Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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10/1/28, 8:46 am wellington francis question 1 a two - column proof has…
2. Segment - Addition Postulate 3. Substitution Property of Equality 4. Subtraction Property of Equality
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what is the area of triangle dfg? round to the nearest whole square uni…
27 square units
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a circular observation window in the side of a tank is modeled on the c…
C. $28.27$ units$^{2}$
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find the cosine of ∠r. simplify your answer and write it as a proper fr…
$\frac{45}{53}$
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triangle abc is a right triangle and cos(22.6°)=\\frac{b}{13}. solve fo…
\(\tan(22^{\circ})=\frac{a}{12}\)
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15 an l - shaped tank has corners plotted at a(0,0), b(4,0), c(4,2), d(…
A. 16 units
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select all the pairs of supplementary angles. ∠lkn and ∠jki ∠mnk and ∠o…
∠LKN and ∠JKI, ∠MNK and ∠ONK, ∠MNK and ∠MNP, ∠JKI and ∠JKN
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when we describe a line, the first thing we notice is its steepness. ma…
1. Vertical change to horizontal change. 2. Positive if rises to the right, negative if falls to the right, zero if flat, undefined if vertical. 3. y - intercept. 4. When a point …
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what is m∠j to the nearest tenth? 3.4 15.1 o 31.9 o 38.5 o 52.5 58.1
$58.1$
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the diagonal of rectangle abcd measures 2 inches in length. what is the…
1 inch
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14 find the surface area of the tank if the height is 80\ and the diame…
A. $4423.36$ in$^{2}$
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find the value of x. round to the nearest tenth. 5 48° o 3.7 5.6 o 4.5 …
5.6
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which classification best represents a triangle with side lengths 10 in…
A. acute, because \(10^{2}+12^{2}>15^{2}\)
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14. if ef bisects cd, cg = 5x - 1, gd = 7x - 13, ef = 6x - 4, and gf = …
45
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find the measure of 4x. 135° 39° m 4x = □°
$24$
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a wire makes a 70° angle with the ground and is attached to the top of …
53 ft
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find the measure of 4x 135° 39° m∠4x = □°
\(384^{\circ}\)
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triangle abc is a sketch of a triangular flower bed that has an area of…
C. 40 feet
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solve the inequality and graph the solution. 8 < j + 6 plot the endpoin…
The solution of the inequality is $j>2$. On the number - line, we have an open - circle at $j = 2$ and an arrow pointing to the right.
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find the measure of ∠x. m∠x = □°
\(99\)
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in the figure below, m∠1 = 29° and m∠2 = 48°. find m∠pqr. m∠pqr = °
$77$
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which angles are vertical angles? ∠hig and ∠hil, ∠mln and ∠jil, ∠hig an…
$\angle MLN$ and $\angle JIL$
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the hypotenuse of a 45 - 45 - 90 triangle measures 22\\sqrt{2} units. w…
C. 22 units
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in the figure below, m∠jkm = 131° and m∠2 = 77°. find m∠1.
\(54\)
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what characteristic of two lines ensures that the intersection is exact…
The lines are distinct
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the hypotenuse of a 45 - 45 - 90 triangle measures 4 cm. what is the le…
$2\sqrt{2}$ cm (corresponding to the option $2\sqrt{2}$ cm which is likely the second option in the multiple - choice list you provided, though the formatting of the options in th…
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find the measure of ∠x. 134° 35° x m∠x = □°
\(396\)
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what defining characteristic of euclids postulates makes them the basis…
Postulates are "obvious" statements that are assumed to be true
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in the figure below, m∠1 = 89° and m∠2 = 67°. find m∠xwy. m∠xwy =
\(24\)
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given right triangle def, what is the value of tan(f)? options: - $\fra…
$\frac{40}{9}$
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what is the cosine ratio of ∠z? x 16 y 12 20 z 20/12 12/16 12/20 16/20
C. $\frac{12}{20}$
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which angles are consecutive interior angles? ∠edg and ∠fgd ∠edg and ∠h…
$\angle EDG$ and $\angle FGD$
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find the measure of ∠x. 134° 35° x m∠x = °
$396$
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how many noncollinear points are needed to define a plane?
3
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find the value of x. round to the nearest tenth 37° 12 x o 9.6 o 9 o 19…
D. 7.2
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the scale of a floor plan is 1 inch : 6 feet. if a hallway is 12 feet l…
2
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solve the inequality and graph the solution. -16 ≤ 16q plot the endpoin…
The solution of the inequality is q ≥ - 1. On the number - line, there is a closed - circle at - 1 (because the inequality includes equality) and the line extends to the right tow…
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what is m∠j to the nearest tenth? o 31.9 o 38.5 o 52.5 o 58.1
$58.1$
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which measures are accurate regarding triangle jkl? select two options.…
$k\approx3.2$ units, so the correct options are: - $k\approx3.2$ units (equivalent to $KL\approx3.2$ units) There is no other correct option among the given ones based on our calc…
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find the value of z. round to the nearest tenth triangle with right - a…
5.6
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directions circle the letter of the answer that correctly completes eac…
1. B. his ideas form the basis of modern economics 2. C. competition 3. D. invisible hand 4. A. governments 5. A. market 6. D. Market economy 7. B. consumers 8. C. incentive 9. B.…
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find the measure of ∠x. m∠x =
\(316\)
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find the value of x. round to the nearest tenth. triangle with a right …
A. $8.7$
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what is the minimum number of points needed to define a line?
2
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which equation correctly uses the law of cosines to solve for y? 9² = y…
$y^{2}=9^{2}+19^{2}-2(9)(19)\cos(41^{\circ})$ (the fourth option)
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find the measure of ∠x. 136° 37° x m∠x = °
$99$
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a wire makes a 20° angle with the ground and is attached to the top of …
$146$ ft
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what is the minimum number of planes needed for their intersection to b…
D. 2
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the lengths of two sides of a right triangle are 5 inches and 8 inches.…
3.2 inches
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a cylindrical fish tank has a radius of 6 inches and a height of 20 inc…
A. $\pi(6)^{2}(20)$
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solve the inequality and graph the solution. $\frac{n}{2} leq -3$ plot …
The solution of the inequality is $n\leq - 6$. On the number line, place a closed circle at - 6 and draw a ray to the left.
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which angles are consecutive interior angles? ∠mlo and ∠kuj ∠mlo and ∠p…
\(\angle MLO\) and \(\angle POL\)
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joey is building a frame for a sandbox. the sandbox is going to be a qu…
a quadrilateral, because angle C and angle X are not right - angles (so it's not a rectangle)
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solve the inequality and graph the solution. 1 > s - 5 plot the endpoin…
The solution of the inequality is $s < 6$. On the number - line, we use an open circle at 6 (because 6 is not included in the solution set) and draw an arrow to the left to repres…
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select all the pairs of alternate exterior angles. ∠lki and ∠mnp ∠lki a…
$\angle LKI$ and $\angle MNP$, $\angle LKI$ and $\angle ONK$, $\angle MNP$ and $\angle ONK$
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in right triangle xyz, the right angle is located at vertex y. the leng…
$39.4^{\circ}$
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solve the inequality and graph the solution. 3m ≤ -6 plot the endpoints…
The solution of the inequality is $m\leq - 2$. On the number - line, a closed circle is at - 2 and the ray extends to the left.
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which equation can be used to find the length of $overline{ac}$? image …
$(10)\sin(40^{\circ}) = AC$
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name: parallel lines practice date: 20) 75° 11x - 2 22) x + 139 132° 23…
Problem 20: $x = 7$ Problem 22: $x=-7$ Problem 23: $x = 9$ Problem 25: All real $x$ Problem 27: $x = 10$ Problem 28: $x=-9$
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solve the inequality and graph the solution. 3 > v + 6 plot the endpoin…
The solution of the inequality is $v < - 3$. On the number - line, we plot an open circle at $-3$ (because the inequality is strict, $v$ cannot equal $-3$) and draw a ray to the l…
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the law of cosines for △rst can be set up as (s^{2}=7^{2}+3^{2}-2(7)(3)…
D. $s = 5$ and $t = 3$ (assuming the sides of the triangle are named $r$, $s$, $t$ and the given equation is set up correctly with respect to the naming convention, and among the …
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f.7 graph solutions to one - step linear inequalities e2z solve the ine…
The solution of the inequality is $p<9$. On the number - line, we use an open - circle at 9 (since 9 is not included in the solution) and draw a ray to the left of 9.
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use the following graphs to answer questions #3 - 5 3. which graph(s), …
A, C, D
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select all the pairs of corresponding angles. you answered:
$\angle MLI$ and $\angle JIG$, $\angle HIG$ and $\angle KLI$, $\angle HIL$ and $\angle KLN$
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the distance formula helps calculate the distance between two points on…
1. coordinate 2. an ordered - pair 3. origin 4. Pythagorean 5. coordinates
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solve the inequality and graph the solution. 4q < 8 plot the endpoints.…
The solution of the inequality is $q < 2$. On the number - line, we plot an open circle at 2 (since the inequality is strict, $q$ cannot equal 2) and draw an arrow to the left to …
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select all the pairs of corresponding angles. you answered:
$\angle MLI$ and $\angle JIG$, $\angle HIG$ and $\angle KLI$, $\angle HIL$ and $\angle KLN$
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the equation $sec(25^{circ})=\frac{9}{c}$ can be used to find the lengt…
19.3 in
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solve the inequality and graph the solution. $\frac{s}{3}geq2$ plot the…
The solution of the inequality is $s\geq6$. On the number - line, we place a closed circle at 6 (since the inequality is $\geq$) and draw a ray to the right of 6 towards positive …
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if the length of the tank is 7, the width is 4, and the height is 5, wh…
The diagonal of the base is $\sqrt{65}\approx8.06$. The two angles are $\arctan(\frac{4}{7})$ and $\arctan(\frac{7}{4})$.
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10. use the diagram below to answer the following questions. a) name th…
a) The transversal connecting ∠1 and ∠5 is the top - horizontal line. b) The transversal connecting ∠7 and ∠14 is the right - vertical line. c) The transversal connecting ∠8 and ∠…
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the distance formula is derived from which mathematical theorem? a. bin…
1. b. Pythagorean Theorem 2. c. Ordered pair
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if the length of the aquarium is 36\, the width is 15\, and the volume …
D. 18"
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the angles are supplementary angles. determine the measures of ∠1 and ∠…
\(m\angle1 = 151^{\circ}\), \(m\angle2 = 29^{\circ}\)
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5 find the surface area of the tank 18\ 8\ a 64 in² b 146 in² c 736 in²…
C. $736$ in²
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what is the formula to calculate the distance between two points on a c…
1. C. $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ 2. B. $\sqrt{25}$
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the angles are supplementary angles. determine the measures of ∠1 and ∠…
\(m\angle1 = 134^{\circ}\), and \(m\angle2 = 46^{\circ}\)
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how was figure a transformed to become figure a\? 1. ? 2. reflect dilate
1. Reflect 2. None (as no dilation occurred)
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if a point is reflected across the x - axis, what happens to the y - co…
1. b. It becomes its opposite. 2. a. y - axis
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how was figure a transformed to become figure a? 1. dilate 2. ? transla…
Rotate
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the angles are supplementary angles. determine the measures of ∠1 and ∠…
$m\angle1 = 142^{\circ}$, and $m\angle2 = 38^{\circ}$
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how was figure a transformed to become figure a\? 1. dilate 2. ? reflec…
Reflect
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what is the distance between the points (3, 4) and (7, 1)? a. 5 b. 6 c.…
1. A. 5 2. A. 25
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solve the inequality and graph the solution. 2z < 10. plot the endpoint…
The solution of the inequality is $z < 5$. On the number line, place an open circle at 5 and draw an arrow to the left.
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how was figure a transformed to become figure a\? 1. ? 2. translate dil…
1. Dilate 2. N/A (no second - step transformation indicated in the problem context)
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how was figure a transformed to become figure a\? 1. dilate 2. ? rotate…
Translate
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solve the inequality and graph the solution. c - 6 > 3 plot the endpoin…
The solution of the inequality is $c>9$. On the number - line, there is an open circle at 9 and a ray extending to the right.
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the angles are supplementary angles. determine the measures of ∠1 and ∠…
\(m\angle1 = 118^{\circ}\), and \(m\angle2 = 62^{\circ}\)
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which sentence from the world on turtles back best illustrates why the …
The woman created a home for herself on this new earth and soon her daughter was born.
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how was figure a transformed to become figure a\? 1. ? 2. reflect dilate
1. Reflect 2. None (since no other transformation like dilation occurred)
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solve the inequality and graph the solution. b + 6 ≥ 10 plot the endpoi…
The solution of the inequality is $b\geq4$. On the number - line, place a closed circle at 4 and draw a ray to the right of 4.
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solve the inequality and graph the solution. 2y ≥ 4 plot the endpoints.…
The solution of the inequality is $y\geq2$. On the number - line, we have a closed circle at 2 and a ray extending to the right.
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the angles shown are complementary angles. determine the measures of ∠1…
$m\angle1 = 87^{\circ}$ $m\angle2 = 3^{\circ}$
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solve the inequality and graph the solution. s - 2 > 4 plot the endpoin…
The solution of the inequality is $s>6$. On the number - line, we use an open circle at 6 (since 6 is not included in the solution) and draw a ray to the right of 6.
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3. the length of a rectangle is $\frac{w + 3}{w^{2}+w - 12}$ and the wi…
$\frac{w + 3}{(w - 3)^{2}}$
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you are designing a top - down view of a rectangular fish tank. the cor…
A. 24 units²
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solve the inequality and graph the solution. q - 7 > 1 plot the endpoin…
The solution of the inequality is $q > 8$. On the number - line, place an open circle at 8 and draw a ray to the right of 8.
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use the image to answer the question. using the aas congruence theorem,…
\(\overline{BI}\cong\overline{CO}\)
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is △abc≅△dfe by aas theorem? (1 point) yes. the aas theorem is used no …
No. The ASA Theorem is used.
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what single rigid transformation maps △abc → △edc? (1 point) dilation t…
D. rotation