Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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1. given the parallelogram, find the missing angle measure: image of pa…
B. 135
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4. explain why this quadrilateral is not a parallelogram.
A parallelogram has both pairs of opposite sides parallel and equal in length. In this quadrilateral, the two pairs of opposite sides do not have equal lengths (verified by counti…
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a) -2, 7 b) -3, 6 c) 4, -1 d) 6, 10 e) -7, -3
d) [6, 10]
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find j. write your answer in simplest radical form. millimeters
\(8\)
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consider the right triangular prism given ac = 9 cm and ad = 10 cm. whi…
- The height of the prism is 10 cm. - $\triangle DFG$ is a base. - The appropriate unit of measure for the volume is cubic centimeters. - The area of the base is 45 square centime…
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question 3 (mandatory) (1 point) find the distance between the points (…
c) 10
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what is the slope of the line that passes through the points (0, -6) an…
The slope is undefined.
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what is the slope of the line that passes through the points (4, 8) and…
\(-\frac{1}{2}\)
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is polygon h a scaled copy of polygon g? are the side lengths scaled by…
Yes
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what is the slope of the line that passes through the points (6, 0) and…
\( -\frac{4}{3} \)
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is polygon f a scaled copy of polygon e? is polygon f a scaled copy of …
No
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for the figure below, do a dilation centered at the origin with a scale…
Original endpoints: \((3, 5)\) and \((7, 5)\); Final (dilated) endpoints: \((9, 15)\) and \((21, 15)\)
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draw the reflection of the quadrilateral across the y - axis.
The reflected quadrilateral has vertices at \((-1,2)\), \((-6,1)\), \((-7,6)\), \((-2,7)\) (and is drawn by plotting these points and connecting them).
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which compound inequality is represented by the graph? (graph: a number…
A. \( x < -4 \) or \( x \geq 3 \)
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question solve for all possible values of x. \\(\\sqrt{8x + 65} = x + 1…
\(x=-5\) or \(x = - 7\)
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question solve for all possible values of x. \\(\\sqrt{44 - 5x} = x - 6…
\(x = 8\)
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question solve for all possible values of x. \\(\\sqrt{5x + 26} = x + 6…
The solutions are \(x=-2\) and \(x=-5\). If we consider the "Additional Solution" option, we can first write \(x=-2\) and then \(x=-5\) as an additional solution. But according to…
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question solve for all possible values of x. \\(\\sqrt{6 - x} = x - 6\\…
$x = 6$
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which graph correctly represents the relationship between arc length an…
A. (The linear graph starting at the origin, reaching $2\pi r$ when the central angle is $\pi$ radians)
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9. zaid wants to hang the pennant shown vertically between two windows …
The pennant will not fit because the height of the pennant (the side opposite the \(30^{\circ}\) angle in the right - triangle) is \(20.5\) inches, which is greater than the 19 - …
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type the correct answer in each box. use numerals instead of words. con…
18.75, 4.78, 35.34
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select the correct answer. what is the equation of the parabola opening…
D. $f(x) = \frac{1}{32}(x - 9)^2 + 19$
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when circle p is plotted on a coordinate plane, the equation of the dia…
C. The slope of the tangent line is $-\frac{1}{4}$.
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which equation represents a circle with a center at (-5,5) and a radius…
C. $(x + 5)^2 + (y - 5)^2 = 9$
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8. if rs = 40, st = 41, and rt = 11, is △rst a right triangle? explain.
\(\triangle RST\) is not a right triangle because for the side lengths \(RS = 40\), \(ST=41\), and \(RT = 11\), none of the combinations of the sum of the squares of two sides equ…
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7. if rs = 35, st = 37, and rt = 71, is △rst a right triangle? explain.…
No, \(\triangle RST\) is not a right triangle because \(35^2 + 37^2 = 2594\) and \(71^2 = 5041\), and \(2594 eq5041\), so the Pythagorean theorem does not hold.
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which equation represents a circle with a center at (-5,5) and a radius…
C. $(x + 5)^2 + (y - 5)^2 = 9$
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select the correct answer. arc cd located on circle a has a central ang…
B. $18\pi$ cm
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casey constructed this figure by using a compass and a straightedge to …
E. She used a compass centered at Q with a radius set equal to PQ.
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6. if rs = 20, st = 21, and rt = 29, is △rst a right triangle? explain.…
Yes, \(\triangle RST\) is a right triangle. Because \(RS^{2}+ST^{2}=20^{2}+21^{2}=400 + 441 = 841\) and \(RT^{2}=29^{2}=841\), so \(RS^{2}+ST^{2}=RT^{2}\), which satisfies the Pyt…
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consider the circle with chords pr and qs intersecting at point t. desc…
1. $PT \times TR = QT \times TS$ 2. $6$ 3. PQ and RS
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5. find the value of x. enter your answer.
$9\sqrt{3}$ (or approximately $15.6$)
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triangle abc is inscribed in a circle centered at point o. order the me…
$m\overset{\frown}{AB} < m\overset{\frown}{BC} < m\overset{\frown}{AC}$
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which point lies on the circle represented by the equation ((x - 3)^2 +…
A. (9,-2)
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4. find the value of x. enter your answer.
\(3.2\sqrt{2}\) (or approximately \(4.53\))
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dylan constructed this figure using a compass with its width set equal …
A. Dylan's reasoning about arc AB is correct, and the hexagon is regular.
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drag each tile to the correct box. the given steps for constructing a l…
D → C → E → A → B
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type the correct answer in each box. use numerals instead of words. if …
$m\angle ACB = 32$ and $m\overset{\frown}{AC} = 146$
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what is the difference of the lengths of \\(\\overarc{bd}\\) and \\(\\o…
B. 1.57 units
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given the information marked on the figures below, classify each quadri…
s: - Top - Left: Parallelogram - Top - Right: Parallelogram - Bottom - Left: Parallelogram - Bottom - Right: Parallelogram (Note: If the top - left figure’s markings were misinter…
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the figure below was made with a scale of 1 unit = 8 cm. draw the figur…
Draw an 8-unit wide, 4-unit tall rectangle on the right grid (1 unit = 2 cm scale).
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mel is teaching travis how to use a compass and a straightedge to const…
B. Chord WX must be a diameter of the circle.
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select the correct answer from each drop - down menu. a parabola is giv…
1. The equation of the directrix of the parabola is $x=6$ 2. The focus of the parabola is $(-6, 0)$
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the figure below was made with a scale of 1 unit = 8 cm. draw the figur…
Draw a 4-unit by 4-unit rectangle on the right (new scale) grid.
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vance wants to construct a circle tangent to all three sides of the acu…
C. Vance should have found the intersection of two angle bisectors of triangle LMN instead of two altitudes.
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what is the ratio of the area of sector abc to the area of sector dbe? …
E. $\frac{1}{4}$
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quadrilateral abcd is inscribed in a circle. m∠a is 64°, m∠b is (5x + 4…
D. $98^\circ$
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type the correct answer in each box. the general form of the equation o…
Standard form: $(x + 4)^2 + (y + 11)^2 = 100$ Center: $(-4, -11)$
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select the correct answer. given the focus (-1, 15) and the directrix x…
A. $x = \frac{1}{6}(y - 15)^2 - \frac{5}{2}$
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select the correct answer. circle c has a center at (-2,10) and contain…
D. $(x + 2)^2 + (y - 10)^2 = 169$
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g the tiles to the boxes to form correct pairs. not all tiles will be u…
1. $\angle COB \longleftrightarrow 114^\circ$ 2. $\angle EOB \longleftrightarrow 124^\circ$ 3. $\overset{\frown}{CE} \longleftrightarrow 122^\circ$ 4. $\angle DFA \longleftrightar…
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find vw. write your answer as an integer or as a decimal rounded to the…
$3.0$
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find bc. write your answer as an integer or as a decimal rounded to the…
$5.1$
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\)
The graph is an ellipse centered at the origin $(0,0)$ with vertices at $(0, 3)$, $(0, -3)$ and co-vertices at $(2, 0)$, $(-2, 0)$, forming a vertical elongated oval shape passing…
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is the dotted line a line of symmetry? yes no
yes
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the movement of the progress bar may be uneven because questions can be…
6
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describe the symmetry of this function. line symmetry only rotational s…
rotational symmetry only
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if $sw = p - 16$ and $tv = -p + 52$, what is the value of $p$? $p = \\s…
$p = 40$
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you move up 3 units and down 7 units. you end at (5, -2). where did you…
$(5, 2)$
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this image has rotational symmetry. what is the smallest number of degr…
\(45\)
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given ( m parallel n ), find the value of ( x ).
$94$
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read the excerpt from the strange case of dr. jekyll and mr. hyde. i ne…
B. character vs. character
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what is the sum of the exterior angle measures, one at each vertex, of …
$360$
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△abc is the image of △abc under a rotation about point p. determine the…
B. \( 90^\circ \) counterclockwise, D. \( 270^\circ \) clockwise
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using the pencil, plot the reflection of point a across the y - axis.
The reflection of point A across the y-axis is the point at coordinates $(-7, 0)$ (plotted on the x-axis at -7, 0).
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use a trigonometric ratio to solve for a. round to two decimal places i…
$101.01$
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what is the length of the hypotenuse? if necessary, round to the neares…
Length of hypotenuse: 39 millimeters $\sqrt{100}$: 10
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using the pencil, plot the reflection of point a across the y - axis.
The reflection of point A across the y-axis is the point at coordinates $(-7, 0)$, plotted on the grid at the position 7 units left of the y-axis on the x-axis.
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write the equation in the form ((x - h)^2 + (y - k)^2 = c). then, if th…
The equation in standard form is $\boldsymbol{(x-5)^2 + (y+2)^2 = 49}$. The equation represents a circle, with center $(5, -2)$ and radius $7$.
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what is the length of the hypotenuse? if necessary, round to the neares…
13 centimeters
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what is the length of the hypotenuse? if necessary, round to the neares…
10 millimeters
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find the sine, cosine, and tangent of $\\angle t$. simplify your answer…
$\sin(T) = \frac{45}{53}$ $\cos(T) = \frac{28}{53}$ $\tan(T) = \frac{45}{28}$
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1. which sequence of transformations will carry the given pre - image o…
A possible sequence is a 90° clockwise rotation about the origin (or a suitable center) followed by a translation to align with the dashed - line image. (If in a multiple - choice…
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the right triangle below is dilated by a scale factor of 5. find the pe…
Perimeter of given right triangle: \(40\) units Perimeter of dilated right triangle: \(200\) units Area of given right triangle: \(60\) units² Area of dilated right triangle: \(15…
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the diagram shows a triangle. what is the value of c? c = \\(\\square\\…
\(10\)
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using the pencil, plot the reflection of point a across the x - axis.
The reflected point is located at coordinates $(6, -8)$ (plot this point on the grid, 6 units right on the x-axis and 8 units down on the y-axis from the origin).
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quadrilateral ( abcd ) is the image of quadrilateral ( abcd ) under a r…
# Explanation: ## Step1: Recall rotation rules For a point \((x,y)\) rotated about the origin: - \(90^\circ\) clockwise: \((x,y)\to(y, -x)\) - \(90^\circ\) counterclockwise: \((x,…
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using the pencil, plot the reflection of point a across the y - axis.
The reflected point is at $(-7, 3)$ (plot this point on the grid at x=-7, y=3)
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solve the inequality $n - 2 \\leq -5$. $n \\leq -3$ graph the solution …
To graph \( n \leq -3 \): 1. Locate -3 on the number line. 2. Place a closed dot (filled circle) at -3 (since the inequality includes equality, \( n = -3 \) is a solution). 3. Dra…
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write the equation of the line in fully simplified slope - intercept fo…
$y = -2x - 6$
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find the slope of a line perpendicular to the line whose equation is $3…
\(-1\)
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fill in the blank 1 point 1. $m\\angle c = \\underline{\\quad\\quad}$ $…
$m\angle C = 101^\circ$ $m\angle E = 46^\circ$
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find ( mangle i ). write your answer as an integer or as a decimal roun…
$53.7$
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find z. write your answer in simplest radical form. miles
14 miles
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a parabola has a vertex at (0,0). the focus of the parabola is located …
A. \(x=-4\)
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a parabola has a vertex at (0,0). the focus of the parabola is located …
A. up
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graph. x ≥ 8 to draw a ray, plot an endpoint and select an arrow. selec…
To graph \( x \geq 8 \): - Plot a **closed dot** (filled circle) at \( x = 8 \) on the number line. - Draw a **ray** starting from the closed dot at 8 and extending to the **right…
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the figures below are similar. the labeled sides are corresponding. 6.9…
34.5 inches
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the figures below are similar. the labeled sides are corresponding. wha…
5:1
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the figures below are similar. the labeled sides are corresponding. 6 c…
32 centimeters
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the figures below are similar. the labeled sides are corresponding. 4 y…
25 yards
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find the cosine of $\\angle h$. write your answer in simplified, ration…
$\frac{8\sqrt{87}}{87}$
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find the sine of $\\angle v$. write your answer in simplified, rational…
$\frac{\sqrt{15}}{5}$
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the diagram shows a regular polygon. what is the value of x? write your…
\( 67.5 \)
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quadrilateral fghi is similar to quadrilateral jklm. find the measure o…
50.4
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for the right triangles below, find the values of the side lengths d an…
(a) \( d\approx4.0 \) (b) \( h\approx7.1 \)
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find the cosine of ∠u. write your answer in simplified, rationalized fo…
$\frac{4\sqrt{89}}{89}$
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many hindu gods are mentioned in scriptures, or religious texts, called…
Describe beliefs (select the circle under "Describe beliefs" for this description) ### For "passages that people regularly chant, or read out loud":
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is the following statement true or false? the intersection of a plane a…
true
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find the area of rectangle ijkl. round your answer to the nearest tenth…
The area of rectangle \( IJKL \) is \( 115.2 \) square inches.