$, $m\angle C = 45^{\circ}$
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in triangle pqr, $overline{qr}$ is extended to point s. the measure of …
C. \(34^{\circ}\)
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8. figure 2 is a scale - drawing of figure 1. the area of figure 1 is 2…
180 square units
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a cylinder has a diameter of 6 inches and a height of 21 inches. what i…
C. $189\pi$
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in this diagram, △bac ~ △edf. if the area of △bac = 6 in², what is the …
$2.7$
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a. eduardo uses a scale - factor of 3 to draw figure l. complete figure…
Check the ratios of the distances from point \(F\) to corresponding vertices of figure \(C\) and the other figures. If the ratios are constant for a figure, then that figure is a …
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chapter 13: complements pages 391 - 92 predicate nominatives 13e. a pre…
1. Linking verb: was; Predicate nominative: a French underwater explorer 2. Linking verb: were; Predicate nominative: ocean life and conservation 3. Linking verb: were; Predicate …
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point f lies on a unit circle in the xy - plane and has coordinates (0,…
D. \(35\pi\)
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evaluate independent practice learning goal i can construct exponential…
$y = 27\cdot3^{x}$
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3x3 systems applications situation c. the interior angles of a triangle…
\(m\angle A = 92^{\circ}\), \(m\angle B = 45^{\circ}\), \(m\angle C = 43^{\circ}\)
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an isosceles triangle has two congruent sides, called legs. the third s…
11 cm
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in right triangle abc, angles a and b are acute, side ac has a length o…
B. 265.5
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complete problems 3 and 4. in woodworking class, eduardo makes a patter…
For part a: Draw figure \(K\) with sides twice as long as the corresponding sides of the original figure with respect to the center of dilation \(M\). For part b: Draw figure \(L\…
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exercise b in the sentences below, circle each verb. then, identify eac…
6. Verb: became; Predicate Nominative: president 7. Verb: describes; Direct Object: him 8. Verb: is; Predicate Nominative: student 9. Verb: has; Direct Object: spots 10. Verb: is;…
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what is the volume of this cylinder in cubic inches? 40π 80π 200π 320π …
$200\pi$
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figure b is a scale copy of figure a. circle the scale factor that was …
$\frac{1}{2}$
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in this diagram, $\triangle bacsim\triangle edf$. if the area of $\tria…
$14.2$
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draw a line representing the “rise” and a line representing the “run” o…
The slope of the line is $-\frac{5}{2}$
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find x. x = meters
$8$ meters
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3. figure 2 is a scale drawing of figure 1. the area of figure 1 is 15 …
375 square units
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5. look at the shape below. how many lines of symmetry does this shape …
5
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sketch θ = -\\frac{2π}{3} radians in standard position on the unit - ci…
$a =-\frac{1}{2}$ $b=-\frac{\sqrt{3}}{2}$ $P=(-\frac{1}{2},-\frac{\sqrt{3}}{2})$
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5. translate the sentence into an equation or formula. the perimeter p …
5. $P = 2l + 2w$ 6. $a=-12$
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graph the compound inequality on the number line. x < -4 and x > -8
Draw an open - circle at \(x = - 8\), an open - circle at \(x=-4\), and shade the region between them on the number line.
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graph the compound inequality on the number line. x < 5 or x > 7
Draw an open circle at \(x = 5\) and shade the number - line to the left of \(x = 5\). Draw an open circle at \(x = 7\) and shade the number - line to the right of \(x = 7\).
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graph the compound inequality on the number line. x≥3 and x<8
Draw a closed - circle at 3, an open - circle at 8, and shade the region between 3 and 8 on the number line.
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1. antoine and bobby each rotated a pentagon about point p, but they ea…
1. One of the rotations is likely incorrect. In a proper rotation (a rigid transformation), the shape and size of the pentagon should remain the same, and only its orientation sho…
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a preschool is building a sandbox as shown. select all the expressions …
D. \((10\times5\times2)+(6\times2\times2)\)
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what is one way you can rewrite the formula for the circumference of a …
divide both sides by $2\pi$ to get $r = \frac{C}{2\pi}$
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check understanding 1. antoine and bobby each rotated a pentagon about …
They are likely not correct because they probably used different angles of rotation about point $P$. ### 2.
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triangle abc was translated according to the rule (x, y) → (x + 1.5, y …
To find the pre - image $\triangle ABC$, apply the rule $(x,y)\to(x - 1.5,y+3.5)$ to the vertices of $\triangle A'B'C'$ and graph the resulting triangle.
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the circumference of the circle is select choice units and its area is …
The circumference of the circle is 40.2 units and its area (not in - choice here but for full - understanding) is approximately 128.6 square units. For the given choices, the circ…
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a school is building a sandbox as shown. select all the expressions tha…
A. \((6\times5\times2)+(4\times5\times2)\) B. \((10\times5\times2)-(4\times2\times2)\)
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draw the following triangle after a 90° clockwise rotation about the or…
Draw the triangle with vertices obtained by applying the 90 - degree clockwise rotation rule $(x,y)\to(y, - x)$ to the original triangle's vertices.
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triangle pqr has coordinates p(-1, 5), q(1, 2), and r(-3, -1). determin…
C. $P(1,5), Q(-1,2),$ and $R(3,-1)$
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triangle pqr has coordinates p(-1, 5), q(1, 2), and r(-3, -1). determin…
C. $P(4,1),Q(6,-2),$ and $R(2,-5)$
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the two figures are scaled copies of each other. figure 1 figure 2 a. w…
a. 2 b. $\frac{1}{2}$
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triangle jkl has coordinates j(2, -5), k(-1, -3), and l(-4, 5). determi…
A. $J(2,5), K(-1,3),$ and $L(-4,-5)$
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in the diagram below, $overline{ab}congoverline{bd}congoverline{bc}$, a…
$65^{\circ}$
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lin and andre used different methods to find the area of a regular hexa…
Lin's method: Approximately $93.53$ square inches. Andre's method: $93.6$ square inches.
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in the diagram, $overleftrightarrow{ab}$ and $overrightarrow{ec}$ are p…
$x = 3$; $m\angle HEB=27^{\circ}$
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the measures of two angles of a triangle are 98° and 20°. find the meas…
\(62^{\circ}\)
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problem #3 - unit 1 (medium) identify two pairs of congruent shapes pro…
Problem #3: A and F, B and D Problem #4: The second shape from the left Problem #5: The first shape on the right
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2. does a triangle with sides of lengths 1.5 ft, 2.5 ft, and 2 ft form …
Yes, because \(1.5^{2}+2^{2}=2.25 + 4 = 6.25\) and \(2.5^{2}=6.25\), satisfying the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\).
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in the figure, $overrightarrow{ca}$ and $overrightarrow{ce}$ are opposi…
$70^{\circ}$
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the measures of two angles of a triangle are 66° and 62°. find the meas…
\(52^{\circ}\)
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which statements are true about triangle abc and its translated image a…
The rule for the translation can be written as \(T_{3,-5}(x,y)\) The rule for the translation can be written as \((x,y)\to(x + 3,y-5)\) The triangle ABC has been translated 3 unit…
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answer attempt 1 out of 2 x = y =
$x = 12$ $y = 120$
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given (lparallel mparallel n), find the value of (x).
\(x = 18\)
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2) given: ptom ≡ cbad grade 8: week of 9/22, math hw - day 2 directions…
\(PT = 41\mathrm{cm}\) \(DA = 50\mathrm{cm}\) \(TO = 79\mathrm{cm}\) \(CD = 112\mathrm{cm}\) \(m\angle B = 144^{\circ}\) \(m\angle O = 40^{\circ}\) \(m\angle M = 60^{\circ}\) \(m\…
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in the figure, $overrightarrow{ca}$ and $overrightarrow{ce}$ are opposi…
D. $\angle GFC$
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grade 8: week of 9/22, math hw - day 2 directions: show all steps of yo…
Rotate Polygon A 90 degrees counter - clockwise about a vertex and then translate it to match Polygon B.
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graph the image of the figure using the transformation given. 9) reflec…
Graph the triangle with vertices obtained by applying the formula $(x,4 - y)$ to each vertex of the original triangle $STU$.
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irina wants to tile her floor using the translation shown below. which …
\(T_{-3,2}(x,y)\)
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find the measure of the missing angle. show all of your work.
For the first triangle, the missing - angle measure is \(81^{\circ}\). For the second triangle, the missing - angle measure is \(77^{\circ}\).
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find the volume of a cone with a height of 10 ft and a base diameter of…
$94.2$ ft³
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13. the average of your 3 quiz grades is 17 points. two of your quiz gr…
$20\frac{2}{3}$ feet ### 14.
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a triangle on a coordinate plane is translated according to the rule (t…
$(x,y)\to(x - 8,y + 4)$
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graph the image of the figure using the transformation given. 9) reflec…
Follow the above - mentioned steps to graph the reflected images for each transformation.
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grade 8: week of 9/22, math hw - day 2 directions: show all steps of yo…
**Problem #1**: Rotate Polygon A 90 - degrees counter - clockwise about a vertex and then translate it to match Polygon B. **Problem #2**: The shapes are congruent. Translate Poly…
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proof write a paragraph proof to prove that if e is the midpoint of $ov…
The proof is completed as shown above. We used the definition of a mid - point to establish equal - length segments and then used the substitution property of equality to prove th…
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problem #5 - unit 1 (medium) a. find a shape congruent to shape a. b. n…
a. D b. C, E Problem #6: F
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trapezoid lmnp was constructed using trapezoid lmnp. for the transforma…
A. \(LL' = PP'\) B. \(LL'=MM'\) C. Trapezoid \(LMNP\) is congruent to trapezoid \(L'M'N'P'\) E. All line segments that connect a point on the pre - image to its corresponding poin…
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10. a custodian secures a ladder of l the school. the ladder makes an a…
The lower end of the lean - to should be approximately $1.48$ m away from the base of the tree. ### Question 12
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which rule represents the translation from the pre - image, ▱abcd, to t…
$T_{1,2}(x,y)$
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classify the triangles by angle measure. acute, obtuse, or right.
Acute; Obtuse; Obtuse; Acute
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problem #5 - unit 1 (medium) a. find a shape congruent to shape a. b. n…
Problem #5 - a: D Problem #5 - b: C, E Problem #6: F
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write a rule to describe each transformation. 5) 6) 7) 8)
5. $(x,y)\to(x - 2,y + 3)$ 6. $(x,y)\to(-x,-y)$ 7. $(x,y)\to(x,-y)$ 8. $(x,y)\to(x + 4,y - 2)$
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the figure below is translated up 5 units. what are the coordinates of …
\((4,-3)\)
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8. a 5 - m - long ladder is leaning up against the side of a barn. it r…
The angle the ladder makes with the ground is approximately $57.1^{\circ}$
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the figure below is dilated with the center of dilation at the origin a…
The coordinates of the image of point \(R\) are \((1, - 2)\).
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the rule as a mapping for the translation of a rectangle is (x, y) → (x…
a translation of 2 units to the left and 7 units up
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6 from unit 1, lesson 10 on the grid, draw three different triangles wi…
Draw three triangles on the grid: one with base 2 and height 8, one with base 4 and height 4, one with base 8 and height 2, and label the base and height of each.
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the diameter of a cylindrical water tank is 12 ft, and its height is 13…
$1470$ ft³
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the \golden rectangle\ is a rectangle that has the following ratio of w…
\(19.42\)
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hexagon defghi is translated 8 units down and 3 units to the right. if …
B. $(-6,-6)$
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3. find x to the nearest tenth of a centimetre. a) b)
a) $25.6$ cm b) $8.0$ cm
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53. geometry the width of a box is 2 m less than the length. the height…
5 m
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rectangle efgh is translated according to the rule t_{-5,9}(x,y). if th…
B. $(-7,6)$
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8. the length of a rectangle is nine more than twice the width. write a…
$6w + 18$
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classify the triangles by side length. equilateral, isosceles, or scale…
1. Scalene 2. Scalene 3. Isosceles 4. Isosceles
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a rectangle is drawn so the width is 5 inches longer than the height. i…
$24.2$
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the image of the figure using the transformation given. reflection acro…
To find the image of a figure reflected across $x = 2$, use the rule $(x,y)\to(4 - x,y)$ for each point $(x,y)$ of the original figure.
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grade 8: week of 9/22, math hw - day 1 directions: show all steps of yo…
1. $\overline{XZ}$, $\angle Q$ 2. $\angle A$, $\overline{XY}$ 3. $\overline{DB}$ 4. a. A b. D and F
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using the transformation given. 4) reflection across x = 2
A point $(x,y)$ is reflected to $(4 - x,y)$ across the line $x = 2$.
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6. what is the solution of the equation below? 0.1(20x + 100)=3x + 10 (…
A. \(x = 0\)
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practice problems from unit 1, lesson 9 a. identify a base and a corres…
a. Base $b = 6$ units (horizontal side), height $h = 2$ units (perpendicular distance from base to opposite vertex) b. 6 square units
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proof complete the flow proof to prove that if point m is the mid - poi…
Drag "LM = MN" to the first blank under "M is the mid - point of LN, L is the mid - point of AB, AL = MN" using the mid - point theorem. Drag "AL = LB" to the second blank under t…
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graph the image of the figure using the transformation given. 3) reflec…
# Explanation: ## Step1: Recall reflection formula For a point $(x,y)$ reflected across the vertical line $x = a$, the new - point $(x',y')$ is given by the formula $x'=2a - x$ an…
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5 from unit 1, lesson 9 a. identify a base and a corresponding height t…
a. Base $b = 8$ units, height $h = 3$ units (answers may vary depending on which side is chosen as the base). b. The area of the triangle is 12 square - units.
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for help with question 1, refer to example 1. 1. use a scientific calcu…
# Explanation: ## Step1: Use scientific - calculator for sine and cosine values Use a scientific calculator to find the sine and cosine of the given angles and round to four decim…
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initial knowledge check question 8 congruent? yes no similar? yes no co…
Top - left: Congruent? No, Similar? No Top - right: Congruent? Yes, Similar? Yes Bottom - left: Congruent? No, Similar? Yes Bottom - right: Congruent? Yes, Similar? Yes
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28. miriam is sewing an appliqué of an ice cream cone on a flag which t…
Approximately 220 square inches.