All Questions ⁺⁰237641 Questions

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Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

CInsbstnkng Aug 5, 2025

Aug 3, 2025

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The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XZ = 5$ and $YZ = 2,$ find $WX.$

CInsbstnkng Aug 3, 2025

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In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $AB = 2$, then find $AC.$

CInsbstnkng Aug 3, 2025

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Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

CInsbstnkng Aug 3, 2025

Aug 2, 2025

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Algebra

bqimath Aug 2, 2025

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A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle?

CInsbstnkng Aug 2, 2025

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Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

CInsbstnkng Aug 2, 2025

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Need help (it's really me!!!)

There is a group of five children, where two of the children are twins. In how many ways can I distribute $12$ identical pieces of candy to the children, if the twins must get an equal amount of candy?

CInsbstnkng Aug 2, 2025

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How many solutions are there to the equation
u + v + w + x + y + z = 6
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $8$ and $y$ is even?

CInsbstnkng Aug 2, 2025

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HELP!!! (From the real Clnsbstnkng)

In the complex plane, z, z2, z3, form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

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Clnsbstnkng Aug 2, 2025

Aug 1, 2025

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The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

CInsbstnkng Aug 1, 2025

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Find constants A and B such that
(2x + 11)/(x^2 - 6x + 5) = A/(x - 3) + B/(x + 4)
for all x such that x neq 7 and x neq 8

CInsbstnkng Aug 1, 2025

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If z is a complex number such that z + 1/z = 3, what is the value of z^2 + 1/z^2?

CInsbstnkng Aug 1, 2025

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Let z1 and z2 be two complex numbers such that |z1| = 5 and (z1/z2)+(z2/z1)=0.
Find z1+z2.

CInsbstnkng Aug 1, 2025

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Counting & Probability

George is planning a dinner party for three other couples, his wife, and himself. He plans to seat the four couples around a circular table for , and wants each husband to be seated opposite his wife. How many seating arrangements can he make, read more ..

bqimath Aug 1, 2025

Jul 31, 2025

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An ellipse has its foci at (-1, -1) and (-1, -3).
Given that it passes through the point (0, 2), its equation can be written in the form ((x-h)2/a2)/((y-k)2/b2)=1 where a, b, h, k are constants, and a and b are positive. Find a+k.

CInsbstnkng Jul 31, 2025

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Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $BY = 2$ and $AZ = 4$, then what is the area of rectangle $WXYZ$?

CInsbstnkng Jul 31, 2025

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In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 2$, $BY = 16$, $\angle ACB = 90^\circ$, and $CY = 2 \cdot CX$, then find $AB$.

CInsbstnkng Jul 31, 2025

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A sphere of radius 4 inches is inscribed in a cone with a base of radius 4 inches. In inches, what is the height of the cone? Express your answer as a decimal to the nearest tenth

CInsbstnkng Jul 31, 2025

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In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

CInsbstnkng Jul 31, 2025

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Suppose a does not equal 0. Compute log base 8a (4^b) in terms of a and b.

CInsbstnkng Jul 31, 2025

Jul 30, 2025

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The ellipse shown below is defined by the equation PF1+PF2=d.
Find d.

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Clnsbstnkng Jul 30, 2025

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Rectangle ADEH is divided into rectangles ABGH, BCFG, and CDEF. If $AC = 15,$ $GE = 15,$ $[ABGH] = 8,$ and $[CDEF] = 8,$ find $[BCFG].$

CInsbstnkng Jul 30, 2025

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In the diagram, XY = 2\cdot AX = 2\cdot YB and $\dfrac{AZ}{BX} = \dfrac{2}{5}$. Find $\dfrac{[YBC]}{[ZYC]}$.

CInsbstnkng Jul 30, 2025

Jul 29, 2025

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