幾何
三角形、円、座標幾何、証明問題。
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find the area of the shaded region
$x^2 - 3x + 36$
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graph the line $y = -1$.
To graph \( y = -1 \), draw a horizontal line parallel to the \( x \)-axis that passes through the point \( (0, -1) \) (and all other points with \( y \)-coordinate \(-1\)) on the…
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19) dilation of 2 about the origin
The dilated coordinates are \( L'(-4, 0) \), \( J'(0, -2) \), and \( K'(4, 2) \). To graph the dilated triangle, plot these points and connect them.
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what is the measure of angle 1 in the figure below? 80° 60° 40° 30°
\(60^\circ\) (corresponding to the option with \(60^\circ\))
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use the given information to complete the proof of the following theore…
- Statement 3: \( \boldsymbol{\overline{RT}} \cong \boldsymbol{\overline{RT}} \) - Statement 4: \( \boldsymbol{\triangle QRT} \cong \boldsymbol{\triangle STR} \) (Reason: SSS Cong…
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graph the line $x = 4$.
To graph \( x = 4 \), draw a vertical line passing through the point where \( x = 4 \) on the x - axis (i.e., the point \( (4,0) \), and extending infinitely in the positive and n…
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which of the following is a pair of complementary angles?
The first pair of angles (the top - first option) are complementary angles (since their sum is \(90^\circ\)). So the correct option is the first one (the top - first circle with t…
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18) dilation of 1.5 about the origin
The dilated triangle has vertices at \( J'(-3,4.5) \), \( K'(4.5,0) \), and \( L'(0,-1.5) \). To draw the dilated figure, plot these points and connect them. (Note: The actual plo…
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apply cavalieris principle the following figures all have the same heig…
A. Only A and B
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consider the following cylinder and cone. marcel tried to use cavalieri…
B. It isn't true that corresponding cross-sections have the same area.
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graph the line $y = -6$.
To graph \( y = -6 \), draw a horizontal line (parallel to the \( x \)-axis) that passes through the point \( (0, -6) \) (and all other points with \( y = -6 \)) on the coordinate…
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graph the line $x = -7$.
To graph \( x=-7 \), draw a vertical line passing through \( x = -7 \) on the x - axis (parallel to the y - axis). The line will include all points where the \( x \)-coordinate is…
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using the diagram, identify the dashed line segment. perpendicular bise…
C. median
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graph the line $y = 8$.
To graph \( y = 8 \), draw a horizontal line parallel to the \( x \)-axis that passes through the point \( (0, 8) \) (and all other points with \( y = 8 \)) on the coordinate grid.
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what is the slope of this line? simplify your answer and write it as a …
\(-\frac{5}{3}\)
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using the given figure, find the length of \\(\\overline{de}\\) if \\(\…
1 unit
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name a segment that is an angle bisector of the given figure.\\(\\overl…
\(\boldsymbol{\overline{AE}}\) (corresponding to the option with \(\overline{AE}\))
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4） what is the area of the triangle? □ square centimeters
6 square centimeters
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a rectangular board is 1100 millimeters long and 900 millimeters wide. …
\( 0.99\space \text{m}^2 \)
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in a plane, lines that never meet are called ______. perpendicular inte…
D. parallel
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1 yard 8 yards what is the area of the triangle? □ square yards
4 square yards
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graph the line $x = -3$.
To graph \( x = -3 \), draw a vertical line passing through \( x = -3 \) on the \( x \)-axis (parallel to the \( y \)-axis, with all points on the line having \( x \)-coordinate -…
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find p. write your answer in simplest radical form. kilometers submit w…
$3\sqrt{3}$ kilometers
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the perpendicular bisector of a line segment does which of the followin…
D. identifies the midpoint of the line segment (assuming the options are labeled A, B, C, D as per the order: first option A, second B, third C, fourth D)
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find c. write your answer in simplest radical form. yards submit work i…
$28\sqrt{3}$ yards
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find n. 8√2 mm 45° 45° n write your answer in simplest radical form. bl…
16 millimeters
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which of the following statements about a bisector is true? it creates …
It creates two equal angles or line segments
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using trigonometry to find lengths find the missing side. round to the …
\(4.7\) ### Problem 3:
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find s. write your answer in simplest radical form. meters
$4\sqrt{3}$ meters
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4 ft 5 ft what is the area of the triangle? square feet
10 square feet
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3. if the medium rectangle represents $10^5$, then what does the large …
### Problem 3 (Large Square and Small Square when Medium Rectangle is \(10^5\)) Assuming the medium rectangle is a product of a small square and a large square (or related by expo…
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a science fair poster is a rectangle 48 inches long and 36 inches wide.…
12 square feet (or $12\ \text{ft}^2$)
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angles 1 and 3 are ______? right supplementary complementary vertical
vertical (the option corresponding to "vertical")
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8. find the surface area of the following figure. round to the nearest …
$205.8$ $\text{mi}^2$
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graph the line $x = 6$.
To graph \( x = 6 \), draw a vertical line passing through the point where \( x = 6 \) on the x - axis (intersecting the x - axis at \( (6,0) \)) and extending parallel to the y -…
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∠1 and ∠2 are called ______. supplementary angles vertical angles compl…
supplementary angles
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solve the inequality graph the solution. |2x + 3| - 14 ≤ -1 select the …
A. The solution is $\boldsymbol{-8 \leq x \leq 5}$ *(For the graph: Draw a number line, place closed circles at -8 and 5, and shade the region between these two points.)*
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solve the absolute value inequality. other than \\( \\varnothing \\), u…
A. $(-\infty, -5) \cup (-5, \infty)$ (With the corresponding number line that has an open circle at $-5$ and shaded lines extending to both the left and right)
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find the measures of the numbered angles in the kite. the figure is not…
\( 90 \)
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six graphs are shown below. click on the tabs to see them. graph 1 grap…
The box for Graph 1 is not checked (i.e., Graph 1 does not represent a function, so we do not mark its corresponding checkbox).
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question two sides of a parallelogram are 9.3 feet and 4.4 feet. the me…
32.7 square feet
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which of the following equations could be used to find the value of x? …
$\frac{\sin(x)}{38} = \frac{\sin(54)}{31}$
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4. find the measure of angle r.
\(75^\circ\)
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list the angle measures of $\\triangle uvw$ in order from smallest to l…
\(m\angle U<m\angle V < m\angle W\)
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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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graph the line that has a slope of $-\frac{2}{3}$ and includes the poin…
To graph the line: 1. Plot the point $(3,2)$ (given point). 2. Use the slope $-\frac{2}{3}$: from $(3,2)$, move 3 units to the right (increase $x$ by 3) and 2 units down (decrease…
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determine the following for the parabola given by the equation $y^2 = 2…
\( (6, 0) \) ### Part 2: Find the equation for the directrix
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given the circle below with chords \\( \\overline{uv} \\) and \\( \\ove…
11.1
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$overline{wx} cong overline{vw}$ and $overline{ux} cong overline{uv}$. …
$\triangle UWX \cong \triangle UWV$
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s is the midpoint of \\(\\overline{rt}\\), \\(\\overline{ru} \\cong \\o…
$\triangle RSU \cong \triangle STV$
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figure pqrs is reflected to form figure wxyz. which side of figure wxyz…
- Side corresponding to \(QR\): \(\overline{XY}\) - Angle corresponding to \(\angle P\): \(\angle W\)
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j is the midpoint of \\(\\overline{hi}\\) and \\(\\overline{gi} \\cong …
$\triangle GIJ \cong \triangle GHJ$
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for what value of x must abcd be a parallelogram? for abcd to be a para…
\(9\)
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find the area of the given triangle. round your answer to the nearest t…
\( 34.2 \)
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$\\angle rqs \\cong \\angle tqu$, $\\angle qsu \\cong \\angle qtr$, and…
7. Reason: Transitive Property of Equality 8. Reason: ASA (Angle-Side-Angle) Congruence Postulate
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graph the image of trapezoid stuv after a dilation with a scale factor …
The dilated trapezoid \( S'T'U'V' \) has vertices at \( S'(-9, -9) \), \( T'(9, -9) \), \( U'(9, 9) \), and \( V'(0, 9) \). To graph it, plot these points and connect \( S' \) to …
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graph each equation. 9) \\(dfrac{x^2}{4} + dfrac{y^2}{9} = 1\\) coordin…
The graph is an ellipse centered at the origin with vertices at \((0, \pm 3)\) and co - vertices at \((\pm 2, 0)\), and the ellipse is drawn through these points on the given coor…
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Question was provided via image upload.
11. \(x = 4\), \(y = 12\) 12. \(m\angle C = 80^\circ\) 13. YES 14. NO 15. YES
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a hot air balloon takes off from the ground and rises 150 meters every …
The line representing $y=150x$ is drawn by plotting the points $(0,0)$, $(1,150)$, $(2,300)$, $(3,450)$ and connecting them with a straight line, extending infinitely in[LLM SSE O…
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graph the line $x = 5$.
The graph of \(x = 5\) is a vertical line passing through the point \((5,0)\) (and all points with \(x\)-coordinate 5) on the coordinate grid, parallel to the \(y\)-axis.
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1. solve. -15 ÷ (-5) 2. rewrite using the distributive property. 8(b + …
\(3\) ### 2. Rewrite \(8(b + 7)\) using the distributive property
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1. solve. -15 ÷ (-5) 2. rewrite using the distributive property. 8(b + …
\(8b + 56\) ### Problem 3: Find the missing side length of the similar shapes.
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2 for each expression, circle any like terms and list any variables. a.…
### Part a: $-2.5x + 3.9 + 1.7x$ #### Step 1: Identify Like Terms Like terms are terms with the same variable (or constant terms). Here, $-2.5x$ and $1.7x$ have the variable $x$, …
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question in \\(\\triangle efg\\), the measure of \\(\\angle g = 90^\\ci…
$0.47$
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question in $\\triangle hij$, the measure of $\\angle j = 90^\\circ$, $…
$\frac{24}{25}$
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find the exact value of tan v in simplest radical form. answer
\(\frac{4}{3}\)
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7. |2y - 7| ≥ 11 show your work below your answer. draw the appropriate…
The solution to the inequality \(|2y - 7| \geq 11\) is \(y \leq -2\) or \(y \geq 9\). On the number line, we would draw a closed circle at \(-2\) with an arrow pointing to the lef…
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find the exact value of \\(\\tan k\\) in simplest radical form.
\(\dfrac{7\sqrt{51}}{51}\)
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graph the line that has a slope of -3 and includes the point (1, 3). cl…
To graph the line: 1. Plot the point $(1,3)$ (given point). 2. Use the slope $m=-3=\frac{\text{rise}}{\text{run}}=\frac{- 3}{1}$. From the point $(1,3)$, move 1 unit to the right …
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think about what you know about expressions. fill in each box. use word…
### Part 1: Defining Terms (Table Completion) | Word | In My Own Words | Examples | |--------------|-------------------------------------------------------------------------------…
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find the y-intercept and the x-intercept of the line below. click on (a…
(a) \(y\) - intercept: \(-1\) (b) \(x\) - intercept: \(3\)
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find the x-intercept and the y-intercept of the line belo (a) x-interce…
(a) \(x\) - intercept: \(4\) (b) \(y\) - intercept: \(-4\)
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from unit 3, lesson 12 the points with coordinates (4, 8), (2, 10), and…
The slope of the line is \(-1\). ### Part c
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invent a story of how jada fills the aquarium that fits the graph 3 fro…
| \( r \) | 3 | 4 | \( \frac{1}{2} \) | 10 | | ---- | ---- | ---- | ---- | ---- | | \( A \) | \( 9\pi \) | \( 16\pi \) | \( \frac{\pi}{4} \) | \( 100\pi \) |
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solving algebraically for unknown values find the values of x and y tha…
\( x=\boxed{80} \), \( y=\boxed{130} \)
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use the law of sines. find the measure x to the nearest tenth.
10.1
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write and solve an inequality to find the values of x for which the per…
C. \( x < 24 \)
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compare the graph to the graph of $f(x)=x^2$. the graph of $g$ is a tra…
To solve the problem of comparing the graph of \( g(x) \) to \( f(x) = x^2 \) (a parabola opening upwards with vertex at the origin \((0,0)\)), we analyze the translation rules fo…
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which system is represented in the graph? $y > x^2 - 2x - 3$ $y > x + 3…
\( y > x^2 - 2x - 3 \) \( y < x + 3 \) (the fourth option, with the circle next to \( y > x^2 - 2x - 3 \) and \( y < x + 3 \))
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write an equation for the area, a, of the triangle shown. a =
$A = \frac{1}{2} \times 10 \times 6$
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a figure has the dimensions shown in inches. 1. find the area of the co…
\( 2(x^2 + 5)(x^3 + 3) \) ### Question 2
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$\\angle gfi \\cong \\angle hfi$ and $\\overline{fi} \\perp \\overline{…
1. Reason for $\overline{FI} \cong \overline{FI}$: Reflexive Property of Congruence 2. Reason for $\triangle FHI \cong \triangle FGI$: Angle-Side-Angle (ASA) Congruence Postulate
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$\\overleftrightarrow{tv}$ bisects $\\angle utw$ and $\\angle uvw$. com…
1. Reason for $\angle UTV \cong \angle VTW$: Definition of angle bisector 2. Reason for $\angle TVU \cong \angle TVW$: Definition of angle bisector 3. Reason for $\triangle TVW \c…
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solve for x. the triangles in each pair are similar. type your answer i…
$x = \frac{26}{3}$ or $x \approx 8.67$
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you may use your notes/cheat sheets show all steps for a grade use $\\t…
1. 17.2 2. D. $\overline{AC} = 12$ and $m < A = 40^\circ$
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$overline{vw} perp overline{tw}$, $angle vtw cong angle tvu$, and $over…
1. $\overline{VW} \perp \overline{TW}$ (Given) 2. $\angle VTW \cong \angle TVU$ (Given) 3. $\overline{UV} \perp \overline{TU}$ (Given) 4. $\angle U \cong \angle W$ (Definition of …
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u is the midpoint of \\(\\overline{qs}\\). complete the proof that \\(\…
ASA (Angle-Side-Angle) Congruence Postulate
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graph the line with slope 3 passing through the point (-2, 5).
To graph the line, plot the point \((-2,5)\), then use the slope \(3=\frac{3}{1}\) to find other points (e.g., \((-1,8)\) by moving 1 right and 3 up from \((-2,5)\), or \((-3,2)\)…
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△qsu is equilateral. complete the proof that △stu ≅ △srq. (image of tri…
Angle-Side-Angle (ASA) Congruence Postulate
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question find the measure of the missing angles. answer attempt 1 out o…
$b = 116^\circ$ $c = 64^\circ$
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y is the midpoint of \\(\\overline{uw}\\) and \\(\\overline{vx}\\) and …
| Statement | Reason | |-----------|--------| | 1. $Y$ is the midpoint of $\overline{UW}$ | Given | | 2. $Y$ is the midpoint of $\overline{VX}$ | Given | | 3. $\overline{VY} \cong…
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△efh is equilateral. complete the proof that △fgh ≅ △eih. | | statement…
### Statement 4: $\overline{FH} \cong \overline{EH}$ ### Reason 4: Sides of equilateral triangle are congruent ### Statement 5: $\triangle FGH \cong \triangle EIH$ ### Reason 5: S…
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$overline{gh} cong overline{ef}$ and $overline{ef} parallel overline{gh…
$\triangle EFG \cong \triangle GHE$
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declarative sentences there are four types of sentences: declarative, i…
### Part 1: Circle the declarative sentences To determine declarative sentences, we use the definition: a telling sentence that gives information, starts with a capital letter, an…
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eh bisects ∠feg and ef ≅ eg. complete the proof that δefh ≅ δegh. 1 eh …
| Statement | Reason | |-----------|--------| | $\overleftrightarrow{EH}$ bisects $\angle FEG$ | Given | | $\overline{EF} \cong \overline{EG}$ | Given | | $\angle FEH \cong \angle…
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k is the midpoint of \\(\\overline{hj}\\) and \\(\\overline{gi}\\). com…
Statement 5: $\angle GKJ \cong \angle IHK$ Reason 5: Vertical Angles Theorem Statement 6: $\triangle GJK \cong \triangle IHK$ Reason 6: SAS Congruence Postulate
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h is the midpoint of \\(overline{gi}\\), \\(overline{hk} \\cong overlin…
$\triangle GHJ \cong \triangle IHK$
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u is the midpoint of \\(\\overline{st}\\). complete the proof that \\(\…
$\overline{RU} \cong \overline{RU}$; $\Delta RTU \cong \Delta RSU$
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u is the midpoint of \\(\\overline{st}\\). complete the proof that \\(\…
$\triangle RTU \cong \triangle RSU$
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$\\overleftrightarrow{gj}$ bisects $\\angle hgi$ and $\\overline{gi} \\…
$\Delta GHJ \cong \Delta GIJ$