幾何
三角形、円、座標幾何、証明問題。
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completing proofs involving linear pairs given: ( mangle elg = 124^circ…
### Step-by-Step Explanation for Step 4 (Reason): ## Step 1: Recall Linear Pair Postulate A linear pair of angles is supplementary, meaning their measures add up to \(180^\circ\).…
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what is the value of x? (the image shows two intersecting lines at poin…
45
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a drum, a drum! macbeth doth come. (dancing together in a circle) the w…
The witches are dancing together in a circle, performing a charm or ritual. They move about in a circular pattern, repeating movements to complete a charm, and then finish the cha…
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use the diagram at the right, with \\( \\overline{jd} \\), \\( \\overli…
\( m\angle MIP = 48^\circ \) \( m\angle MRQ = 78^\circ \) (For \( MQ \), maybe a length, but if it's a segment, maybe equal to \( KQ \), but without more info, assuming the angles…
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draw the image of $\\triangle abc$ under a dilation whose center is $p$…
The image $\triangle A'B'C'$ is a smaller triangle, with each vertex lying halfway between point $P$ and the corresponding vertex of $\triangle ABC$, and side lengths half of $\tr…
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calculate the volume of liquid in the tank sketched below. give your an…
\( 2.5 \)
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1. decide whether there is enough information to prove that $m \\parall…
Yes, we can prove \(m\parallel n\). The theorem used is the Alternate Interior Angles Theorem (since the alternate interior angles are congruent, each equal to \(138^\circ\)). ###…
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complete the following sentence. the figure below has rotational symmet…
The figure below has **4-fold** rotational symmetry. $\boldsymbol{90^\circ}$ is the smallest possible rotation that results in the figure being mapped onto itself.
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determine the period of the following graph.
The period of the graph is \( 2\pi \)
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the diagram shows a triangle. what is the value of t? t = \\square^\\ci…
$7$
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graph the equation below. x = 9 show your work here
To graph \( x = 9 \), draw a vertical line parallel to the \( y \)-axis passing through the point where \( x = 9 \) on the \( x \)-axis (i.e., the line includes all points with \(…
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convert the angle 2 radians to degrees, rounding to the nearest 10th.
\(114.6\) degrees
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convert the following angle from degrees to radians. express your answe…
\( \frac{8\pi}{3} \)
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use the pythagorean theorem to find the missing leg of the triangle bel…
12
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use the pythagorean theorem to find the length of the hypotenuse of the…
The length of the hypotenuse is \(10\).
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find the distance between the points (5, 10) and (5, 2).
8 units
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two sides of an obtuse triangle measure 9 inches and 14 inches. the len…
17 inches
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use the given information to prove that $\\triangle def \\cong \\triang…
1. Reason: Given 2. \(\overline{DF} \cong \boldsymbol{\overline{HF}}\) 3. Reason: Vertical angles are congruent 4. Reason: SAS (Side - Angle - Side) Congruence Criterion
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in the diagram below, \\(\\overline{ts}\\) is parallel to \\(\\overline…
14.40 units
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question 6 of 10 (1 point) | question attempt: 1 of unlimited use the g…
3. \(\angle PRS\) 4. Given 5. Reflexive Property of Congruence 6. AAS (Angle - Angle - Side) Congruence Theorem
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the measure of each interior angle of a regular polygon is 150°. find t…
12
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question find an angle \\( \\theta \\) coterminal to \\( -255^\\circ \\…
105°
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question find an angle \\( \\theta \\) coterminal to \\( 1013^\\circ \\…
293°
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finding coterminal angles this is the only question in this section. qu…
\( 190^\circ \)
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use the pythagorean theorem to find the missing leg of the triangle bel…
6
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use the pythagorean theorem to find the length of the hypotenuse of the…
The length of the hypotenuse is \(5\).
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use the image to answer the question. identify these key features of th…
vertex: \((4,2)\) (smaller) x - intercept: \((2,0)\) (larger) x - intercept: \((6,0)\) y - intercept: \((0,-6)\)
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given the following side lengths of a triangle, use the pythagorean the…
True
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given the following side lengths of a triangle, use the pythagorean the…
True
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given the following side lengths of a triangle, use the pythagorean the…
The triangle with side lengths \(a = 33\) yd, \(b = 56\) yd, and \(c = 65\) yd is a right triangle because \(33^{2}+56^{2}=65^{2}\) (i.e., \(1089 + 3136=4225\) and \(65^{2}=4225\)…
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given the figure shown below, determine the length of c. 25 cm² 16 cm²
The length of \( c \) is \( \sqrt{41} \, \text{cm} \) (or approximately \( 6.40 \, \text{cm} \)).
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given the figure shown below, determine the length of c. 16 cm² 64 cm²
\(4\sqrt{5}\space cm\) (or approximately \(8.94\space cm\))
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given the figure shown below, determine the length of c. 16 cm² 64 cm² c
\( 4\sqrt{5} \, \text{cm} \) (or approximately \( 8.94 \, \text{cm} \)) Wait, no, wait, wait—wait, no, I think I made a mistake. Wait, the first square is 16, so side 4, second sq…
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each of the following quadratic equations can be solved by factoring. w…
\(x^2 + 4x + 4 = 0\) (the fourth option, or D. \(x^2 + 4x + 4 = 0\) if we consider the options as labeled, though the original labels are circles; the equation is \(x^2 + 4x + 4 =…
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do the \find the syllable type\ activity have your child circle the wor…
### Circled (v-e words) & Crossed Out (non-v-e words): Circled: lime, chase, bike, wife, wave, smile, fire, cake, vote, quake Crossed out: blond, trap, punch, flap, steps ### Writ…
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click on a link below to learn the concepts. each component includes a …
The measure of $\angle KGW$ is $\frac{1796}{17}^\circ$ (or approximately $105.7^\circ$)
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e the linear inequality for k and graph the answer in the number line. …
The solution to the inequality \( k + 1 < -2 \) is \( k < - 3 \). To graph this on the number line, we would place an open circle at \( - 3 \) (since \( k\) is not equal to \( - 3…
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solve the linear inequality for k and graph the answer in the number li…
The solution to the inequality \( 1>k - 1 \) is \( k < 2 \). To graph this on the number line, we would have an open circle at \( k = 2 \) (since the inequality is strict, \( k e…
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for 8a math ms. hyacinth there is a coordinate grid with a rectangle fo…
s: - \(B'(-8, 8)\) - \(C'(-1, 8)\) - \(D'(-1, 5)\) - \(E'(-8, 5)\) (Note: If the rotation is different (e.g., 90° counterclockwise or 180°), adjust the rule. The above assumes 90°…
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solve the linear inequality for k and graph the answer in the number li…
The solution to the inequality \( 4 \geq k - 4 \) is \( k \leq 8 \). To graph this on the number line, we would have a closed circle at 8 (since the inequality is "less than or eq…
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$\\triangle ijk$ is a translation of $\\triangle ijk$. write the transl…
\( (x, y) \to (x + 9, y - 8) \)
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solve the linear inequality for w and graph the answer in the number li…
The solution to the inequality \( 5 \leq w - 5 \) is \( w \geq 10 \). For the number line graph, we would have a closed circle at 10 (since the inequality is "greater than or equa…
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given: ∠2 and ∠4 are vertical angles. prove: ∠2 ≅ ∠4 (there is a diagra…
To prove \( \angle 2 \cong \angle 4 \) (vertical angles are congruent), we follow these steps: 1. **Given**: \( \angle 2 \) and \( \angle 4 \) are vertical angles. 2. **Linear Pai…
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solve the linear inequality for y and graph the answer in the number li…
The solution to the inequality \( y - 2 < 5 \) is \( y < 7 \). To graph this on the number line, we would have an open circle at 7 (since the inequality is strict, \( < \), not \(…
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linear pairs and vertical angles proving vertical angles are congruent …
The correct reason for the statement \(m\angle3 + m\angle4 = 180\) is "linear pairs are supp." (linear pairs are supplementary).
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solve the linear inequality for x and graph the answer in the number li…
The solution to the inequality \( 2 > x - 4 \) is \( x < 6 \). To graph this on the number line, we would have an open circle at 6 (since \( x \) is not equal to 6) and a line ext…
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ear inequality for x and graph the answer in the number line. then writ…
The solution to the inequality \( 2>x - 4 \) is \( x < 6 \). The graph has an open circle at 6 and shading to the left. The interval notation is \( (-\infty, 6) \)
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find the distance between the points a and b given below. (that is, fin…
\( 6.32 \)
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9. given the ratio for tan θ, find the remaining ratios. $4^2 + 5^2 = x…
$\sin\theta = \frac{4\sqrt{41}}{41}$ $\csc\theta = \frac{\sqrt{41}}{4}$ $\cos\theta = \frac{5\sqrt{41}}{41}$ $\sec\theta = \frac{\sqrt{41}}{5}$ $\cot\theta = \frac{5}{4}$
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in the rectangular prism below, $ru = 16$, $ut = 35$, and $st = 37$. fi…
20
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△tuv is a translation of △tuv. write the translation rule. (x, y) ↦ (x …
The first blank is 8, the second blank is 7. So the translation rule is \((x, y) \to (x - 8, y + 7)\), so the boxes are 8 and 7.
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△pqr is a translation of △pqr. write the translation rule. (x, y) → (x …
\((x,y)\to(x + 6,y + 5)\)
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8. find the values of the six trigonometric functions for $\\theta$. (r…
$\csc\theta = \frac{4\sqrt{7}}{7}$ $\cot\theta = \frac{3\sqrt{7}}{7}$
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determine the equation of the circle graphed below.
$\boldsymbol{x^2 + y^2 = 36}$
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line gh contains points g(-2, 6) and h(5, -3). what is the slope of \\o…
\(-\frac{9}{7}\) (corresponding to the option with \(-\frac{9}{7}\))
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question what type of angle is this? angle diagram answer attempt 1 out…
obstue (obtuse)
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what type of angle is this? answer attempts 1 out of 2 acute right obtu…
acute
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1) choose the wrong name for this angle: a) $\\angle cde$ b) $\\angle e…
B) $\angle E$
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name the marked angle in 2 different ways. (there is a triangle with ve…
$\angle R$ $\angle QRS$
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d since there is a 4 in front of the x, separate the rectangles and squ…
$x = -1$
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find $m\\angle abd$ and $m\\angle dbc$. enter deg after any value that …
a) \(m\angle ABD = 94\) deg b) \(m\angle DBC = 86\) deg
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find the missing term. 1 $(4x + 3) (9x^2 + 7x - 3) = 36x^3 + 55x^2 + ? …
\(9x\) ### Problem 2:
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name the marked angle in 2 different ways. answer attempt 1 out of 2 ∠ …
$\angle T$ $\angle STR$
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solve the system of inequalities by graphing. $x \\leq 3$ $y < 4x - 9$ …
To solve the system: 1. Graph \( x \leq 3 \) as a **solid vertical line** at \( x = 3 \), shading **left** of the line. 2. Graph \( y < 4x - 9 \) as a **dotted line** (using \( y …
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name: js poillon warm up #4 \\(\\overline{be}\\) altitude of \\(\\trian…
$\triangle ABE \cong \triangle DCE$ (proven by AAS congruence). ### Problem 2: Prove $\overline{BD}$ is the perpendicular bisector of $\overline{AC}$
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$\\angle pqr$ is a right angle. find $m\\angle pqs$ and $m\\angle sqr$.…
a) $m\angle PQS = 60$ deg b) $m\angle SQR = 30$ deg
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name the marked angle in 2 different ways.
$\angle M$, $\angle KML$
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name the marked angle in 2 different ways. answer attempt 1 out of 2
$\angle X$ $\angle YXW$
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name the marked angle in 2 different ways. (there is a triangle - like …
$\angle ROP$ $\angle O$ *(Note: $\angle POR$ is also an acceptable alternative to $\angle ROP$)*
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these shapes are reflections of each other in the mirror line marked m.…
False
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directions. for each of the following items, circle the letter of the c…
B. heinous... bulwarks ### Question 22
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which of diagrams a and b shows a correct reflection in the mirror line…
B. Diagram B
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use the graph at the right. find the vertices of the image of qrtw for …
\((-1, 2)\)
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exercise 1 sentence completion directions: for each of the following it…
To solve these sentence completion questions, we analyze each one by considering the context and the meaning of the vocabulary options: ### Question 21 - **Context**: The sentence…
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name the marked angle in 2 different ways.
1. $\angle U$ 2. $\angle TUV$
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name the marked angle in 2 different ways.
$\angle W$, $\angle XWV$
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triangle classification theorems which best explains whether a triangle…
The triangle is a right triangle because $5^2 + 12^2 = 13^2$.
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the longest side of an acute isosceles triangle is 8 centimeters. round…
5.7 cm
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which classification best represents a triangle with side lengths 6 cm,…
A. obtuse, because $6^{2}+10^{2}<12^{2}$
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two sides of an acute triangle measure 5 inches and 8 inches. the lengt…
B. 9 inches
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triangle classification theorems which best explains whether a triangle…
The triangle is not acute because $2^2 + 4^2 < 5^2$.
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which set of numbers can represent the side lengths, in inches, of an a…
C. 5, 7, 8
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to get from his house to the lecture hall at school, lin walked west 65…
Lin walked south, creating a right triangle.
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ramon wants to make an acute triangle with three pieces of wood. so far…
less than $\sqrt{58}$ inches but greater than 7 inches
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on the packaging for a triangular sail, the edge measurements for the s…
obtuse
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find the values of the variables. then find the side lengths of the squ…
$x=6$, $y=5$ Side length of the square: $2$
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what is the measurement of this angle?
70°
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critiquing work ella’s geometry teacher asked each student to devise a …
Ella's procedure is incorrect, but her conclusion is correct.
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identifying possible side lengths 9 in. 12 in. three, the triangle is o…
A. 5 inches, C. 6 inches, B. 7 inches
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applying the converse of the pythagorean theorem janice examines the gi…
It is over by approximately 0.6 units.
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what will be the value, when substituted for x, that would represent an…
14
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classifying triangles with known side lengths which sets of three of nu…
3, 5, 6 2, 2, 3
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there is a coordinate grid with two lines, line a (blue) passing throug…
The equation of Line \( b \) is \( \boldsymbol{y = 0.8x - 3.2} \) (or \( y = \frac{4}{5}x - \frac{16}{5} \) in fractional form).
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there is a coordinate grid with two lines, line a (blue) and line b (gr…
The slope of Line \( b \) is \( 0.8 \)
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6.2 assignment find the value of x. (there is a geometric figure with a…
42
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12. make sense and persevere the base and height of a triangle are each…
$3x + 14$ ### Problem 12:
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given the following two parallel lines cut by a transversal. which pair…
\( \angle 6 \) and \( \angle 5 \)
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what values of u and v make $\\triangle def \\cong \\triangle jhi$? (th…
$u = 4$ $v = 8$
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bonus given the two parallel lines cut by a transversal, what is the me…
71° (assuming the related angle is 71°, if the diagram has a 71° angle, the measure of ∠5 is 71° due to parallel lines and transversal angle relationships like corresponding angle…
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the vertex is (4, - 9). a pair of symmetrical points are: (-9, 4). the …
s: - Vertex: \(\boldsymbol{(4, -9)}\) (correct as per the vertex definition for the upward - opening parabola) - Symmetrical Points: The given \((-9, 4)\) is incorrect. A correct …