幾何
三角形、圓、解析幾何與證明題。
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drag each angle pair to classify them as same - side exterior angles, c…
To solve this, we recall the definitions of each angle pair type (assuming two parallel lines cut by a transversal, with angles labeled in standard position): ### Same - Side Exte…
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line rv is perpendicular to line ac. line ac is represented by the equa…
- Slope of Line \( AC \): \( \frac{3}{2} \) - Slope of Line \( RV \): \( -\frac{2}{3} \) - Point - Slope Form of Line \( RV \): \( y - 3=-\frac{2}{3}(x - 0) \) (or \( y - 3=-\frac…
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line rv is perpendicular to line ac. line ac is represented by the equa…
\( y = -\frac{2}{3}x + 3 \)
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line bn is represented by the equation $y = \\frac{3}{4}x + \\frac{7}{4…
\( y = -\frac{4}{3}x - 1 \)
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multiple choice 10. the point which is not in the solution region of th…
C. \((1,-2)\)
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line fn is represented by the equation $y = x + 19$. determine the equa…
\( y = x + 16 \)
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line ql is represented by the equation $y = x + 1$. line gn is parallel…
\( y = x - 2 \)
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find the area and perimeter of each of the following shapes. show all o…
Area: \( 18.8 \) square feet, Perimeter: \( 18.7 \) feet ### Problem 2: Parallelogram (base 3 yd, height 2 yd, sides 3 yd, 4 yd)
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find the slope of the line. graph of a line on a coordinate plane with …
\(m = -\frac{1}{2}\) (corresponding to the option \(m = -\frac{1}{2}\))
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find the slope of the line. graph of a line on a coordinate plane with …
\(m = \frac{1}{2}\)
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slope of line tg, slope of line cz, point - slope form of line cz; $m_1…
If perpendicular: \( \boldsymbol{\frac{3}{2}} \) If parallel: \( \boldsymbol{-\frac{2}{3}} \) (Assuming perpendicular, the slope of \( CZ \) is \( \frac{3}{2} \).)
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y = (3/2)x + 15; try again; you can determine the slope from the given …
To determine the slope of line \( TG \) from the equation \( y = \frac{3}{2}x + 15 \), we use the slope - intercept form of a line, which is \( y=mx + b \), where \( m \) is the s…
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y = \\frac{3}{2}x + 15 try again you can determine the slope from the g…
The slope of line \(TG\) (\(m_1\)) is \(\frac{3}{2}\)
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the equation for line p is $y = 2x - 7$. line n is perpendicular to lin…
3
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which of the following lines are parallel to $y = \\frac{4}{3}x - 8$? s…
- \( 8x - 6y = 12 \) - \( y - 1=\frac{4}{3}(x + 6) \)
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line p goes through the points (-5, 9) and (1, -3). line q goes through…
To graph line \( q \), first determine its equation: slope \( \frac{1}{2} \), equation \( y=\frac{1}{2}x + 5 \). Plot the point \( (4, 7) \), then use the slope to find additional…
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a) is it possible for reina to find the distance across the crater usin…
98
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a) is it possible for reina to find the distance across the crater usin…
Yes ### b)
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1. write two expressions that represent the area of the rectangular reg…
First expression: \(6x + 15\); Second expression: \(3(2x + 5)\) ### Problem 2a
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plastic pollution essay persuasive essay outline introduction thesis st…
The correct option is: Another effect of plastic pollution is the waste of money it causes.
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lesson 17 | session 1 complete problems 3–5. 3 the hanger diagram model…
The value of \( b \) is 2. ### Problem 4 #### Part a
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circle the equations. justify your answer. x + 2 \t\t x + 2 = 4 \t\t x …
The equations are \( \boldsymbol{x + 2 = 4} \), \( \boldsymbol{4 = x} \), and \( \boldsymbol{5 + 7 = 12} \). These should be circled as they are mathematical statements with the "…
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priya says, \i know everything about a right triangle with a 30 degree …
Missing angles: \(60^\circ\) and \(90^\circ\) Missing side lengths: \(1.732\) cm (adjacent to \(30^\circ\)) and \(1\) cm (opposite to \(30^\circ\))
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given a line has a slope of $-\frac{3}{4}$, what is the slope of a line…
\(\frac{4}{3}\) (corresponding to the middle option)
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given a line has a slope of $-\frac{5}{4}$, what is the slope of a line…
The slope of the line parallel to the given line is $-\frac{5}{4}$, so the correct option is the third one: $-\frac{5}{4}$
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given a line has a slope of \\(\\frac{4}{5}\\), what is the slope of a …
B. $\frac{4}{5}$
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use the two points to find the slope of this line. m =? remember: slope…
\(\frac{1}{3}\)
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is the slope of this line positive or negative? a) positive b) negative…
a) positive
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use the two points to find the slope of this line. m = -2/? remember: s…
\(3\)
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is the slope of this line positive or negative? a) positive b) negative…
b) negative
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which graph matches this table? input (x) -1 0 1 output (y) 5 3 1
The second graph (the middle one)
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recognizing necessary information for similarity what additional inform…
- \(\triangle ABC\) was rotated and dilated by a scale factor between 0 and 1. - \(\angle B\cong\angle M\) - \(\angle C\cong\angle L\)
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the composition $d_{o,0.75}(x,y) \\circ d_{o,2}(x,y)$ is applied to $\\…
- \( \angle M \cong \angle M'' \) (the option with \( \angle M \cong \angle M'' \)) - \( \triangle LMN \sim \triangle L''M''N'' \) (the option with \( \triangle LMN \sim \triangle…
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9) find the surface area: (figure of a three - dimensional shape with d…
The surface area is \(\boldsymbol{228}\) square feet.
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graph the following system of inequalities by plotting all lines in the…
To graph the system: 1. Draw a solid vertical line at \( x = 0 \) and shade left of it. 2. Draw a dashed horizontal line at \( y = 4 \) and shade above it. 3. Draw a dashed line \…
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given a line has a slope of \\(\\frac{6}{5}\\), what is the slope of a …
A. $\frac{6}{5}$
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given a line has a slope of $-\frac{3}{4}$, what is the slope of a line…
A. $-\frac{3}{4}$
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given a line has a slope of $-\frac{3}{7}$, what is the slope of a line…
A. $-\frac{3}{7}$
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given a line has a slope of $-\frac{4}{9}$, what is the slope of a line…
B. $-\frac{4}{9}$
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given right triangle abc with altitude \\(\\overline{bd}\\) drawn to hy…
The length of \( \overline{BD} \) is \( 9 \).
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5. which is the equation of the circle shown below? a. $(x - 3)^2 + y^2…
C. \( 113,040\space\text{cm}^3 \)
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1. kelvin is at his house located at (3, 4) on a coordinate plane and w…
D. 8.9 ### Question 2
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the focus and directrix of a parabola are shown. what is the equation o…
\(x=\frac{1}{8}(y - 2)^{2}-1\) (corresponding to the option \(x=\frac{1}{8}(y - 2)^{2}-1\) in the table)
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find the perimeter and area of the figure below. 3 cm 4 cm 2 cm 6 cm pe…
Perimeter = $\boldsymbol{20\ \text{cm}}$ Area = $\boldsymbol{18\ \text{cm}^2}$
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find the perimeter and area of the figure below. 155 146 123 143 306 pe…
Perimeter = \(\boldsymbol{750}\) Area = \(\boldsymbol{28351.5}\)
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find the perimeter and area of the figure below. (figure of a parallelo…
Perimeter = 110 Area = 400
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find the slope of the line graphed below.
\(-\frac{4}{3}\)
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find the perimeter and area of the figure below. triangle with side len…
Perimeter = 1134 Area = 53454
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the city council is planning to construct a park on north street that h…
B. at the center of the inscribed circle of the park
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7) $\\triangle pqr \\sim \\triangle cba$ 8) $\\triangle srq \\sim \\tri…
s: - Problem 7: $x = 6$ - Problem 8: $x = 13$ - Problem 9: $x = 9$ - Problem 10: $x = 7$
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find the perimeter and area of the figure below. 300 126 126 300 perime…
Perimeter = 852 Area = 37800
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24 a figure is shown. use the add arrow tool to draw the line of reflec…
The line of reflection is the perpendicular bisector of the two parallel sides of the trapezoid (drawn using the Add Arrow tool as described).
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23 the equation of a circle is shown. $(x - 3)^2 + (y - 2)^2 = 4$ the c…
\((x - 5)^2 + (y - 6)^2 = 36\)
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9-3 practice #2 - similar triangles find the missing length. the triang…
s: 1) $\boldsymbol{63}$ 2) $\boldsymbol{109}$? Wait, no—wait, in Problem 2, maybe I made a mistake. Wait, let's recheck: $\triangle DSR \sim \triangle DEF$, so $\frac{DS}{DE} = \f…
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5) △uvw ~ ______ 6) △fed ~ ______ 7) △abc ~ ______ 8) △lkj ~ ______ 9) …
$\triangle UST$ (or $\triangle SUT$) ### Problem 6:
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figure o is the result of a transformation on figure n. which transform…
A. A translation 2 units right and 1 unit down
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practice solve each system of equations by graphing. 1. $y = x + 4$ $y …
The solution to the system of equations \( \begin{cases}y=x + 4\\y=-2x-2\end{cases} \) is the point of intersection of the two lines, which is \( (-2,2) \)
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★★★ 7. the volume of a shape is the number of cubes it will take, all t…
s: a. \( \boldsymbol{10} \) \( \text{cm}^3 \) b. \( \boldsymbol{8} \) \( \text{cm}^3 \) c. \( \boldsymbol{7} \) \( \text{cm}^3 \)
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find the measure of the missing angles. answer attempt 2 out of 2 b = \…
\( b = 146^\circ \), \( c = 34^\circ \)
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7. farm an animal pen is in the shape of a regular heptagon. what is th…
\( 128.6^{\circ} \)
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5. architecture in the uffizi gallery in florence, italy, there is a ro…
The measure of the angle formed by two consecutive walls (interior angle) of the regular octagonal room is \( 135^{\circ} \).
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1. match the inequality with the correct boundary line. answers may be …
(for part a): The boundary line of \(-x + 3y\leq0\) is \(y=\frac{1}{3}x\) (b) (Note: There seems to be an inconsistency with the second inequality and the given lines, but based o…
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20) diagram of two rectangles: left rectangle with sides 40, 56, 40, x;…
\( x = 40 \) ### Problem 22:
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find the equation of the line parallel to $y = -\frac{9}{4}x - 3$, that…
The equation of the line is \( y = -\frac{9}{4}x-14 \), so the first box (numerator of the slope) is \( 9 \), the second box (denominator of the slope) is \( 4 \), and the third b…
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there is a right triangle, one of the acute angles is 67 degrees, the l…
\(x\approx33.3\) cm (or more precisely \(x\approx33.27\) cm)
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graph the image of rectangle stuv after a translation 12 units down.
The translated rectangle \( S'T'U'V' \) has vertices at \( S'(-5,-8) \), \( T'(-2,-8) \), \( U'(-2,-6) \), \( V'(-5,-6) \). To graph it, plot these points and draw the sides conne…
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find the equation of this line. simplify your answer completely. the gr…
The slope of the line is \(1\), so the equation of the line is \(y = 1x+3\) (and the value in the box is \(1\)).
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38. write the equation of a circle with a center at (-2,3) and a point …
A. \((x+2)^{2}+(y-3)^{2}=16\) ### Question 39
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is the graph of this equation a horizontal or vertical line? x = 7 hori…
vertical line
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which number in the ordered pair (3, 2) represents the x - coordinate? …
3
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finding equivalent fractions name: shade in the visual fraction to find…
s: 1. $\boldsymbol{\frac{4}{10}}$ 2. $\boldsymbol{\frac{1}{2}}$ 3. $\boldsymbol{\frac{3}{4}}$ 4. $\boldsymbol{\frac{2}{6}}$ 5. $\boldsymbol{\frac{2}{3}}$ 6. $\boldsymbol{\frac{0}{…
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1. classify each triangle using its side lengths. (a) (b)
(a) Isosceles triangle (b) Scalene triangle
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6. a regular hexagon is inscribed in a circle with a diameter of 32 uni…
The area of the regular hexagon is \( 384\sqrt{3}\approx665.1 \) square units (exact form \( 384\sqrt{3} \) square units).
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c. which word does not belong?: choose the word that is not word given,…
b. declare ### 2. For "psychologist" row:
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1. dans chaque cas, nommez la condition minimale qui permet daffirmer q…
HL (Hypoténuse - Catété) ### Question 1b
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this question has two parts. answer part a. then answer part b. part a …
C. mounds like animals ### Part B
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parallel lines and transversals find the measure of each numbered angle…
Let's solve these problems one by one. We'll start with the "Parallel Lines and Transversals" section (problem 10), then "Special Right Triangles" (problem 13 as an example), and …
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which features of the figure stay the same with every transformation? c…
The shape of the figure, The size of the figure
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30. the shape below was created by rotating a two dimensional shape abo…
A ### Question 31
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read each short answer question carefully and be sure to show all neces…
To solve the problem of matching each graph with its function, we analyze the key features of each graph (such as the direction of opening, vertex, x - intercepts, y - intercepts)…
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10/20 the y - axis is: a positive line a vertical line a negative line …
B. A vertical line
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2x + 3y = 6 -4x + 8y = 8 -5x - 10y = -20 6x - 2y = -12
For \(2x + 3y=6\): Intercepts \((0,2)\) and \((3,0)\) For \(-4x + 8y=8\): Intercepts \((0,1)\) and \((-2,0)\) For \(-5x-10y=-20\): Intercepts \((0,2)\) and \((4,0)\) For \(6x-2y=-…
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1/20 the x-axis is: negative line a horizontal line positive line a ver…
B. A horizontal line
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which number in the ordered pair, (5,7) represents the y-coordinate? ty…
7
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if you were to plot the point (4,12) what would be the correct method? …
C. Start at the origin, then go over 4 and then go up 12
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plot the following point on the coordinate plane below: (partially obsc…
The problem seems to be about plotting a point on a coordinate plane, but the coordinates of the point are not fully visible (only part of it is shown, like maybe (x, 2) but the x…
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find the area and perimeter. 1 trapezoid with top base (4x^2 + 4x + 1),…
### Problem 1: Trapezoid (Area and Perimeter) #### Area of Trapezoid The formula for the area of a trapezoid is \( A = \frac{1}{2} \times (b_1 + b_2) \times h \), where \( b_1 \) …
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6. jeremy wants to make sure that the walls he is building are at right…
Yes, the walls are at right angles to each other. We know this by using the Pythagorean theorem. For a triangle with side lengths 3 m, 4 m, and 5 m, we check if \(3^{2}+4^{2}=5^{2…
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5. determine the area of the square that would be attached to the hypot…
The area of the square on the hypotenuse is \( \boldsymbol{965} \) square centimeters. ### Part (b)
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17) there are two rectangles. the first rectangle has a top side length…
9
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volume of a rectangular prism to find the volume of a rectangular prism…
\( 0.064 \, \text{mm}^3 \) ### Part b
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(a) can the hl congruence property be used? \fbox{yes} \fbox{no} (b) ca…
Yes ### Part (b)
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graph the following lines given the equation in slope - intercept form …
### For \( y = 3x - 1 \) # Explanation: ## Step1: Identify slope and intercept Slope \( m = 3 \), y - intercept \( b=-1 \). Plot the y - intercept \((0, - 1)\). ## Step2: Use slop…
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question 6 of 20 (1 point) | question attempt: 1 of unlimited can the h…
Yes ### Part 2 (Second pair of triangles)
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solve for x and graph the solution on the number line below. 26 < 5x + …
Inequality Notation: \(4 < x < 12\) For the number line: Plot an open circle at 4 and 12, then draw a line segment between them (since \(x\) is greater than 4 and less than 12, no…
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7. which coordinate is a solution for $3x - 4y = 8$? $(-4, -4)$ $(-2, 4…
(4, 1)
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3. what is the y-value when x = 7? type a response
\(-10\)
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throwback: find the slope of the line from the graph: for each graph, c…
To solve for the slope \( m \) of each line, we use the formula \( m = \frac{\text{rise}}{\text{run}} \), where "rise" is the vertical change (change in \( y \)) and "run" is the …
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use the following key features to graph the line: x-intercept: (3,0) y-…
The line is graphed by plotting the points $(0,6)$ (y - intercept) and $(3,0)$ (x - intercept) and drawing a straight line through them (with a slope of - 2, confirming the line's…
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vertical lines a vertical line is written in the form x = a, where a re…
If we consider the left vertical line, the equation is \( \boldsymbol{x=-1} \) (or if it's the y - axis, \( x = 0 \), but likely \( x=-1 \) for the non - y - axis vertical line).