blackpanther

344 Questions
15 Answers

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Geometry

In the diagram below, D is a point on segment CE such that segments AD and BE are parellel and point A is not on segment BC. Line segments AD and BC intersect at point P.
If angle CAD = 67 degrees, then what is angle read more ..

blackpanther May 14, 2024

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Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

blackpanther May 14, 2024

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Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

blackpanther May 14, 2024

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Geometry

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

blackpanther May 14, 2024

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Algebra

Find t if the expansion of the product of 2x^3 + x^2 - 3x + 5 and x^4 - 7x^3 + tx^2 - 11x + 15 has no x^2 term.

blackpanther Apr 12, 2024

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Algebra

In class, we derived that
\frac{1}{n(n + 1)} = \frac{1}{n} - \frac{1}{n + 1}.
Fill in the blanks to make a true equation:
\frac{5x}{(x - 1)(x^2 + 2)(x + 7)^3)} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + 2} + \frac{D}{x + 7} read more ..

blackpanther Apr 12, 2024

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Algebra

Compute
\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10}

blackpanther Apr 11, 2024

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Algebra

Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is $4.$ The sum of the cubes of all the terms is $10.$ Find the common ratio.

blackpanther Apr 11, 2024

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help geometry

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.

blackpanther Mar 24, 2024

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Trapezoid

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

blackpanther Mar 24, 2024

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Polygons

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

blackpanther Mar 24, 2024

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Triangle

In triangle $ABC,$ $AC = BC$ and $\angle ACB = 90^\circ.$ Points $P$ and $Q$ are on $\overline{AB}$ such that $P$ is between $A$ and $Q$ and $\angle QCP = 45^\circ.$ If cos ACP = 2/3, then find cos BCQ.

blackpanther Mar 24, 2024

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Triangle

In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect AX at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

blackpanther Mar 24, 2024

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geometry problem

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 2 and QC = 3. Find sin angle PAQ.

blackpanther Mar 24, 2024