Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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question 4 of 10 what is cos 45°? a. $\frac{1}{2}$ b. $sqrt{2}$ c. $\fr…
C. $\frac{1}{\sqrt{2}}$
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the perimeter of a geometric figure is the sum of the lengths of its si…
a. A. $x + x+x + 2x+2x=14$ b. 2 c. The shorter sides have a length of 2 centimeters. The longer sides have a length of 4 centimeters.
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question 3 of 10 what is tan 60°? 1 60° 2 90° 30° √3 a. 1/2 b. 2/√3 c. …
E. $\sqrt{3}$
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according to this diagram, what is sin 16°? a. $\frac{24}{7}$ b. $\frac…
E. $\frac{7}{25}$
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let (3, - 4) be a point on the terminal side of θ. find the exact value…
$\cos\theta=\frac{3}{5}$ $\csc\theta=-\frac{5}{4}$ $\tan\theta=-\frac{4}{3}$
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6. higher order thinking talia is packing a moving box. she has a squar…
Yes, the poster will lie flat in the box because the side - length of the square - framed poster ($3$ feet) is less than the side - length of the cube - shaped box (approximately …
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question 1 of 10 what is cos 30°? 60° 2 1 90° 30° √3 a. $\frac{1}{sqrt{…
B. $\frac{\sqrt{3}}{2}$
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talia is packing a moving box. she has a poster with an area of 9 squar…
Yes, the poster will lie flat in the box because the area of one face of the cube - shaped box (approximately 9.65 square feet) is greater than the area of the poster (9 square fe…
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what is the length of leg s of the triangle below? a. $sqrt{6}$ b. $sqr…
F. 6
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in each sentence, one of the nouns in boldface should be plural. circle…
2. borders 3. islands 4. No error 5. communities 6. months 7. patches 8. grasses 9. mosses 10. bushes 11. valleys 12. berries 13. mines 14. companies 15. explorers
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a 12 foot ladder is leaning against a building. the ladder makes a 45 d…
A. $6\sqrt{2}$ feet
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which is a true statement about a 45 - 45 - 90 triangle? a. the hypoten…
B. The hypotenuse is $\sqrt{2}$ times as long as either leg.
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a certain triangle has two 45° angles. what type of triangle is it? a. …
A. Right isosceles
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what is the length of the hypotenuse of the triangle below? a. 10 b. 10…
A. 10
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what is the length of leg s of the triangle below? 45° 8√2 s 90° 45° a.…
C. 8
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what is the length of the hypotenuse of the triangle below? 45° 3√2 h 9…
C. 6
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what is the length of side s of the square shown below? a. 1 b. 4 c. 2 …
F. $\sqrt{2}$
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what is the length of each leg of the triangle below? 45° 22 90° 45° a.…
F. $11\sqrt{2}$
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solve the inequality. graph the solution set and write it in interval n…
The correct graph is A (open - circle at - 2 and arrow to the left). The solution in interval notation is $(-\infty,-2)$
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an isosceles right triangle is always a 45-45-90 triangle. a. true b. f…
A. True
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the base of a triangle is b units long, and the height of the triangle …
$\frac{1}{2}bh$
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based only on the information given in the diagram, it is guaranteed th…
A. True
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ryan places a mirror on the ground 42 feet from the base of a tree. he …
B. 36 feet
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what is the value of m in the figure below? in this diagram, △abd ~ △bc…
A. $\sqrt{126}$
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what is the value of h in the figure below? in this diagram, △bad ~ △cb…
E. 8
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what is the length of $overline{cd}$? in this diagram, $\triangle abcsi…
B. 5
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based only on the information given in the diagram, it is guaranteed th…
A. True
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in right triangle δqrs, m∠s = 73°. in right triangle δtuv, m∠v = 73°. w…
B. AA
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scale: 1 inch : 3 feet 15 inches actual height of the tree =
# Explicación: ## Paso 1: Identificar la proporción de escala La proporción es 1 pulgada : 3 pies. ## Paso 2: Multiplicar la altura en la representación por la proporción Tenemos …
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based only on the information given in the diagram, it is guaranteed th…
B. False
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use the graph below to enter a single translation rule. complete the ru…
\((x,y)\to(x + 4,y)\)
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in △ghi, (overline{gh}paralleloverline{jk}). given that (ig = 16), (ij …
$15$
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angle parking spaces are at a ______-degree angle. 45 30 90 10
45
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draw in the complex plane the set {z ∈ c: im(1/z)=1/4}
Describe the set as a circle in the complex - plane. Let \(z=x + iy\), then \(\frac{1}{z}=\frac{1}{x + iy}=\frac{x-iy}{x^{2}+y^{2}}\). The imaginary part of \(\frac{1}{z}\) is \(-…
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5. in the diagram shown, mo bisects ∠nmp. if m∠nmp = 74° and m∠nmo = 4(…
$x = 7.25$
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et {z ∈ ℂ: im $\frac{1}{z}=\frac{1}{4}$}
A circle in the complex - plane. Let \(z=x + iy\), then \(\frac{1}{z}=\frac{1}{x + iy}=\frac{x-iy}{x^{2}+y^{2}}\). The imaginary part of \(\frac{1}{z}\) is \(-\frac{y}{x^{2}+y^{2}…
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find the area of the square in the figure. the area is (simplify your a…
242 square units
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3.2 practice with ca in exercises 1 - 4, find (mangle1) and (mangle2). …
Exercise 1: \(m\angle1 = 117^{\circ}\), \(m\angle2 = 63^{\circ}\) Exercise 3: \(m\angle1 = 122^{\circ}\), \(m\angle2 = 58^{\circ}\) Exercise 5: \(x = 64\)
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match the graph with the correct equation. xmin = - 10, xmax = 10, xscl…
$(x - 6)^2+(y - 1)^2=1$
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question 24, 2.4.45 match the graph with the correct equation. xmin = -…
$(x - 1)^2+(y + 2)^2=4$
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question 1 click on the blue link below to view the problem. then answe…
# Explicación paso a paso: ## Paso 1: Definir factor de escala El factor de escala es el cociente entre una medida de triángulo B y la medida correspondiente de triángulo A. Sin e…
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the perimeter of a rectangle is to be no greater than 100 centimeters a…
45
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structure in exercises 13 - 16, classify the angle pair as correspondin…
13. Corresponding angles 14. Consecutive interior angles 15. Alternate interior angles 16. Alternate exterior angles
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5) reflection across y = x
$S'(-3,1)$ $T'(1,3)$ $U'(-3,3)$
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find the standard form of the equation of the circle with center (6, - …
$(x - 6)^2+(y + 5)^2=81$
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find the standard form of the equation of the circle with endpoints of …
$(x - 1)^2+(y - 7)^2=65$
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question 5 of 10 the four subjects of the quadrivium? arithmetic, geome…
numbers
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two sides of a triangle are 25 and 25. find the range of possible side …
\(0<x<50\)
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two sides of a triangle are 14 and 15.8. find the range of possible sid…
\(1.8 < x < 29.8\)
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question two sides of a triangle are 12.5 and 17.8. find the range of p…
$5.3<x<30.3$
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two sides of a triangle are 10 and 17. find the range of possible side …
\(7<x<27\)
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question do the three lengths form a triangle? type yes or no. you only…
NO
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classify each figure as a line, ray, or line - segment. then, show how …
(a) line segment, \(\overline{PQ}\) (b) ray, \(\overrightarrow{TU}\) (c) ray, \(\overrightarrow{RS}\)
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stalled on railroad tracks if your vehicle stalls on the railroad track…
1. B. Seeing, thinking, and responding while driving 2. B. Four times greater
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the triangles are congruent by sss. which transformation(s) can be used…
reflection only, rotation, then translation
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point h is the midpoint of side fk. for the triangles to be congruent b…
\(x = 6\), so the answer is C. 6
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5. determine a series of transformations that would map figure u onto f…
5. Translation right 8 units, reflection over the x - axis 6. Translation down 10 units, 180° rotation (clockwise or counter - clockwise)
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examine this figure. which two pieces of information, if true, would he…
B. Line MK is the perpendicular bisector of \(\overline{LN}\), D. \(\overline{ML}\cong\overline{MN}\)
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the triangles are congruent by sss or hl. the diagram shows the sequenc…
rotation, then reflection, then translation
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math 8 term 1 homework #3 1. which transformation would take shape a to…
1. A. A reflection over the y - axis 2. C. A reflection over the y - axis 3. B. A rotation 180° clockwise about the origin 4. D. A translation 1 unit down
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which explains whether △fgh is congruent to △fjh? they are congruent be…
They are not congruent because only two pairs of corresponding sides are congruent.
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in the figure below, s is the center of the circle. suppose that lk = 2…
$x = 4$ $PS = 9.5$
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the triangles are congruent by sss and hl. which transformation(s) can …
reflection, then translation
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the triangles shown are congruent by the sss congruence theorem. the di…
rotation, then reflection, then translation
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rs of angles of the given type. (see example 3.) 10. alternate interior…
10. Alternate - interior angle pairs: $\angle3$ and $\angle6$, $\angle4$ and $\angle5$ 12. Consecutive - interior angle pairs: $\angle3$ and $\angle5$, $\angle4$ and $\angle6$
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the two triangles below are similar. also, m∠r = 15° and m∠t = 105° as …
$m\angle D = 15^{\circ}$ $m\angle E = 105^{\circ}$ $m\angle F = 60^{\circ}$
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graph the inequality on a number line. then write the solution in inter…
The correct graph is the one with an open circle at $\frac{1}{7}$ and an arrow pointing to the left. In interval notation, the solution is $(-\infty,\frac{1}{7})$.
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quadrilateral opqr is dilated by a scale factor of $\frac{3}{4}$ to for…
6
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quadrilateral ijkl is dilated by a scale factor of $\frac{3}{4}$ to for…
$26.8$
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which letter in the word happy has an order 2 rotational symmetry? o h …
A. H
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quadrilateral jklm is dilated by a scale factor of $\frac{3}{4}$ to for…
32
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which angle of rotation is an angle of rotational symmetry for all figu…
D. 360°
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check your understanding 1. in the triangle shown, pq = 5.6, pr = 6.1, …
### 1. # Explicación: ## Paso 1: Aplicar la relación lado - ángulo En un triángulo, el ángulo más pequeño está enfrente del lado más corto y el ángulo más grande está enfrente del…
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which type of triangle will always have at least 1 - fold reflectional …
isosceles triangle
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6. a triangle with vertices p(1, 4), q(3, -2), r(-2, 1) is reflected ac…
a. P''(-1,-4), Q''(-3,2), R''(2,-1) b. A 180 - degree rotation about the origin.
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if the smallest angle of rotation for a regular polygon is 18°, how man…
C. 20
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how can a regular hexagon be folded to show that it has reflectional sy…
Fold the hexagon along a line that bisects two vertex angles.
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(see example 2.) 6. name a pair of perpendicular lines. 8. is $overline…
8. Yes, $\overline{PR}\perp\overline{NP}$ because they intersect at a 90 - degree angle. 10. $\angle3$ and $\angle6$, $\angle4$ and $\angle5$ 12. $\angle3$ and $\angle5$, $\angle4…
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which statements are true about the lines of symmetry of a regular pent…
C. Every line bisects a vertex angle. D. Every line bisects a side. E. Every line is perpendicular to a side.
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a rock climber is using a pulley to lower supplies 20\\frac{3}{4} meter…
1. The words to circle are "change in elevation per minute". 2. The change in elevation should be represented with a negative number. Since the supplies are being lowered (going d…
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if a quadrilateral has exactly 2 lines of symmetry, and both are angle …
The figure could be a rhombus because the 2 lines of symmetry bisect the angles.
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for the equation x² + y² - 8x - 4y - 16 = 0, do the following. (a) find…
A. $(4 + 4\sqrt{2},0),(4 - 4\sqrt{2},0),(0,2 + 2\sqrt{5}),(0,2 - 2\sqrt{5})$
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graph the set of numbers given in interval - notation. then write the i…
The graph with an open circle at $-6$ and an arrow pointing to the left is the correct one. The inequality statement is $x < - 6$.
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for the equation $x^{2}+y^{2}-8x - 4y-16 = 0$, do the following. (a) fi…
(a) $(4,2)$ (b) To graph the circle, plot the center $(4,2)$ and then use the radius $r = 6$ to draw the circle around the center. (c) **x - intercepts**: Set $y = 0$ in the equat…
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which polygon will always have 4 - fold reflectional symmetry and order…
D. square
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(see example 2.) 6. name a pair of perpendicular lines. 8. is $overleft…
6. $\overleftrightarrow{NP}$ and $\overleftrightarrow{PR}$ 8. Yes, because there is a right - angle symbol at their intersection. 10. $\angle3$ and $\angle6$, $\angle4$ and $\angl…
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what is the smallest angle of rotational symmetry for the regular octag…
$45$
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a circle has the equation 3(x - 3)^2 + 3y^2 = 3. (a) find the center (h…
(a) Center: $(3,0)$; Radius: $1$ (b) Cannot be shown in this text - based format. Use a graphing utility (e.g., Desmos, Geogebra) to graph the circle with center $(3,0)$ and radiu…
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the right triangle on the right is a scaled copy of the right triangle …
$\frac{15}{16}$
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a circle has the equation 3(x - 3)^2+3y^2 = 3. (a) find the center (h,k…
(a) The center of the circle is $(3,0)$ The radius of the circle is $1$ (b) To graph the circle: Plot the center $(3,0)$. Then, from the center, move 1 unit up, 1 unit down, 1 uni…
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whether the activity is not allowed. circle or highlight the appropriat…
| Activity | Business | Tourism | Not Allowed | |--|--|--|--| | Consult with business associates | Allowed (implied by classification) | Not applicable | Not applicable | | Medica…
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a circle has the equation 3(x - 3)^2+3y^2 = 3. (a) find the center (h,k…
(a) $(3,0)$ (b) To graph the circle: Plot the center $(3,0)$. Then, from the center, move 1 unit up, down, left, and right to get points on the circle and draw a smooth curve pass…
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a circle has the equation x² + y² = 121. (a) find the center (h,k) and …
A. The intercept(s) is/are $(-11,0),(11,0),(0, - 11),(0,11)$
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word study: synonyms and antonyms each group of words contains two word…
1. A. enduring, ephemeral; A 2. S. altercation, quarrel; S 3. S. endow, grant; S 4. A. chary, reckless; A 5. No pair; N/A 6. No pair; N/A 7. A. alien, indigenous; A
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a circle has the equation x² + y² = 121. (a) find the center (h,k) and …
(a) $(0,0)$ (b) To graph the circle: Plot the center at the origin $(0,0)$. Then, using a compass with a radius of $11$ units, draw a circle around the center. (c) x - intercepts:…
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one triangle has side lengths 19, 13, and 17. (a) compute the sum of th…
(a) Compute the sum of the squares of the shorter lengths: $458$ Compute the square of the longest length: $361$ What kind of triangle is it? Acute triangle (b) Compute the sum of…
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1. that contain the segments in the figure and the figure. all angles a…
2. $\overrightarrow{BC}$, $\overrightarrow{AD}$, $\overrightarrow{FG}$, $\overrightarrow{EH}$ 4. Plane $ABF$ 6. $\overrightarrow{NP}$ and $\overrightarrow{PR}$ 8. Yes, because the…
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math menu: windowpane need 12 points total date: 3pts complete the foll…
a) 24 b) 16 c) 29 d) \(MH\), \(TA\)
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write the standard form of the equation and the general form of the equ…
$(x - 4)^2+(y + 2)^2=7$
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4pts: prove ∠wxz≅∠suv
\(\angle WXZ\cong\angle SUV\) (by the corresponding - angles postulate as \(WY\parallel TV\) and \(SZ\) is a transversal)