几何
三角形、圆、解析几何与证明题。
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which angles are adjacent angles?\ \ image of intersecting lines with p…
$\angle LKN$ and $\angle LKI$
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act math problem set #1 ① graph $y = \\sqrt{x}$
The graph of \( y = \sqrt{x} \) is a curve starting at the origin \((0,0)\), lying in the first quadrant, increasing as \( x \) increases, and having a concave - down shape (passi…
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4. write equation of the horizontal line that passes through the point …
\( y = -2 \)
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a rectangular pan has a length that is \\(\\frac{4}{3}\\) the width. th…
18 in
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4. the perimeter of a square is 4 times as great as the length of any o…
Yes, the perimeter of a square is proportional to its side length because the perimeter formula \( P = 4s \) fits the proportional relationship form \( y = kx \) (where \( k = 4 \…
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consider the work shown to solve for x in the following right triangle.…
\(10.04\)
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which angles are alternate exterior angles? ∠wxz and ∠yxu ∠tus and ∠vux…
\( \angle VUS \) and \( \angle YXZ \)
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stacey has a square piece of cloth. she cuts 3 inches off of the length…
6 in (corresponding to the option "6 in")
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which angles are alternate exterior angles? image of intersecting lines…
\( \angle TUS \) and \( \angle YXZ \)
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find the value of ( x ). round your answer to two decimal places. enter…
\( 54.87 \)
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level 157 which statement is true? select an answer a s is at $2\\frac{…
A. S is at $2\frac{4}{10}$
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2. write equation of the vertical line that passes through the point (3…
The equation of the vertical line passing through \( (3,5) \) is \( x = 3 \). For the hints: - \( m=\) undefined - Axis: x - axis - Intercept: 3 (x - intercept) - Equation: \( x =…
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1. write the equation of the line that is graphed below.
\(y=-2x + 3\)
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which angles are vertical angles? ∠sru and ∠qru ∠qru and ∠srp ∠srp and …
$\angle SRP$ and $\angle TUR$ (the fourth option: $\boldsymbol{\angle SRP}$ and $\boldsymbol{\angle TUR}$)
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which angles are alternate interior angles? ∠srp and ∠sru ∠sru and ∠tur…
$\angle SRU$ and $\angle TUR$
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which angles are alternate interior angles? ∠srp and ∠sru ∠sru and ∠tur…
$\angle SRU$ and $\angle TUR$ (corresponding to the option with $\angle SRU$ and $\angle TUR$)
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which angles are consecutive interior angles? ∠srt and ∠qrt ∠srt and ∠s…
∠SRO and ∠POR
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in a scale drawing of a painting, 1 centimeter represents 10 inches. sc…
s: (a) \(\boldsymbol{9}\) (assuming real height is 90 inches, as per (b)'s context) (b) \(\boldsymbol{90}\)
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use the figure below to answer the following questions. round all answe…
a) \( 25.00 \) deg b) \( 8.03 \) c) \( 17.22 \)
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which angles are supplementary angles? ∠vwy and ∠utr ∠vwy and ∠xwt ∠vwy…
\(\angle VWY\) and \(\angle XWY\) (the third option: \(\boldsymbol{\angle VWY}\) and \(\boldsymbol{\angle XWY}\))
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nd the distance between point i and point j.
6
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find the distance between point c and point d. distance:
4
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find the distance between point g and point h.
The distance between point G and point H is 5.
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determine \\(\\cos(a)\\) and \\(\\cos(b)\\).
$\cos(A) = \frac{4}{5}$, $\cos(B) = \frac{3}{5}$
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determine \\(\\sin(a)\\) and \\(\\sin(b)\\). image of a right triangle …
\(\sin(A)=\frac{20}{29}\), \(\sin(B)=\frac{21}{29}\)
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which equation can be used to find the value of x? $x + 45 + 40 = 360$ …
\(x + 45 + 40 = 180\) (the second option)
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timed problem score: 5/10 current time: 62.3 which inequality is repres…
\(x > -10\)
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the figure shows a triangle with unknown angles. which equation shows t…
\(m\angle4 = m\angle1 + m\angle2\) (the third option: \(m\angle4 = m\angle1 + m\angle2\))
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timed problem score: 1/10 current time: 12.3 which inequality is repres…
\(x < 4\)
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find the y-intercept of the parabola with the following equation. enter…
\((0, 6)\)
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a radio tower is located on a coordinate system measured in miles. the …
\(\begin{cases}y - 2(x - 4)^2=2\\5x + 11y = 62\end{cases}\) (the first system of equations)
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timed problem score: 5/10 current time: 70.9 which inequality is repres…
\( x < 3 \) (the first option with the open circle symbol and \( < 3 \))
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part 2 for each rectangle, write one multiplication expression for the …
Area of gray rectangle: $4\times7$ Area of white rectangle: $3\times7$ Total area of rectangle: $4\times7 + 3\times7 = 7\times7$ (or $49$)
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which equation can be used to find the value of x? $x = 68 + 72$ $x = 7…
\(x + 68 + 72 = 180\) (the fourth option)
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a lighthouse is located at (1, 2) in a coordinate system measured in mi…
The second option: \(\begin{cases}(x - 1)^2+(y - 2)^2 = 25\\y=\frac{14}{81}(x - 2)^2-6\end{cases}\) (the option with the circle equation \((x - 1)^2+(y - 2)^2 = 25\) and the quadr…
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12) (figure of a geometric diagram with triangle and right angles, labe…
\( 12.6 \) inches
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use triangles to find the sum of the interior angle measures of the po …
\( 360 \)
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find the value of x and y. 27 30°
\(x = 54\), \(y=27\sqrt{3}\)
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timed problem score: 1/10 current time: 22.5 which inequality is repres…
\( x < 0 \) (the first option: \( x < 0 \))
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the circumference of a circle is 12.56 centimeters. what is the circle’…
4.00
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use the scale drawing to solve each problem. show your work. 1. what is…
15 feet ### Problem 2: Width of the Living Room
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find the value of x and y.
\( x = 3 \), \( y = 3\sqrt{3} \)
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the diameter of a circle is 2 kilometers. what is the circle’s circumfe…
6.28
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lines, angles, and polygons creating triangles from given side lengths:…
- First figure: Triangle possible (side lengths 3, 3, 5) - Second figure: No triangle possible (side lengths 3, 5, 9)
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the radius of a circle is 8 kilometers. what is the circles circumferen…
50.27
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find the value of $x$. (there is a right triangle with a right angle, a…
\(x = 6\sqrt{2}\)
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the radius of a circle is 4 meters. what is the circles circumference? …
25.13
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the measure of angle abc is 130°. the measure of angle abd is 95°. the …
35
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find the value of $x$. $15\\sqrt{10}$ $x$ $45^{\\circ}$
\(30\sqrt{5}\)
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solve the inequality and graph the solution on the line provided. $-18 …
Inequality Notation: \( x > 8 \) For the number line: Place an open circle at 8 (since the inequality is \( > \), not \( \geq \)) and draw an arrow to the right to represent all n…
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learn with an example or watch a video the diameter of a circle is 6 ki…
18.85
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the measure of angle jkl is 75°. the measure of angle jkm is 25°. the m…
\( x = 50 \)
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \( x \leq -5 \) For the number line: We would place a closed circle at -5 (because the inequality is "less than or equal to") and shade to the left of -5 to r…
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the radius of a circle is 16 kilometers. what is the circles area? roun…
\( 804.25 \)
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write an equation of the line that passes through (0, 4) and (0, -3). x…
\(0\)
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solve the inequality and graph the solution on the line provided. 3x - …
Inequality Notation: \( x < -3 \) For the number line: We draw an open circle at -3 (since the inequality is strict, \( < \), not \( \leq \)) and shade the region to the left of -…
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write an equation in slope-intercept form of the line that passes throu…
The problem is incomplete. Please provide the second point (or the slope) of the line to find the equation in slope - intercept form.
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the measure of angle jkl is 150°. the measure of angle jkm is 110°. the…
\( x = 40 \)
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drag the yellow dot until \\( \\overleftrightarrow{ac} \\) and \\( \\ov…
When \( \overleftrightarrow{AC} \parallel \overleftrightarrow{DF} \), \( \angle ABE \) and \( \angle DEH \) are equal (e.g., both \( 60^\circ \) or another equal measure depending…
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write an equation of the line that passes through $(-1, 0)$ and $(0,0)$…
\( y = 0 \)
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4. what is the length of segment il? options: 11cm, 22cm, 11√2 cm, 22√2…
11√2cm (Option B: 11√2cm)
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solve the inequality and graph the solution on the line provided. $5 + …
Inequality Notation: \( x < -8 \) For the number line: We place an open circle at -8 (because the inequality is strict, \( < \), not \( \leq \)) and draw a line to the left of -8 …
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a tributary joins a river at an angle. find the value of x. 16 x = \\sq…
\( 53 \)
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3. what is the ratio of the sides for triangle xyc? image of a geometri…
\(1:1:\sqrt{2}\) (corresponding to the option with this ratio, e.g., if the options are as given, the option with \(1:1:\sqrt{2}\))
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given a(1, -3) and b(-7, -7) are on the same line. write the equation f…
\( \frac{1}{2} \) #### b. Equation of \( \overleftrightarrow{AB} \)
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \( x < -8 \) For the number line: We would place an open circle at -8 (because the inequality is strict, \( < \), not \( \leq \)) and draw an arrow to the lef…
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which angles are supplementary angles? ∠vwy and ∠utr ∠vwy and ∠xwt ∠vwy…
\(\angle VWY\) and \(\angle XWY\) (the option \(\angle VWY\) and \(\angle XWY\))
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which angles are alternate exterior angles? ∠gfh and ∠gfc ∠efc and ∠bca…
$\angle DCA$ and $\angle EFH$
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→qs and ↔tv are parallel lines. which angles are supplementary angles? …
\(\angle TUW\) and \(\angle TUR\)
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consider the work shown to determine the value of x in the following tr…
\(8\)
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write an equation in slope-intercept form of the line that passes throu…
$\frac{1}{4}x + 1$
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lesson 9.12 solve each problem. be sure to write an equation. show your…
The flagpole is 24 ft tall. ### Problem 2:
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great work finding those x-values! however, both solutions should be wr…
To fix the ordered pair notation, for a given x - value, find the corresponding y - value (using the relevant equation/function) and write the ordered pair as \((x,y)\) (e.g., if …
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2. what is the measure of angle x? options: 30°, 45°, 60°, 90°
\(30^\circ\) (corresponding to the option with \(30^\circ\))
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graph the line with the equation $y = \\frac{2}{3}x + 4$.
The line is graphed by first plotting the y - intercept \((0,4)\), then using the slope \(\frac{2}{3}\) to find additional points (e.g., \((3,6)\), \((-3,2)\)) and drawing a strai…
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1. what is the length of segment ab? (image of a geometric figure with …
20cm (the option with 20cm)
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write an equation in slope-intercept form of the line that passes throu…
$y = x + 4$
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solve for x and graph the solution on the number line below. 5x - 10 ≤ …
Inequality Notation: \( x \leq -9 \) or \( x \geq -5 \) (For the number line: Plot a closed circle at -9 and shade to the left, and a closed circle at -5 and shade to the right.)
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1. what is the length of segment ab? options: - $10\\sqrt{3}$cm - $20\\…
\( 20\,\text{cm} \) (the option is "20cm")
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the measure of the exterior angle equals the sum of the measures of the…
Yes, because \(50^{\circ}+60^{\circ}=110^{\circ}\).
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similar triangles in problems 5-10, tell whether the triangles are simi…
s: 5) Similar (by AA) 6) Similar (by AA) 7) Similar (by SSS or congruence) 8) Similar (assuming proportional sides and equal angles, or isosceles with proportional sides) 9) Simil…
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \( x < 1 \) (For the number line: Plot an open circle at 1 and draw an arrow to the left to represent all values less than 1.)
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7. find the value of x in the figure below if \\(\\overline{mp}\\) is p…
4.5 units
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question solve the inequality and graph the solution on the line provid…
Inequality Notation: \( x \geq 6 \) For the number line: We place a closed circle at 6 (since the inequality is "greater than or equal to") and draw an arrow to the right to repre…
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18. in the figure below, ad and bc are parallel. what is the value of x?
\( \boxed{50} \)
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using the graph, determine the equation of the axis of symmetry.
\(x = - 4\)
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the solid below is made from cubes. find its volume. (there is a diagra…
\( 24 \)
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given △abc with coordinates: a(1,2), b(4,6), c(7,2) and △def, with coor…
The triangles are not similar because the corresponding side lengths are not proportional. (The fourth option, assuming the options are ordered as: 1. The triangles are similar be…
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write the standard form of an equation given two points (-1, \\frac{1}{…
The standard form of the equation is \(2x + 3y=-1\)
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im1 parallel & perpendicular lines project record of evidence c project…
b. Two points: \( (0, 2) \) and \( (3, 2) \) (answers may vary, any points with \( y = 2 \) are correct) c. Horizontal ### Problem 2:
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write the standard form of an equation given the points (-1, \\frac{1}{…
The standard form of the equation is \(x + 3y=0\)
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30. in the diagram below, line mn is a perpendicular bisector. which of…
\(\overline{MT} \cong \overline{MS}\) (the first option)
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29. triangles abc and def are similar. find d. image of two triangles, …
12
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solve each problem. show your work. 1. a 5-ft-tall boy casts a shadow t…
The height of the tree is \( 20 \) ft. ### Problem 2:
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28. what changes would you make to turn this formal proof into a paragr…
D. Write the statements and reasons in sentence format.
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write the standard form (-1, 3), (4, -3)
The standard form is \(5 + 15i\)
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which rule explains why these triangles are similar? j k g h i sss sas …
SAS (assuming the sides with arrows give the proportional sides and the included angle is common)
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a, b, c and d are points on a circle. pcq is a tangent to the circle. a…
By using the Alternate Segment Theorem, Isosceles Triangle Property, Sum of Angles in a Triangle, and Cyclic Quadrilateral Property (supplementary opposite angles), we have proven…
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note: triangle may not be drawn to scale. suppose a = 9 and b = 11. fin…
\( \sin(A) \approx 0.63 \) \( \cos(A) \approx 0.77 \) \( \tan(A) \approx 0.82 \) \( \sec(A) \approx 1.29 \) \( \csc(A) \approx 1.58 \) \( \cot(A) \approx 1.22 \)
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which rule explains why these scalene triangles are similar? (image of …
AA