image imagewidth (px) 139 1.6k | problem stringlengths 13 430 | answer stringclasses 383
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|---|---|---|
<image>Find $y$ and so that each quadrilateral is a parallelogram.
Choose the correct answer from the following options:
A. -12
B. \[x = 0\]
C. \frac{4}{3}
D. \frac { 4 } { 3 }
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>In $\triangle A B C, \overline{B D}$ is a median. If $A D=3 x+5$ and $C D=5 x-1$, find AC . | 28 | |
<image>Find y
Choose the correct answer from the following options:
A. 36.74
B. 38.33
C. 38.2
D. 32.6
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Find the area of the figure. Round to the nearest tenth if necessary.
Choose the correct answer from the following options:
A. 78 m^2.
B. the following dimensions:
C. area of the figure is 96 square meters
D. 261
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, et... | D | |
<image>Find $m \angle B$. | 30 | |
<image>Find $m \angle 2$.
Choose the correct answer from the following options:
A. 8°
B. 52
C. 120^\circ
D. 60^\circ
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | B | |
<image>The triangle is inscribed into the circle. Find the exact circumference of the circle. | 17 \pi | |
<image>Find the area of the triangle. Round to the nearest tenth if necessary.
Choose the correct answer from the following options:
A. 293.8
B. 126.5
C. area of the triangle is 425 square millimeters
D. 137.5
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Use parallelogram MNPR to find $m \angle MQN$ | 97 | |
<image>Find x. | 20 \sqrt { 2 } | |
<image>If $a=4,$ find $b$ | 4 \sqrt { 3 } | |
<image>In the figure, $m ∠1 = 53$. Find the measure of $∠6$. | 53 | |
<image>Find the area of the quadrilateral. | 240 | |
<image>Find $JK$. | 14 | |
<image>Find $AB$. | 29 | |
<image>Find x. Assume that segments that appear to be tangent are tangent. | 145 | |
<image>Find $x$. | 2 | |
<image>Find $z$.
Choose the correct answer from the following options:
A. 20
B. length of side $z$ is \(6\sqrt{8
C. \sqrt{306}
D. length of side $z$ is approximately 17
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>$\overline{PM}$ is a diameter of $\odot R$. Find $m \widehat {MQ}$.
Choose the correct answer from the following options:
A. 230
B. 45^\circ
C. 65
D. it passes through the center R of the circle
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>Find y. | 30 | |
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.
Choose the correct answer from the following options:
A. 418
B. 1448.0
C. area of the parallelogram is 968 square feet
D. in this case:
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, et... | B | |
<image>Assume that the segment is tangent, find the value of $x$. | 3 | |
<image>Express the ratio of $ \cos C $ as a decimal to the nearest hundredth. | 0.80 | |
<image>Find the area of the triangle. Round to the nearest hundredth. | 6.79 | |
<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. | 38.4 | |
<image>Find x. | 6 | |
<image>If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PQ | 6 | |
<image>Find y
Choose the correct answer from the following options:
A. \frac{19\sqrt{3}}{3}
B. \frac{19 \sqrt{2}}{2}
C. value of \( y \) is \( \frac{19\sqrt{2}}{2} \)
D. \frac { 19 \sqrt { 2 } } { 2 }
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Find $x$ so that the quadrilateral is a parallelogram. | 8 | |
<image>Find the area of the shaded region. Round to the nearest tenth.
Choose the correct answer from the following options:
A. 14.6
B. 18.2
C. 7.9
D. \frac{13}{4} \times \pi \]
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>If $ABCDE \sim PQRST,$ find the perimeter of $PQRST$.
Choose the correct answer from the following options:
A. Not determined
B. perimeter of pentagon PQRST is 17 units
C. \frac{P_{ABCD}}{1} \times \left( \frac{8}{3} + 1 + \frac{6}{5} + 1 \right)
D. 22.5
Think and explain why do you choose it, then provide you... | D | |
<image>Find the value of the variable $x$ in the figure. | 70 | |
<image>Each triangle in the figure is a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle. Find $x$.
Choose the correct answer from the following options:
A. \frac { 3 } { 2 }
B. value of $x$ is $3\sqrt{2}$
C. $x = \frac{3\sqrt{2}}{2}$
D. \[x = 3\]
Think and explain why do you choose it, then provide your final answer as \... | A | |
<image>Find $m\angle L$ | 52 | |
<image>The segment is tangent to the circle. Find $x$. | 20 | |
<image>Find the area of the triangle. Round to the nearest tenth if necessary.
Choose the correct answer from the following options:
A. The area of the triangle is 60 square inches
B. 60
C. we can plug these values into the formula:
D. 20
Think and explain why do you choose it, then provide your final answer as \boxe... | D | |
<image>Find the area of the parallelogram.
Choose the correct answer from the following options:
A. 396
B. area of the parallelogram is approximately 269
C. 648 \text{ mm}^2
D. 792 \text{ mm}^2 \]
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Find $x$ in parallelogram $ABCD$.
Choose the correct answer from the following options:
A. $x = 9$
B. - \(AB = 15\) (horizontal)
C. \(AD = BC = 9\) and \(AB = CD = 15\)
D. 7.2
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>If QRST is a parallelogram, Find $z$ | 11 | |
<image>Refer to the figure at the right. Find the value of $m ∠ ABD $ if $ p \parallel q $. | 75 | |
<image>Find $KL$. | 24 | |
<image>In $\odot D, \overline{D E} \cong \overline{E C}, m \widehat{C F}=60,$ and
$\overline{D E} \perp \overline{E C} .$ Find $m \angle 5$ | 30 | |
<image>For trapezoid $D E G H, X$ and $Y$ are midpoints of the legs. Find $D E$ | 8 | |
<image>Point $S$ is the incenter of $\triangle JPL$. Find $m \angle MPQ$.
Choose the correct answer from the following options:
A. 56
B. 73.75^\circ
C. 52.5^\circ
D. 21^\circ
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Find x.
Choose the correct answer from the following options:
A. length of side \( x \) is \( 20 \)
B. 40
C. 10\sqrt{3}
D. value of x is 10√5
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | B | |
<image>Find $m \angle 8$.
Choose the correct answer from the following options:
A. ∠8 = 180° - 57° = 123°
B. 28.5
C. - \( \angle V = 67^\circ \)
D. 132
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | B | |
<image>Find the height of the parallelogram given its area with 100 square units. | 5 | |
<image>Find y | 16 | |
<image>The height of a triangle is 5 centimeters more than its base. The area of the triangle is 52 square centimeters. Find the height. | 13 | |
<image>Find the diameter of circle M.
Choose the correct answer from the following options:
A. 24.04
B. 34
C. diameter is (17 + 17 + 10
D. 38.0
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Find $RT$. | 8 | |
<image>Find $x$. | 20 | |
<image>$\overline{E C}$ and $\overline{A B}$ are diameters of $\odot O$. Find its measure of $\widehat{A C B}$. | 180 | |
<image>Use parallelogram $JKLM$ to find $m \angle JML$. | 80 | |
<image>Find $m\angle C$ | 127 | |
<image>If QRST is a kite, find $m\angle RST$.
Choose the correct answer from the following options:
A. 97.33^\circ
B. $\angle RTS$ is half of $\angle RST$
C. 78
D. angle QSR is the supplementary angle to angle QTS
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>In $\odot P, m \widehat{E N}=66$ and $m \angle G P M=89$ .
Find $m \angle G M E$
Choose the correct answer from the following options:
A. 66
B. 81
C. 57
D. 58^\circ
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>Find $x$ if $AC=x-3$, $BE=20, AB=16,$ and $CD=x+5$ | 35 | |
<image>Find $ED$ if $AE=3, AB=2$, $BC=6,$ and $ED=2x-3$ | 9 | |
<image>Use a Pythagorean Triple to find x. | 34 | |
<image>Find $x$. | 5 | |
<image>Find EC
Choose the correct answer from the following options:
A. x + 2
B. the value of x, we can find CE:
C. -29
D. 4.8
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Find $m \angle R$. | 32 | |
<image>Find x. | 4 \sqrt { 2 } | |
<image>Find x
Choose the correct answer from the following options:
A. 30
B. 72
C. 18
D. value of x is 36 degrees
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Find the area of the figure. Round to the nearest tenth if necessary.
Choose the correct answer from the following options:
A. 255
B. 280
C. 340
D. 240
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>Find the perimeter of the triangle.
Choose the correct answer from the following options:
A. 71.7
B. perimeter of the triangle is 48 cm
C. 877\]
D. perimeter of the triangle is approximately 33
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Find the value of $x$ in the diagram.
Choose the correct answer from the following options:
A. value of \(x\) is approximately 3
B. \frac{180}{17}
C. \frac{41}{11}
D. 13
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>$\overline{AD}$ and $\overline{CG}$ are diameters of $\odot B$. Find $m \widehat {CGD}$.
Choose the correct answer from the following options:
A. it is $180^\circ$
B. 305
C. 145^\circ
D. 220^\circ
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | B | |
<image>Lines $l$, $m$, and $n$ are perpendicular bisectors of $\triangle PQR$ and meet at $T$. If $TQ = 2x$, $PT = 3y - 1$, and $TR = 8$, find $y$. | 3 | |
<image>Find x
Choose the correct answer from the following options:
A. we have:
B. 44.43^\circ
C. 44.9
D. 42.61^\circ
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | C | |
<image>Find the measure of $\angle 7$ if $\overline{A B} \perp \overline{B C}$. | 140 | |
<image>Find the area of the figure. Round to the nearest tenth if necessary.
Choose the correct answer from the following options:
A. 47.5
B. 53.4
C. 49.7
D. 79.8
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | B | |
<image>In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\angle 6$. | 38 | |
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.
Choose the correct answer from the following options:
A. area of the parallelogram is 357 square feet
B. 315
C. \[ A = 21 \, \text{ft} \times 17 \, \text{ft} \]
D. 357 \, \text{square feet}
Think and explain why do you choose it, then... | B | |
<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear
to be tangent are tangent. | 6 | |
<image>Find y. | 3 | |
<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. | 46 | |
<image>Find x. | 15 | |
<image>Find $x$. | 50 | |
<image>If $R T=16, Q P=24,$ and $S T=9,$ find $P S$ | 13.5 | |
<image>Find $CP$. | 8 | |
<image>Circle $O$ has a radius of $10, A B=10$ and $m \overrightarrow{A B}=60 .$ Find $m\widehat{A Y}$ | 30 | |
<image>Let $\overline{J K}$ be the median of $A B T Q .$ Find $J K$
Choose the correct answer from the following options:
A. length of the median $\overline{JK}$ is 70
B. 78
C. 43
D. 114
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | B | |
<image>Find the perimeter of each polygon for the given information.
$B Y=C Z=A X=2.5$
diameter of $\odot G=5$ | 15 \sqrt { 3 } | |
<image>In the figure, $a ∥ b, c ∥ d$, and $m∠4 = 57$. Find the measure of $\angle 1$. | 123 | |
<image>Find y | 30 | |
<image>Find $m \angle T$. | 55 | |
<image>Find $m\angle B$ | 120 | |
<image>Find $m \angle 3$. | 51 | |
<image>Find x. | 7 \sqrt { 2 } | |
<image>Each pair of polygons is similar. Find y
Choose the correct answer from the following options:
A. 48.45
B. 65
C. \frac{21(y + 3)}{29}
D. value of y is 32
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | A | |
<image>Find $CD$ if $AB=6, AF=8, BC=x, CD=y$, $DE=2y-3,$ and $FE=x+\frac{10}{3}$ | 9 | |
<image>Find the measure of $ \angle 1$ in the figure. | 80 | |
<image>Find $x$ so that the quadrilateral is a parallelogram | 3 | |
<image>What is the area of the shaded region if $r=4$.
Choose the correct answer from the following options:
A. 4\pi
B. 12\pi
C. 0
D. 64 - 16 \pi
Think and explain why do you choose it, then provide your final answer as \boxed{A}, \boxed{B}, etc. | D | |
<image>Rhombus $RSTU$ has an area of 675 square meters. Find $SU$. | 45 | |
<image>Use parallelogram $JKLM$ to find JK | 6 | |
<image>Find x in the figure. | 16 | |
<image>$\overline{QS}$ is a diameter of $\odot V$. Find $m \widehat {STP}$. | 147 |
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