Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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solve the compound inequality. use graphs to show the solution set to e…
1. Graph for $4(3-x) < -6$: B. <graph with open circle at 4.5, arrow right> 2. Graph for $\frac{x-2}{3} \leq -2$: B. <graph with closed circle at -4, arrow left> 3. Compound inequ…
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equations in real - world situations 9. match each situation with the e…
a. $15=5x$ b. $15=x+5$ c. $15=x-5$ d. $5=15x$ --- ### Question 10
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how many rays are shown in the drawing? number of rays:
3
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what is the volume of the following triangular prism? 9 m 6 m 13 m 351 …
351 \( \text{m}^3 \) (corresponding to the option: 351 \( \text{m}^3 \)) ### Second Question (Rectangular Prism Volume)
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which expression represents the volume, in cubic units, of the composit…
$\boldsymbol{\pi(5^2)(13) + \frac{1}{3}\pi (5^2)(12)}$ (the third option)
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the base of a solid right pyramid is a regular hexagon with a radius of…
$\boldsymbol{6x^2\sqrt{3}}$ units² (corresponding to the last option)
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to solve: 1. figure out how tall the stack of cards is. □ inch(es). v =…
1. 1 inch(es) 2. 4 inches 3. 25%
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camille has two boxes with the dimensions shown. she wants to use the b…
Box A Volume = $172\frac{1}{2}$ cubic inches Box B Volume = $172\frac{1}{8}$ cubic inches Which box should Camille use? Box A Should she use box C? YES
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a solid oblique cone with a slant length of 17 units is placed inside a…
$640\pi$ cubic units
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an oblique prism with a square base of edge length x units has a volume…
$\boldsymbol{\frac{1}{2}x}$ units (the second option)
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an oblique prism has a volume of 144 cubic units. the area of its base …
C. 6 units
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max observes the zoo and the library from a helicopter flying at a heig…
400 feet
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an oblique cylinder is shown. which represents the volume of the cylind…
300π
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a solid oblique pyramid has a regular pentagonal base. the base has an …
19 ft³
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a solid right pyramid has a regular hexagonal base with an area of 7.4 …
14.8 units$^3$
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two ropes, ad and bd, are tied to a peg on the ground at point d. the o…
10 feet
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9. explain why rotating a figure 180° about any point results in a poin…
A \(180^\circ\) rotation about a center \(O\) for any point \(P\) in the figure creates an image \(P'\) such that \(O\) is the midpoint of \(\overline{PP'}\) (as \(\angle POP' = 1…
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a source of laser light sends rays ab and ac toward two opposite walls …
$30 + 40 = 70$ m
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3. consider the given right triangular prism and the cross section form…
a. The cross section is an isosceles triangle with side lengths labeled: two sides of 11 inches and one side of 9 inches (congruent to the given base triangle). b. Yes, the cross …
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13. we can prove that two triangles are similar because their angles ar…
A. AA Theorem
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solve the compound inequality. use graphs to show the solution set to e…
1. Correct graph for $x>7$: D. <graph with open circle at 7, shading right> 2. Solution set of the compound inequality $x>7$ and $x<-1$: $\emptyset$ (empty set)
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question 2 (5 points) what is significant about the geometric dilution …
Geometric dilution (used in pharmacy/compounding) ensures uniform mixing of potent substances (e.g., drugs) by adding diluent in geometric - ratio steps (e.g., mixing a small amou…
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2. consider the given cube and the cross section formed by a plane inte…
a. The cross section is a square identical to the base: ``` 5.4 cm ┌───────────┐ │ │ 5.4 cm │ │ └───────────┘ 5.4 cm ``` (All four sides are labeled 5.4 cm, matching the base's di…
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how are the binomial factors of $x^2 + 7x - 18$ and $x^2 - 7x - 18$ sim…
The trinomial \(x^2 + 7x - 18\) factors into \((x + 9)(x - 2)\) and \(x^2 - 7x - 18\) factors into \((x - 9)(x + 2)\). The signs in each binomial are reversed for the linear - ter…
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4) the number line is shown with a ray starting from 0 (or near 0) and …
The inequality represented is \( \boldsymbol{x < 0} \) (or all real numbers less than 0).
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find st in rectangle qrst. st = submit
22
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solve for ( x ). round to the nearest tenth, if necessary.
$38.6$
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find m∠f in parallelogram efgh. m∠f = \\boxed{}^\\circ submit
$51$
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5) 51 m, 68 m, 85 m
The lengths 51 m, 68 m, 85 m form a right - angled triangle (by the Pythagorean theorem).
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solve for x. round to the nearest tenth, if necessary.
13.5
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4) 2 yd, 3 yd, √13 yd
These side lengths form a right triangle (by the Pythagorean theorem).
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in $\\triangle uvw$, the measure of $\\angle w = 90^\\circ$, $uw = 36$,…
$\frac{77}{85}$
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3) 21 mm, 24 mm, 32 mm
The lengths 21 mm, 24 mm, and 32 mm can form a triangle.
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question in △def, the measure of ∠f = 90°, ed = 53, df = 45, and fe = 2…
$\frac{28}{53}$
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a shipping company uses an inclined conveyor belt to load and unload pa…
$4^2 + 10^2 = c^2$ $16 + 100 = c^2$ $116 = c^2$ $10.8 = c$ The length of the conveyor belt is about $10.8$ feet.
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a triangle has sides with lengths 8 inches, 15 inches, and 17 inches. i…
No, because $8^2 + 15^2 eq 17^2$
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in $\\triangle jkl$, the measure of $\\angle l = 90^\\circ$, $kj = 17$,…
$\frac{8}{15}$
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question in $\\triangle tuv$, the measure of $\\angle v = 90^\\circ$, $…
$\frac{56}{65}$
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1) 4 in., 5 in., 7 in. 2) 5 cm, 12 cm, 13 cm
s: 1) 4 in., 5 in., 7 in. do not form a right triangle. 2) 5 cm, 12 cm, 13 cm form a right triangle.
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determine the value of ( x ). enter the correct value in the box. ( x =…
\(100\)
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directions the lengths of the sides of various triangles are given belo…
No (the triangle with sides 4 in, 5 in, 7 in is not a right triangle)
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determine the value of x. enter the correct value in the box. x = \\squ…
\(x = 42\)
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in $\\triangle vwx$, the measure of $\\angle x = 90^\\circ$, $vx = 45$,…
$\frac{45}{28}$
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two dimensions of a right triangle are 5 units and 13 units. a student …
D. No. $5^2 + 13^2 = 25 + 169 = 194$. $\sqrt{194}$ is about 13.9, which is not an integer. B. The student is incorrect. The correct equation is $5^2 + b^2 = 13^2$, $b^2 = 144$, $b…
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y = x + 2 y = x + 1 click to select points on the graph.
The system of equations \( \begin{cases}y = x + 2\\y = x + 1\end{cases} \) has no solution because the two lines are parallel (same slope, different y - intercepts).
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5. two sides of a triangle measure 9 cm and 15 cm. which expression rep…
B. $6 < x < 24$
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4. in △pqr, side pq = 10 cm, qr = 14 cm, and pr = 16 cm. which angle is…
B. $\angle Q$
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in the right triangle, there are segments labeled 20, 25, and a side la…
\( \boxed{30} \)
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timed problem score: 2/10 current time: 29.9 find: \\(\\tan a\\) \\(\\t…
$\boldsymbol{\frac{45}{60}}$ (matches the third option)
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find: \\(\\tan a\\) *the figure is not drawn to scale* answer \\(\\frac…
$\frac{48}{20}$ (matches option B. $\frac{48}{20}$)
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timed problem score: 0/10 current time: 2.0 find: \\(\\cos a\\) *the fi…
$\frac{4}{5}$
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express the trig ratios as fractions in simplest terms. answer attempt …
$\sin K = \frac{3}{5}$ $\cos J = \frac{3}{5}$
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4) a = 9 b = □ c = 36
If we assume a geometric sequence relationship (which gives an integer answer, likely the intended case), \(b = 18\). If we assume the Pythagorean theorem with \(c\) as hypotenuse…
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in the right triangle diagram, there are lengths 18, 22, and an unknown…
\( x = 6\sqrt{11} \approx 19.9 \) (or if we round to a whole number, \( 20 \))
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3) a=□ b=8 c=14
If we leave it in radical form, \(a = 2\sqrt{33}\); if we use a decimal approximation, \(a\approx11.49\) (rounded to two decimal places)
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2) a=□ b=6 c=10
\(a = 8\)
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$\\overleftrightarrow{dy}$ is tangent to circle $o$ at point $d$, and $…
$61^\circ$
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directions: complete each proof. 1. given: $overline{de} \\parallel \\o…
| Statements | Reasons | |------------|---------| | $\overline{DE} \parallel \overline{GH}$ | Given | | $\angle D \cong \angle G$, $\angle E \cong \angle H$ | Alternate Interior A…
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directions use the pythagorean theorem and a calculator to find the mis…
\(7.3\)
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2. in a given triangle, the measurement of each angle is (2x+10), (x+20…
C. 50
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nevaeh leans a 22-foot ladder against a wall so that it forms an angle …
19.77 feet
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directions: complete each proof. 1. given: $overline{de} \\parallel \\o…
| Statements | Reasons | |------------|---------| | $\overline{DE} \parallel \overline{GH}$ | Given | | $\angle D \cong \angle G$, $\angle E \cong \angle H$ | Alternate Interior A…
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in the right triangle, there are side lengths 3, 9, 30 and a segment x …
\( \frac{27}{10} \) (or \( 2.7 \))
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$overleftrightarrow{yg}$ is tangent to circle $o$ at point $y$. if $mov…
$51^\circ$
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to solve the problem. mr. jiang is building a deck on his house. he can…
\( s = \frac{P}{4} \) ### Question 10
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question 1 of 12 select the correct answer. what is the best approximat…
25 units
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10) is mr. jiangs deck in the shape of a square or a rectangle? explain…
To determine if Mr. Jiang's deck is a square or a rectangle, we need to know the side lengths (or at least the relationship between length and width). However, since the problem a…
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graph these equations: $y = -x$ $y = 4$ click to select points on the g…
To graph \( y=-x \): Plot points such as \((0,0)\), \((1, - 1)\), \((-1,1)\) and draw a line through them. To graph \( y = 4\): Draw a horizontal line through \((0,4)\), \((1,4)\)…
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geometry chapter 7 review a rectangular gate is shown below. if the gat…
19 inches
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there is a right triangle with a height drawn to the hypotenuse. the le…
\(x = 9\sqrt{2}\) (or approximately \(12.73\))
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11. given rectangle pqrs below find all the missing measurements. er = …
$ER = 6$, $QS = 12$, $SR = 6$, $m\angle PQE = 90^\circ$, $m\angle SER = 90^\circ$, $m\angle EPS = 45^\circ$
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12. find the measure of each numbered angle in the rhombus shown below.…
$m\angle1 = 70^\circ$, $m\angle2 = 40^\circ$, $m\angle3 = 70^\circ$, $m\angle4 = 70^\circ$, $m\angle5 = 40^\circ$
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state whether the slope of the line is positive, negative, 0, or is und…
B. positive
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the rectangle below is dilated by a scale factor of \\(\\frac{1}{4}\\).…
Perimeter of given rectangle: \( 140 \) units Perimeter of dilated rectangle: \( 35 \) units Area of given rectangle: \( 1176 \) units² Area of dilated rectangle: \( 73.5 \) (or \…
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is this a function? yes no
Yes
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the right triangle below is dilated by a scale factor of 3. find the pe…
Perimeter of given right triangle: 56 units Perimeter of dilated right triangle: 168 units Area of given right triangle: 84 units² Area of dilated right triangle: 756 units²
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question find the distance between the two points in simplest radical f…
$3\sqrt{10}$
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solving problems using trigonometric ratios a 25 - foot long ladder is …
B. The second diagram (with 18° at the wall-ladder intersection, ladder labeled 25)
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practice using trigonometric ratios to solve for missing lengths. which…
D. $XY = \frac{22}{\sin(41^\circ)}$
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the graph of a function is given below. give all y-intercepts and x-int…
(a) \(y\)-intercept(s): \(0\) (b) \(x\)-intercept(s): \(0\)
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which graph shows a function?
The top-right parabola graph (opening upwards with vertex below the x-axis) shows a function.
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in circle q with m∠psr = 33°, find the measure of minor arc pr. m pr =
$66^\circ$
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in circle q with m∠psr = 24°, find the measure of minor arc pr. m pr =
$48^\circ$
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three noncollinear points determine three lines, as shown in the figure…
(a) 6 (b) 10 (c) $\frac{n(n-1)}{2}$
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five lines are drawn in the plane (a) what is the smallest number of po…
(a) The smallest number of intersections is 0 (b) The largest number of intersections is 10 (c) Yes, every integer $m$ with $0 \leq m \leq 10$ is achievable. You can arrange lines…
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question 8, 9.1.22 part 2 of 2 hw scor o points: 0 of 1 a hiker starts …
What direction must the hiker turn to resume heading due north? - The hiker must turn left How many degrees must the hiker turn? - $19^\circ$
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plot the points a(5,-3), b(-4, 2), c(10, 6) on the coordinate axes belo…
$D=(19, 1)$
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find the length of the third side. if necessary, write in simplest radi…
8
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find the length of the third side. if necessary, write in simplest radi…
$2\sqrt{5}$
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choose all answers that describe the quadrilateral rstu if $rs = 31$, $…
Quadrilateral
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choose all answers that describe the quadrilateral (abcd) if (mangle a …
Quadrilateral
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choose all answers that describe the polygon below. answer attempt 1 ou…
Quadrilateral, Parallelogram, Rectangle, Rhombus, Square
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choose all answers that describe the quadrilateral bcde if m∠b = 150°, …
Quadrilateral
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choose all answers that describe the polygon ghij if gh = 15, hi = 17, …
Parallel, Quadrilateral
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given parallelogram uvwx below. if uy = 35, find yw.
35
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given rectangle opqr below. if ( mangle rso = 112^circ ), find ( mangle…
$68^\circ$
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given parallelogram opqr below. if os = 29, find sq.
29
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given rectangle fghi below. if m∠ijf = 112°, find m∠gjh.
$112^\circ$
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given rectangle fghi below. if ( \text{m}angle ijf = 112^circ ), find (…
$\text{m}\angle GJH = 68^\circ$
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given rectangle hijk below. if $ik = 5$, find $hj$.
$HJ = 5$