Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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triangle xyz is isosceles. the measure of the vertex angle, y, is twice…
- The perpendicular bisector of \( \overline{XZ} \) creates two smaller isosceles triangles. - Angle Y is a right angle. - The measure of angle Z is 45°.
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one of the digits in your answer is wrong. check your work carefully. t…
\( 1318.8 \)
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19. identify which figure is formed by the rotation of a rectangle and …
The cylinder is formed by the rotation of a rectangle, and the cone is formed by the rotation of a triangle.
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triangle abc is an isosceles right triangle. what is the measure of one…
\(45^\circ\) (the option with \(45^\circ\))
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find distances between ordered pairs, limited to either the same x - co…
- Distance between T(4, 7) and S(4, - 3): \(10\) - Distance between P(-6, 5) and U(3, 5): \(9\)
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court quest court study guide name: azrie guerrero-rios directions. wha…
### Lower Courts - Family Court: State; Hears cases about: Divorce, child custody, family disputes. - Juvenile Court: State; Hears cases about: Minors’ delinquency, neglect, statu…
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mara carried water bottles to the field to share with her team at halft…
B. \(12(5x^2 + 4x + 2)\) (Wait, the options are labeled with circles, but in the problem, the second option is "12(5x² + 4x + 2)". So the correct option is the second one, which i…
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Question was provided via image upload.
The Left Graph (red)
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16. state whether the following have a circular or rectangular cross se…
- Square Pyramid: Rectangular - Rectangular Prism: Rectangular - Cone: Circular - Cylinder: Circular (when cut parallel to base) or Rectangular (when cut vertically) - Triangular …
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triangle abc is equilateral. \\(\\overline{bd}\\) bisects \\(\\angle ab…
\( x = \frac{29}{5} \) (or \( 5.8 \))
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what is always true about the angles of an isosceles triangle? at least…
At least two of the angles are congruent.
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the vertex angle of an isosceles triangle measures $40^{circ}$. what is…
\(70^\circ\) (the option with \(70^\circ\))
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15. find the volume of the following figures. a. b. c. d. (images of fo…
a. \( 2000m^{3} \) b. \( 48cm^{3} \) c. \( 200 \) (units not specified, assume consistent with given) d. \( 36\pi cm^{3}\approx113.04cm^{3} \)
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find the value of sin d rounded to the nearest hundredth, if necessary.…
$0.71$
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find the value of tan b rounded to the nearest hundredth, if necessary.
\( 0.42 \)
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find the point that divides the directed line segment from (-6, -9) to …
The point is \((-10,-13)\)
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isosceles triangles triangle abc is isosceles. what is true about the m…
(Assuming the correct option is the one stating angle \(B\) is equal to angle \(C\), e.g., if the option is like "A. It is equal to the measure of angle C" (adjusting based on the…
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wyatt’s eye - level height is 120 ft above sea level, and shawn’s eye -…
\( 3\sqrt{5} \) mi (corresponding to the option "3√5 mi")
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applying theorems about isosceles triangles triangle wxy is isosceles. …
\( 150^\circ \) (the option with \( 150^\circ \))
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9. a) find the measure of arc eu if arc eq is 112 degrees and the measu…
### Part A # Explanation: ## Step1: Recall Inscribed Angle Theorem The measure of an inscribed angle is half the measure of its intercepted arc. Also, in a triangle formed by chor…
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the formula $s = \\sqrt{\\frac{sa}{6}}$ gives the length of the side, $…
\(\boldsymbol{\sqrt{30} - 2\sqrt{5}}\) m (corresponding to the option \(\sqrt{30} - 2\sqrt{5}\) m)
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8. a) triangle abc is inscribed in circle g. find the measures of angle…
- \( \angle A = 30^\circ \) - \( \angle B = 90^\circ \) - \( \angle C = 60^\circ \) ### Part B: Triangle \( QUE \) inscribed in circle \( O \)
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question 9 (1 point) (01.06 mc) what is m∠abc? justify your reasoning. …
d. Using the Angle Addition Postulate, \( 15 + 40 = m\angle ABC \). So, \( m\angle ABC = 55^\circ \) after simplifying.
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question 6 (1 point) (01.06 mc) if (overline{us}) is an angle bisector …
a. \(m\angle RUT = 80^\circ\)
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if e is the midpoint of \\(\\overline{ab}\\) and \\(ab = 30\\), what is…
b. 15 ### Question 8 (PR length):
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determine the domain of the graph below.
The domain of the graph is \((-10, 5)\) (or \(-10 < x < 5\))
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7. a) point p (1, 0) partitions \\(\\overline{mn}\\) in the ratio of 5:…
The coordinates of \( N \) are \( (5, -4) \)
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question 4 (1 point) (01.06 lc) what angle relationship best describes …
d. Vertical angles
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what are the coordinates of the vertex of the quadratic $y=(x - 2)^2+3$…
\((2, 3)\)
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what ordered pairs are the solutions of the system of equations shown i…
The ordered pairs are \(\boldsymbol{(-1, 4)}\) and \(\boldsymbol{(4, -4)}\) (Note: Depending on the exact graph, maybe I misread, but based on the grid, these are the intersection…
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4. rectangle lmno has vertices l (-2, 4), m (-1, 6), n (-5, 8), o (-6, …
(Problem 4): 10
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the graph shows g(x), which is a translation of f(x) = |x|. write the f…
\( g(x)=|x + 5| \)
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select the type of quadrilateral that best describes the figure. kite s…
Kite
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select the type of quadrilateral that best describes the figure. explai…
Quadrilateral (the option labeled "Quadrilateral")
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the triangle below is equilateral. find the length of side x in simples…
\( 2\sqrt{3} \)
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select the type of quadrilateral that best describes the figure. kite s…
Square
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16 gr.1.1 plot ordered pairs in all four quadrants and on both axes wit…
- I: \((-4, 3)\) - M: \((-1, 2)\) - F: \((2, 2)\) - H: \((4, 0)\) - T: \((-2, -2)\) - N: \((-3, -3)\) - U: \((0, -3)\) - S: \((2, -2)\) - A: \((3, -4)\)
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sydney is cutting the crust from the edges of her sandwich. the dimensi…
B. \( 8x^2 + 34 \); 45.52 centimeters
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the triangle below is equilateral. find the length of side x in simples…
\(\frac{5\sqrt{3}}{2}\)
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pablo folds a straw into a triangle with side lengths of $4x^2 - 3$ inc…
A. \( 12x^2 - 6 \); 21 inches
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12. use the diagram below to find each ratio. (right triangle jlk with …
\( \sin J=\frac{21}{29} \), \( \cos J=\frac{20}{29} \), \( \tan K=\frac{20}{21} \), \( \sin K=\frac{20}{29} \)
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st bisects \\( \\overline{pr} \\) at point q. \\( pr = 7x - 15 \\) and …
\( 10 \)
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14. write an expression that represents the total surface area (includi…
\(\boldsymbol{(4n + 2)s^2}\) (or equivalent forms like \(2s^2(2n + 1)\))
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graph the following figure in the coordinate plane. find the perimeter.…
\( 19 + \sqrt{37} \)
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k is the midpoint of (overline{ij}) and (overline{hk} perp overline{ij}…
Statement 6: \( \overline{HI} \cong \overline{HJ} \) Reason 6: Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
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find the length of side x in simplest radical form with a rational deno…
\(\frac{\sqrt{2}}{2}\)
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u is the midpoint of \\(\\overline{rt}\\) and \\(\\overline{qs}\\). com…
Statement 6: \(\triangle QTU \cong \triangle SRU\); Reason: SAS Congruence Postulate
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which graph represents a function with direct variation?
The Middle Graph (the second graph in the top row, with the circle below it)
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find the length of side x in simplest radical form with a rational deno…
\(\boxed{\dfrac{7\sqrt{3}}{3}}\)
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which is the graph of the equation $y - 1 = \\frac{2}{3}(x - 3)$? (grap…
The upper graph (the first graph shown)
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a circular fountain has a radius of 12 m and a central angle of 75°. a)…
a) The area of the sector is \( 30\pi\space m^{2}\approx94.2\space m^{2} \). b) The length of the arc is \( 5\pi\space m\approx15.7\space m \).
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find the length of side x in simplest radical form with a rational deno…
\(4\sqrt{3}\)
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the graph shows the relationship between the volume of a rectangular pr…
3
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the figure below is a square. find the length of side x in simplest rad…
\( 5\sqrt{2} \)
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example 6 ex6: which congruency theorem can be used to prove that these…
SAS (the option corresponding to SAS, depending on the checkbox, but the theorem is SAS)
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example 5 ex5: which congruency theorem can be used to prove that these…
AAS
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adjust point d so the measure of angle bad is equal to the measure of a…
The true statements are: - $\boldsymbol{\overline{AD}}$ bisects $\boldsymbol{\angle BAC}$. - $\boldsymbol{\overline{AD}}$ forms right angles with $\boldsymbol{\overline{BC}}$. - $…
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proving the converse of the isosceles triangle theorem given: in triang…
1. First blank: triangle parts relationship theorem (theorem that larger side has larger opposite angle) 2. Second blank: (converse of triangle parts relationship theorem applicat…
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question 6 solve the equation \\(\\sqrt{8x + 16} + 1 = x + 2\\) answer …
$x = 3 + 2\sqrt{6}$ (or approximately $x \approx 7.899$)
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ex4: which congruency theorem can be used to prove that these triangles…
HL (the option corresponding to HL, with its checkbox selected)
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find the length of side x in simplest radical form with a rational deno…
\(\frac{\sqrt{2}}{2}\)
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example 3 ex3: which of the following congruency theorem can be used to…
AAS (the option with "AAS" as the text)
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example 2 ex2: which of the following congruency theorems can be used t…
AAS (assuming the option is labeled as "AAS" in the list, e.g., if the options are like: SSS, SAS, AAS, ASA, HL, then the answer is the option with "AAS")
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example 1 ex1: which congruency theorem can be used to prove that these…
SSS (the checkbox next to "SSS" should be selected)
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triangle congruence theorems sss (side-side-side) sas (side-angle-side)…
B. BC
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welcome to the game show, \which is greater?\ choose the card that show…
The left card (the first rectangle with 3 shaded sections)
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the triangle below is equilateral. find the length of side ( x ) in sim…
$4$
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3. use the diagram to complete each equation.\\(\\frac{b}{a} = \\frac{y…
For \(\frac{b}{a}=\frac{\underline{}}{h}\), the answer is \( y \); for \(\frac{c}{a}=\frac{b}{\underline{}}\), the answer is \( h \); for \(\frac{c}{a}=\frac{a}{\underline{}}\), t…
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reflect triangle efg across the line $y = x$. plot a point for each ver…
Reflected vertices: \( E'(5, -2) \), \( F'(2, -3) \), \( G'(2, 0) \) (plot these points).
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write a similarity statement comparing the three triangles to each diag…
1. $\triangle PRS\sim\triangle PSQ$; $\triangle PRS\sim\triangle PRQ$; $\triangle QPS\sim\triangle QPR$ 2. $\triangle BCE\sim\triangle DCE$; $\triangle BCE\sim\triangle BDE$; $\tr…
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there are three options a, b, c with different colored (blue, pink, cya…
B. The pink - colored structure (Option B)
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problem 6 here are two points: $(-3,4)$, $(1,7)$. what is the slope of …
B. \(\frac{3}{4}\)
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the image of a point is given by the rule $r_{y=-x}(x,y)\\to(-4,9)$. wh…
\((-9, 4)\)
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7. triangle def is formed by connecting the midpoints of the sides of t…
A. Triangle BDE is congruent to triangle EFC, B. Triangle BDE is congruent to triangle FDA, D. The length of BC is 8
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point p is located at (-4, -7). p is reflected across the x-axis to cre…
Quadrant II
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an architect’s sketch of the roof of a garage in the shape of a pentago…
B. about 77 ft
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point p is located at (-4, -7). p is reflected across the x-axis to cre…
Quadrant II
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7. triangle def is formed by connecting the midpoints of select all tru…
# Explanation: ## Step1: Recall Midline Theorem In a triangle, the segment connecting midpoints is parallel to the third side and half its length. Let's assume \(D\), \(E\), \(F\)…
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determine the missing length in each right triangle using the pythagore…
1. \(BC = \boldsymbol{9}\) yd 2. \(PQ\approx\boldsymbol{5.4}\) in 3. \(UW\approx\boldsymbol{6.7}\) ft 4. \(XZ\approx\boldsymbol{14.3}\) in 5. \(EF = \boldsymbol{6}\) ft 6. \(JL\ap…
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6. in the diagram, lines bc and de are both vertical. what is the lengt…
C. 7.5
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consider reflections of △jkl. what line of reflection maps point k to p…
First line: \(x = 1\) (vertical line), Second line: \(x = 0\) (y-axis) (assuming the second question is a typo and refers to reflecting L over y-axis)
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find k. (image of a right triangle with angles 30°, 60°, 90°, one leg 7…
\(7\sqrt{3}\)
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what is an equation of the line that passes through the points (-2, -1)…
Una ecuación de la línea es \(y=\frac{3}{2}x + 2\) (o en forma estándar \(3x - 2y=-4\))
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the perimeter of the scalene triangle is 54.6 cm. which equation can be…
\( 34.8 + b = 54.6 \) (the fourth option, i.e., \( 34.8 + b = 54.6 \))
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determine the range of the following graph: graph of a function with op…
\((-5, 3)\)
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think back on the properties and theorems you explored in this lesson 1…
(a) Transitive Property (b) Addition Property of Equality (c) Substitution Property (d) Congruent Supplement Theorem (e) Reflexive Property (f) Vertical Angle Theorem
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select the correct answer from each drop-down menu. the hexagonal seati…
To solve the problem, we analyze the hexagonal seating section: ### Step 1: Side Length of Hexagon A regular hexagon can be divided into 6 equilateral triangles. The walkway (30 f…
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5. in the diagram, segment ab is parallel to segment ab. \\(\\overline{…
a. The length of segment \(A'A\) is \(\boldsymbol{18}\). b. The length of segment \(B'B\) is \(\boldsymbol{9}\).
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from a hot - air balloon, ian measures a 30° angle of depression to a l…
The balloon's vertical distance above the ground is approximately 721.7 feet.
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4. quadrilateral abcd is similar to quadrilateral abcd. write 2 equatio…
Two possible equations are \(\boldsymbol{\frac{AB}{A'B'}=\frac{BC}{B'C'}}\) and \(\boldsymbol{\frac{BC}{B'C'}=\frac{CD}{C'D'}}\) (or other valid proportionality equations of corre…
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which graph represents the solution set for the inequality 20 ≥ x + 16?…
(The correct graph option, e.g., if Graph A has a closed circle at 4 and arrow left, then) A. Graph A
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the isosceles triangle has a perimeter of 7.5 m. which equation can be …
\( 2.1 + 2x = 7.5 \) (the last option, e.g., if options are labeled as A, B, C, D with D being \( 2.1 + 2x = 7.5 \), then D. \( 2.1 + 2x = 7.5 \))
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17. slope (m) = y-intercept (b) = equation: y =
slope (\(m\)) = \(\frac{1}{2}\) y - intercept (\(b\)) = \(0\) equation: \(y=\frac{1}{2}x\)
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what is an equation of the line that passes through the points (-1, -2)…
La ecuación de la recta es \(y = 3x + 1\) (o en forma estándar \(3x - y=-1\))
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4. quadrilateral abcd is similar to quadrilateral abcd. write 2 equatio…
Two equations are \(\boldsymbol{\frac{AB}{A'B'}=\frac{BC}{B'C'}}\) and \(\boldsymbol{\frac{CD}{C'D'}=\frac{DA}{D'A'}}\) (other valid proportional equations of corresponding sides …
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identify the slope and y-intercept of the line below. draw slope = y-in…
slope = \(3\) y - intercept = \(-6\)
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2 in this figure, \\(\\overleftrightarrow{pq}\\) intersects \\(\\overle…
- \((x + 24)^\circ = 62^\circ\) - \((3x + 4)^\circ = 118^\circ\) - \(y^\circ = 118^\circ\) (vertical to \(118^\circ\)) - \(z^\circ = 62^\circ\) (vertical to \(62^\circ\)) (Explana…
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happy, mika, and lily are frogs in a frog jumping competition. find the…
3 meters (corresponding to the "3 meters" option)
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graph the line that passes through the points (7, -4) and (-6, -4) and …
\( y = -4 \)
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the number line shows two unknown numbers, s and t. is t + s positive o…
negative