Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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in circle a, measure of arc cfe is 240°. what is the measure of ∠ cae? …
\( 120^\circ \) (corresponding to the option with \( 120^\circ \))
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draw a line of symmetry through the pentagon by connecting two black po…
The line of symmetry is drawn by connecting the left - most black point and the right - most black point (the two black points on the horizontal line passing through the top of th…
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what is the slope of the line that passes through the points (8, 2) and…
\( 0 \)
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what is the measure of the arc bc? 65° 32.5° 180° 130°
\( 130^\circ \) (the option corresponding to \( 130^\circ \))
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what is the slope of the line that passes through the points (4,7) and …
The slope of the line is \( 3 \).
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which statements are true for the equation $x^2 = -4y$? check all that …
The true statements are: - The axis of symmetry is \(x = 0\). - The focus is at \((0,-1)\). - The value of \(p=-1\).
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belle made a scale drawing of a restaurant. in real life, a countertop …
3
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the parabola has a focus at (-3, 0) and directrix x = 3. what is the co…
\(y^{2}=-12x\) (the option: \(y^{2}=-12x\))
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you walk along the outside of a park starting at point p to point q. th…
2.0
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find the distance between p(4,2) and q(6,6). the distance between p and…
\( 2\sqrt{5} \)
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find the distance between f and g. the distance between f and g is (typ…
\(2\sqrt{29}\)
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the shape of a satellite dish can be described as parabolic. satellite …
\((0, 2)\)
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lauren describes a parabola where the focus has a positive, nonzero x c…
- \( y^2 = x \) - \( y^2 = 10x \) - \( y^2 = 5x \)
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point b has coordinates (5,1). the x - coordinate of point a is - 7. th…
(-7, - 8) or (-7, 10) (if we take one, either (-7, - 8) or (-7, 10); but since the distance is 15, both are possible. The previous answer had a formatting error, the ordered pair …
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the derivation for the equation of a parabola with a vertex at the orig…
\(x^2 = 4py\) (the first option)
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when the focus and directrix are used to derive the equation of a parab…
focus
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when the focus and directrix are used to derive the equation of a parab…
a point on the parabola
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point b has coordinates (5,1). the x - coordinate of point a is - 7. th…
(-7, -8), (-7, 10)
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find the midpoint of points a(10,1) and b(4,−5) graphically. you may pr…
The midpoint of points \( A(10,1) \) and \( B(4,-5) \) is \( (7,-2) \).
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point b has coordinates (5,1). the x - coordinate of point a is 0. the …
\((0,13)\) or \((0,-11)\)
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suppose a park is located 2.4 miles east of your home. the library is 3…
4
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4. addition & subtraction amy went to the garden store. she bought 965 …
4. 397 5. C. $(90×6)+(4×6)$ 9. 169 10. C. 7, 14, 21, 28, 35 14. C. $1/5 + 1/5 + 1/5 + 1/5$ 15. 2 pounds 19. C. 12 yards is less than 40 feet 20. $\$2.33$ 24. Obtuse angle (measure…
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describe the key features of a parabola with the equation $x^2 = 40y$. …
\(y = -10\)
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describe the key features of a parabola with the equation $x^2 = 40y$. …
(0,10)
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describe the key features of a parabola with the equation $x^2 = 40y$. …
up
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describe the key features of a parabola with the equation $x^2 = 40y$. …
10
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which angle is vertical to $\\angle 3$?
$\angle 1$
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which angles are adjacent to each other? ∠14 and ∠11 ∠15 and ∠9 ∠14 and…
∠14 and ∠15
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gths in each figure. 22 sq. in. ? in. 10 in.
2.2 in.
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suppose triangle abc will be dilated using the rule $d_{q,\frac{2}{3}}$…
4 units (corresponding to the option "4 units")
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what is the slope of the line that passes through the points (-9, -9) a…
The slope is undefined.
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find the value of each trigonometric ratio. express answers as simplifi…
$\frac{5}{13}$
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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 $\boldsymbol{(x-1)^2 + (y-6)^2 = -4}$. The equation represents a degenerate case with no real solution set (since the right-hand side is negative,…
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look at the diagram on the right. which pair of angles are not compleme…
B. \(\angle PQS\) and \(\angle TQU\)
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solve for ( x ) and graph the solution on the number line below. ( -36 …
Inequality Notation: \(x < 9\) or \(x \geq 11\) For the number line: - For \(x < 9\), draw an open circle at 9 and shade to the left. - For \(x \geq 11\), draw a closed circle at …
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find the value of each trigonometric ratio. express answers as simplifi…
$\frac{12}{13}$
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the table below gives the dimensions of a statue and a scale drawing of…
\(\frac{1}{4}\)
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sketch the graph of the equation. if the graph is a parabola, find its …
B. The graph is a circle with radius \(4\). The center is located at \((0,0)\)
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line wy is dilated to create line wy using point q as the center of dil…
2.75 (or \( \frac{11}{4} \)) ### Second Question: Length of \( QY \)
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a dilation centered at the origin is applied to figure a. the result is…
\(3\)
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find the coordinates of the focus and equation of the directrix for the…
The value of \( p \) is \(-1\). The coordinates of the focus are \((-1,0)\). The equation of the directrix is \( x = 1 \).
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equation that represents the set of points that are 5 units from (2, -7…
$\boldsymbol{(x-2)^2+(y+7)^2=25}$
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write an equation for the area, a, of the parallelogram shown. a = \\sq…
$A = 3 \cdot \frac{2}{3}$
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in a scale drawing of a house, 1 inch represents 4 feet. scale 1 in : 4…
(a) 24 feet (b) 7 inches
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given the equations, identify which way the parabola opens by matching …
- \(x^2=-10y\) matches down - \(y^2 = 6x\) matches right - \(x^2=3y\) matches up - \(y^2=-2x\) matches left
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given a circle where the center is (-8, -2) and another point on the ci…
### Part 1 of 4: The **radius** of the circle is the distance between a point on the circle and the center. ### Part (a): $(x+8)^2+(y+2)^2=25$ ### Part (b): To graph the circle: 1…
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$x^{2}+y^{2}=16$ a. b. c.
C. The graph with center at \((0,0)\) (on the y - axis) and radius \(4\)
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you can transform δefg to δefg by translating it and then performing a …
Translation: $(x, y) \to (x-9, y-8)$ Scale factor: $\frac{3}{5}$
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write an equation to show how ( mangle 1 ) and ( mangle 2 ) are related.
\( m\angle1 + m\angle2 = 180^\circ \)
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a portion of a city map is shown in the figure at the right. if you wal…
176.4 yd
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in the figure below, $\\triangle abc \\sim \\triangle mnp$. $\\overline…
\(10\)
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a circle has the equation $4(x - 5)^2 + 4y^2 = 16$. (a) find the center…
2
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find the midpoint of points ( a(-8, -7) ) and ( b(0, -3) ) graphically.…
The midpoint of points \( A(-8, -7) \) and \( B(0, -3) \) is \( (-4, -5) \)
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given a circle where the center is (-2, -4) and another point on the ci…
Part 1 of 4: radius (a) $(x+2)^2+(y+4)^2=100$ (b) To graph: 1. Plot the center at $(-2, -4)$ on a coordinate plane. 2. Plot 4 key points: 10 units right $(-2+10, -4)=(8, -4)$, 10 …
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the parabola opens to the right. the focus is given as f(p, 0) and dire…
\(4px\)
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given a circle with center (0, 0) and radius 2.2, (a) write an equation…
(a) $x^2 + y^2 = 4.84$ (b) To graph: 1. Plot the center at the origin $(0,0)$. 2. Plot four key points: $(2.2, 0)$, $(-2.2, 0)$, $(0, 2.2)$, $(0, -2.2)$. 3. Draw a smooth, closed …
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the perimeter. simplify your answer. 4y+4 4y+4 8y+5
\(16y + 13\)
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can 650 be evenly divided by 6? circle: 650 is not evenly divisible by …
650 is NOT evenly divisible by 6
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find the area of the figure below by first finding the areas of the rec…
Area of the rectangle: \( 24 \) square units Area of the triangle on the top: \( 6 \) square units Area of the triangle on the bottom: \( 6 \) square units Area of the figure: \( …
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are the triangles similar? options: no, yes, cannot be determined
No
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part 1 of 2 two fire - lookout stations are 260 miles apart, with stati…
164.6
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which statements describe a parabola? check all that apply. a parabola …
A. A parabola is the set of all points equidistant from the directrix and focus. C. The focus is a fixed point inside the parabola. D. The line of symmetry intersects the focus an…
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triangle f is a scaled copy of triangle e. triangle e triangle f what i…
\(138\)
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abcd is a trapezoid. if ac = 5x - 7 and bd = 2x + 8, find the value of …
15
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quadrilateral u is a scaled copy of quadrilateral t. quadrilateral t ha…
\( 115 \)
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part 6 of 6 reject ( x approx -11.5 ) because the measure of a side mus…
The width of the rectangle is given by \( x \approx \boldsymbol{3.5} \) yd. The length of the rectangle is given by \( x + 8 \approx \boldsymbol{11.5} \) yd. (Note: The specific v…
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solve for ( x ) and graph the solution on the number line below. ( 3x -…
Inequality Notation: \( x < -6 \) or \( x \geq -3 \) For the number line: - For \( x < -6 \), draw an open circle at -6 and shade to the left. - For \( x \geq -3 \), draw a closed…
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triangle o is a scaled copy of triangle n. what is the value of m?
\(68.2\)
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can 345 be evenly divided by 5? circle: 345 is evenly divisible by 5 34…
345 is evenly divisible by 5
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investigating the role of the focus and directrix the graph shows a par…
\( \text{PF} = \text{PQ} \) (Option: \( \text{PF} = \text{PQ} \))
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which items have parallel lines? circle the items that have lines that …
The items with parallel lines are: the two horizontal arrows, the two slanted straight lines, the vertical straight lines, and the three slanted straight lines. (Visually, you wou…
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pentagon e is a scaled copy of pentagon d. pentagon d has sides 10, 7.6…
0.75
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quadrilateral m is a scaled copy of quadrilateral l. quadrilateral l ha…
\( \boxed{55} \)
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a rectangular garden covers 40 yd². the length is 8 yd longer than the …
\( x + 8 \)
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write the coordinates of the vertices after a dilation with a scale fac…
\( A'(-3, -3) \), \( B'(1, -3) \), \( C'(1, 2) \), \( D'(-3, 2) \)
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polygon q is a scaled copy of polygon p. what scale factor takes polygo…
\(\frac{1}{2}\)
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find the perimeter. simplify your answer. (there is a right triangle wi…
\( a + 7 \)
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quadrilateral r is a scaled copy of quadrilateral q. what scale factor …
0.75 (or $\frac{3}{4}$)
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7. consider the triangle shown. for each angle measure given, determine…
a. Yes: Copy the $36^\circ$ angle twice, adjacent to one another, to form $72^\circ$. b. Yes: Copy the $36^\circ$ and $52^\circ$ angles adjacent to one another to form $88^\circ$.…
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6. a box is in the shape of a square prism. the height of the box is 10…
138 square inches --- For question 8, the cone's dimensions (radius/height) are missing. Please provide the full details of the cone to solve for its volume.
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5. refer to the diagram shown. determine the values of t and u. show or…
For Question 5: $t = 3^\circ$, $u = 28^\circ$ For Question 6: $a = 3^\circ$, $b = 38^\circ$
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part b indicate whether each point is a reflection of ( p(3, 4) ) acros…
To solve this, we use the rules for reflecting a point \((x, y)\) across the axes: - Reflection across the \(y\)-axis: \((-x, y)\) - Reflection across the \(x\)-axis: \((x, -y)\) …
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complete the tables in part a and part b. part a indicate whether each …
### Part A Explanation (for each point, we use the rule of quadrants: Quadrant I: (+, +); Quadrant II: (-, +); Quadrant III: (-, -); Quadrant IV: (+, -); points on axes are "None"…
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4. ray o is perpendicular to line p in the diagram shown. determine the…
$x = 20^\circ$
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use the image to answer the question. mike draws a triangle and dilates…
75
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6. mai says that angles a and b are vertical angles and complementary a…
Tyler is correct. Mai is wrong because angles $a$ and $b$ are complementary (they form a $90^\circ$ angle) not vertical angles. Tyler is correct because angles $c$ and $d$ are bot…
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similar figures and area quick check determine how dilation affects the…
The area decreases more rapidly than the lengths of the sides decrease.
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similar figures and area quick check kierra draws a triangle with a bas…
27 cm²
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similar figures and area quick check use the image to answer the questi…
A. \( 2\frac{1}{4} \)
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use the image to answer the question a triangle has a base of 8 cm and …
The original triangle has an area of $12 \, cm^2$ and the dilated triangle has an area of $108 \, cm^2$; therefore, the dilated triangle has an area 9 times the size of the origin…
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solve for x and graph the solution on the number line below. -12 < 3x -…
Inequality Notation: \( -2 < x \leq 1 \) For the number line: Plot an open circle at -2 (since \( x > -2 \), not including -2) and a closed circle at 1 (since \( x \leq 1 \), incl…
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5. line segments ad, be, and cf are all diameters of the circle. the me…
$\boldsymbol{20^\circ}$
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part 3 of 4 label the center and the radius r. (h, k) = (6, 2) and r = …
$(x-6)^2 + (y-2)^2 = 25$
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solve for x and graph the solution on the number line below. -x - 5 ≥ 1…
Inequality Notation: \(x \leq -6\) or \(x > 3\) For the number line: - For \(x \leq -6\), draw a closed circle at \(-6\) and shade to the left. - For \(x > 3\), draw an open circl…
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4. determine whether the statements about the relationships between the…
a. True b. False c. True d. True e. False f. False
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$\\overline{ts}$ is the midsegment of trapezoid $hjkl$. if $kl = 17$ an…
\( 13 \)
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3. select all the equations that represent a true relationship between …
A. $x = 25$ B. $w = 90$ C. $y = 65$
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ts is the midsegment of trapezoid hjkl. if lk = 19 and ts = 15, find hj…
\(HJ = 11\)
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given that $\\angle 1$ and $\\angle 2$ are supplementary, $\\angle 2$ a…
$\boldsymbol{\angle 1 \cong \angle 3}$ is proven using the transitive and subtraction properties of equality, along with definitions of supplementary and congruent angles.
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given: ∠1 and ∠2 are supplementary m∠1 = 53° prove: m∠2 = 127° steps re…
| Step | Steps | Reasons | |------|-------|---------| | 1 | $\angle 1$ and $\angle 2$ are supplementary | Given | | 2 | $m\angle 1 + m\angle 2 = 180^\circ$ | Definition of Supplem…