幾何
三角形、圓、解析幾何與證明題。
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graphing an inequality graph the inequality on a number line. 24. $r \\…
1. For $r \leq -9$: Closed circle at $-9$, shade left. 2. For $g > 2.75$: Open circle at $2.75$, shade right. 3. For $x \geq -3\frac{1}{2}$: Closed circle at $-3.5$, shade right. …
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which point has coordinates (1, -5)?
Point R
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4) graph each equation with or without a table of values. a) y = -4 and…
- $y=-4$: A horizontal line passing through all points where the $y$-coordinate is $-4$, spanning the entire grid horizontally. - $x=6$: A vertical line passing through all points…
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graph the solution of this inequality: $-2x + 13 < 9$
The correct solution to the inequality \( -2x + 13 < 9 \) is \( x > 2 \). To graph this, we would have an open circle at 2 (since the inequality is strict, \( x > 2 \) not \( x \g…
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example 3 5. family maria is 11 inches shorter than her sister clara. l…
When Maria is shorter than Luna, Clara is shorter than Chad (\( C_a < C_h \)). When Maria and Luna are the same height, Clara and Chad have the same height (\( C_a = C_h \)).
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which set of angles can form a triangle? 1 acute, 1 right, and 1 obtuse…
2 acute and 1 right
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in the diagram, the measure of ∠1 is 55°. if line y is rotated 5° clock…
$50^\circ$
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10. proof consider \\(\\overleftrightarrow{ps}\\). a. complete the two …
1. Given 2. \(PQ = RS\) 3. Segment Addition Postulate 4. Substitution Property of Equality 5. Commutative Property of Addition 6. Transitive Property of Equality 8. \(\overline{PR…
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$\\angle qsr \\cong \\angle sqt$, $\\overline{rs} \\perp \\overline{qr}…
For statement 5, the reason is "Reflexive Property of Congruence". For statement 6, the reason is "AAS (Angle - Angle - Side) Congruence Criterion".
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$\\triangle prt$ is equilateral. complete the proof that $\\triangle pq…
For statement 3: Vertical Angles Theorem For statement 4: Sides of an equilateral triangle are congruent For statement 5: ASA (Angle - Side - Angle) Congruence Postulate
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2. proof complete the two - column proof. given: $overline{su} \\cong \…
The completed two - column proof is as shown in the table above. The key steps are using the given congruences, segment addition postulate, and properties of equality to show that…
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2. △smr is similar to △sat. find the length of \\(\\overline{st}\\).
\(5\)
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△bri is similar to △ght. find the length of overline{gt}.
The length of $\overline{GT}$ is $8.16$.
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read each question. then circle the best answer. 1. which word means \a…
b. reusable ### 2.
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isosceles triangles (image of a coordinate grid with a blue triangle la…
The measure of each base angle is \( \boxed{55^\circ} \) (assuming the triangle is isosceles with \( AC = AB \)).
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use the distance formula to determine the measures of the sides of $\\t…
- For \(AB\): First blank \(0\), second blank \(3\), length \(\boldsymbol{\sqrt{41}}\) units. - For \(AC\): First blank \(-4\), second blank \(-2\), length \(\boldsymbol{\sqrt{41}…
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explanation: consider the expression (2x - 3) - (-3x + 4). first, distr…
The simplified form of the expression \((2x - 3)-(-3x + 4)\) is \(5x-7\).
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given: abcd is a parallelogram, ∠gec ≅ ∠hfa and ae ≅ fc. prove: △gec ≅ …
The proof shows that \( \triangle GEC \cong \triangle HFA \) using the AAS congruence criterion, with the necessary angle and side congruences derived from the properties of paral…
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using triangle theorems m∠eal + m∠eaj = 180° m∠h + m∠l + m∠j = 180° m∠h…
The diagram shows the derivation of the equation \( m\angle H + m\angle HEA+ m\angle EAJ + m\angle J = 360^\circ \) by using the triangle angle - sum theorem (\( m\angle H + m\ang…
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expand ((5x + 4y)^6) using pascal’s triangle. ((5x + 4y)^6 = square) (s…
\(15625x^{6}+75000x^{5}y + 150000x^{4}y^{2}+160000x^{3}y^{3}+96000x^{2}y^{4}+30720xy^{5}+4096y^{6}\)
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question 3 of 10 which of the following circles lie completely within t…
A. \((x - 9)^2+(y + 9)^2=16\) C. \((x - 5)^2+(y + 5)^2=9\)
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there is a diagram of two parallel lines cut by a transversal, forming …
$\boldsymbol{\angle 2}$ and $\boldsymbol{\angle 8}$ are alternate interior angles (the option "∠2 and ∠8 are alternate interior angles" should be selected).
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lesson 5 worksheet name: allison sanchez period: 1st date: jan 12 2026 …
No (the puck's height at the goal is approximately 5.36 feet, which is more than 5 feet, so it will not score) ### Problem 2:
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name: date: period: segment addition postulate color by number instruct…
1. $x = 5$ (Dark Purple) 2. $x = -3$ (White) 3. $x = -7$ (Black) 4. $x = 0$ (Dark Blue) 5. $x = -11$ (Grey)
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there are two right triangles with a common vertex (the intersection of…
\( x = 8 \)
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the quadrilaterals abcd and jklm are similar. find the length x of \\ov…
\( 3.2 \)
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graph the line $y = 5$.
The line \( y = 5 \) is a horizontal line parallel to the \( x \) - axis, passing through all points with \( y \) - coordinate 5 (e.g., \((0,5)\), \((1,5)\), \((- 1,5)\) etc.) on …
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4. \\begin{cases} 3y = 4x - 6 \\\\ 8x - 6y = -30 \\end{cases}
There is no solution (the system is inconsistent, as the lines are parallel and never meet).
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isaiah sketches a model of a skateboard ramp. the model has two surface…
\(4\sqrt{2}\) in. (Option: \(4\sqrt{2}\) in.)
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class e general knowledge question #9 / 50 if you are preparing to tow …
B. At least one brake light if the trailer hides the brake lights on your vehicle.
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consider that △abc is an equilateral triangle, and \\(\\overline{ad}\\)…
First box: \( x \) Second box: \( 4 \) Third box: \( 3 \) Fourth box: \( x \)
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7. from point c, both ends a and b of a bridge are visible. if ac = 21 …
$25.3$ m
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10. starting at point a, a ship sails 22.4 km on a course of 174°, then…
$\approx26.0$ km (rounded to one decimal place)
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which figure appears to be correctly marked with a line of symmetry? fo…
The bottom-left figure (the chevron-shaped figure with the vertical dashed line of symmetry) is correctly marked with a line of symmetry.
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which figure appears to be correctly marked with a line of symmetry? fo…
The bottom-left figure (the chevron-shaped figure with the vertical dashed line of symmetry) is correctly marked with a line of symmetry.
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select the two correct figures. which figures appear to have line symme…
1. Yellow cross figure 2. Purple crescent figure
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find the value of x. triangle with angles 63°, 81°, and x°
$36$
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angle acb and ∠acd are , so their measures have a sum of . the measure …
- Angle \( ACB \) and \( \angle ACD \) are a linear pair, so their measures have a sum of \( 180^\circ \). The measure of \( \angle ACB \) is \( 25^\circ \). - The sum of \( \angl…
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given: a = 16, b = 18, m∠a = 60° c = m∠b = m∠c =
\( c\approx10.5 \) (assuming the handwritten note is correct), \( m\angle B = 43^\circ \), \( m\angle C = 77^\circ \) (Note: There might be an error in the problem setup or the ha…
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graph this inequality: $x > -3$ plot points on the boundary line. selec…
1. Draw a dotted vertical line at $x=-3$ (through points like $(-3,0)$, $(-3,2)$, $(-3,-2)$). 2. Shade all area to the right of this dotted line.
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20. determine the area of the shaded region. use 3 for π. there is a sq…
36 square inches
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9. proof $overline{ac} cong overline{gi}$, $overline{fe} cong overline{…
(10a two - column proof filled): | Statement | Reason | | --- | --- | | 1. $\overline{PQ}\cong\overline{RS}$ | 1. Given | | 2. $PQ = RS$ | 2. Definition of congruent segments | | …
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18. mjhs is refinishing the basketball court and decided to paint every…
Approximately \( 189.27 \) square feet (or \( 150 + \frac{25\pi}{2} \) square feet)
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13. jackie always sat in the front row because she liked to focus on th…
These appear to be sentence correction problems (likely for grammar, such as comma splices, run - on sentences, or incorrect conjunctions). Let's take problem 13 as an example: ##…
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find the slope of the line that passes through the following points: (0…
\( \frac{1}{2} \)
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26. the two triangles below are similar. what is the perimeter of trian…
The perimeter of triangle \( XYZ \) is \( 24 \, \text{cm} \).
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choose the graph of the inequality -3 > x. choose 1 answer: a: number l…
D. <graph with open circle at -3 and arrow pointing left to negative infinity>
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choose the graph of the inequality -1 > x. choose 1 answer: a (number l…
D. <The number line with an open circle at -1 and shading extending to the left towards -5>
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lesson 2 homework date period the diagram shows measurements for $\\tri…
# Explanation: ## Step 1: Analyze $\triangle WNB$ For $\triangle WNB$, the opposite side to $\angle N$ is $WB = 5$, hypotenuse is $WN = 6.5$, and adjacent side is $BN = 6$. - $\si…
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23. triangle abc is shown below. its original lengths are multiplied by…
The new perimeter of \( A'B'C' \) is \( 75 \, \text{cm} \).
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3. use the graph shown to complete each statement below a. give a verba…
a. Verbal description: Reflection over the y-axis b. Algebraic representation: $(x,y) ightarrow (-x,y)$ c. - Size of the figure: Stayed the same - Orientation of the figure: Chang…
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practice write an equation for each line. express each equation in stan…
s: a. $x - y=3$ b. $9x-2y=-10$ c. $y = 10$ (or $0x + y=10$) d. $x=10$ (or $x - 10=0$ or $1x+0y=10$)
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what is the area of the triangle? 0.6 m, 0.4 m, 0.3 m (with a right - a…
\( 0.06 \)
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hapes and scale drawings. 22. shelby drew a map of the appalachian trai…
The actual length of the Appalachian Trail is 3500 kilometers.
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i can solve problems involving similar shap21. the photo below is being…
The scale factor is \( 6 \).
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how can you show that the interior angles of $\\triangle qrs$ have a su…
- Angle QSR and ∠QST are \boxed{supplementary}, so the sum of their angle measures is \boxed{180} degrees. The measure of ∠QSR is \boxed{110} degrees. So, the sum of the measures …
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find the slope of each line. 1) 3) 5)
\(\frac{-7}{3}\) ### Problem 3:
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13. a figure skater prepares for her performance by skating 6 laps in a…
The figure skater traveled \( 360\pi \) (or approximately 1130.4) feet.
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2. practice graph each line below. a. $y = -\\frac{3}{4}x - 4$ b. $-3x …
### Part a: Graph \( y = -\frac{3}{4}x - 4 \) # Explanation: ## Step 1: Identify slope and y-intercept The equation is in slope - intercept form \( y=mx + b \), where \( m =-\frac…
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a circle is centered on point b. points a, c and d lie on its circumfer…
\(61\)
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a circle is centered on point b. points a, c and d lie on its circumfer…
\(40\)
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12. the circumference of a circle is 28.26 cm. what is the radius? $c =…
The radius of the circle is \( 4.5 \) cm.
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there is a right triangle k l m, with a right angle at l. angle at k is…
To solve this, we analyze the right triangle \( \triangle KLM \) (with \( \angle L = 90^\circ \)) and the straight line \( MN \) (so \( \angle KML + 137^\circ = 180^\circ \), henc…
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six graphs are shown below. click on the tabs to see them. graph 1 grap…
Graph 1: \(\boldsymbol{\square}\) (unchecked, since it is not a function) (Note: For other graphs, we need to analyze them similarly, but only Graph 1 is visible here.)
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find the slope of the line passing through the points (-6, -5) and (4, …
\(\frac{9}{10}\)
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use what youve learned about the volume of cylinders to answer each que…
7. 7 inches 8. 5 feet 9. 14.14 cubic meters 10. Beau's water bottle holds more water; it holds 63.64 cubic inches more.
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from little journeys to the homes of the great, vol. 3: little 1. \tnin…
C. Unfamiliar
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3) matt drove his car 40 miles due east. from there, he veered off at 5…
\(75.6\)
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what is the area of the shaded region? 29 mi 15 mi 21 mi 39 mi write yo…
408
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question find m∠gfe. (there is a triangle feg with fe and fg marked as …
\( 64^\circ \)
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the movement of the progress bar may be uneven because questions can be…
B
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question find m∠dcb. (there is a triangle with vertices b, c, d. sides …
\( 86^\circ \)
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Question was provided via image upload.
1. A. $130^\circ$ B. $80^\circ$ C. $140^\circ$ D. $50^\circ$ 2. $\angle AFB$ and $\angle AFD$ $\angle AFC$ and $\angle AFB$ $\angle AFD$ and $\angle DFE$ 3. $\angle BFC$ and $\ang…
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complementary and supplementary angles 1. underline the measure of each…
1. - A. $130^\circ$ - B. $100^\circ$ - C. $80^\circ$ - D. $60^\circ$ 2. - $\angle AOB$ and: None - $\angle AOD$ and: $\angle AOC$ - $\angle AOE$ and: None 3. - $\angle AOC$ and: N…
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what can you say about the angle measures in $\\triangle abc$? triangle…
∠ACB measures \(82^\circ\), because the sum of the measures of ∠ACB and ∠ACD is \(180^\circ\). The sum of the measures of ∠BAC, ∠ABC, and ∠ACB is \(180^\circ\). This proves that t…
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on the number line below. $-4x \\leq -8$
The solution to the inequality is $x \geq 2$. For the number line graph: closed circle at 2, shaded to the right.
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e, and 2 centimeters high. what is the ume of the box? hat is the volum…
1. (Incomplete question: missing length and width values, cannot calculate volume) 2. $28$ cubic centimeters 3. $56$ cubic feet
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what is the area of the composite figure? image of composite figure wit…
A. 100 square inches
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read the following passage, which is modeled after an encyclopedia entr…
patted into thin circles
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calculate the area of the composite figure given below. enter the value…
38
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18. if ad = 24, db = 27, and eb = 18, find ce.
16
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read the following passage, which is modeled after an encyclopedia entr…
most major grocery stores
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ne area of the following figure and write your in the empty box. figure…
$434$
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a (a pink rectangle with length 5 cm and width 3 cm) b (a brown right -…
A. The rectangle with dimensions 3 cm and 5 cm
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8. x√2 = 19√2 · √2 19√(2·2) = 19√4 √4 √2 = (right triangle with right a…
If we follow the calculation \(19\sqrt{2}\times\sqrt{2}=19\times2 = 38\), and if we assume the equation was to find \(x\) when \(x\sqrt{2}=19\sqrt{2}\times\sqrt{2}\), then \(x = 3…
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find the missing length of the following figure if the area of the shad…
4
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graphing inequalities graph the inequality. 3. ( a geq -12 ) 4. ( x leq…
1. For $a\geq -12$: Closed circle at $-12$, shade right. 2. For $x\leq -7$: Closed circle at $-7$, shade left. 3. For $w<5$: Open circle at $5$, shade left. 4. For $d>13$: Open ci…
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a rectangle is placed around a semicircle as shown below. the width of …
\( 1.72 \) square centimeters (or \( 1.72 \, cm^2 \))
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for 16 - 17, determine whether $overleftrightarrow{jk} parallel overlef…
16. no 17. yes
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find the missing length of the following figure (the area of the figure…
4 mm.
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which of the following figure has the greate a 9 m 9 m b 6 m 10 m 10 m …
B. The trapezoid (figure B)
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find the cosine of ∠e. f 12 d 5 e simplify your answer and write it as …
\( \frac{5}{13} \)
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24. a circle is inscribed in a square so that the circle touches each s…
a. \( 5\pi \) cm
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find the area of the shaded region of the triangle giver the appropriat…
The second triangle (right triangle with legs 8 yd and 9 yd) has an area of 36 square yards, so this is the shaded region matching the given result.
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find the area of the figure given below and write your answer in the em…
$260 + 84 = 344$ $\text{cm}^2$
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the radius of a quarter circle is 4 kilometers. what is the quarter cir…
12.57 square kilometers
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the radius of a circle is 17 meters. what is the circle’s circumference…
106.81 meters
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given: \\(\\overline{ab} \\cong \\overline{cd}\\), \\(\\overline{ad} \\…
The reason for \( \overline{AF} \cong \overline{CE} \) is the **Addition Property of Congruence** (or "Segment Addition Postulate and Addition Property of Congruence") because we …
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find the area of the triangle below. be sure to include the correct uni…
$50$ square feet (or $50\ ft^2$)
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step statement reason - abcd is a parallelogram 1 (overline{bg} cong ov…
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)