Stanry

93 Questions
11 Answers

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Geometry

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
The line is y = x + 3, and A = (7,1).

Stanry Sep 30, 2024

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Geometry

Let a be a real number such that 0 < a < \frac{\pi}{2}. Show that \left(\sin(a)\right)^7 + \left(\cos ( a)\right)^7< 2*sin(a)^4*cos(a)^4.

Stanry Sep 30, 2024

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Geometry

Let $ABC$ be a triangle. Let $D$ be a point on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 30^\circ$, $\angle C = 90^\circ$, and $AC = 12$, then find the area of triangle $ABD$. Give your answer in exact read more ..

Stanry Sep 30, 2024

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Algebra

The graphs of x = y^4 and x + y^2 = 1 + x^2 - y^3 intersect at two points. The distance between these points is of the form sqrt(u + v*sqrt(5)), where u and v are integers. Find the ordered pair (u,v).

Stanry Sep 14, 2024

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Algebra

A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to five times the number of units in the sum of the lengths of its legs. What is the sum of all the different possible areas of cool right read more ..

Stanry Sep 14, 2024

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Algebra

Let a and b be positive real numbers such that a + b = 1. Find the set of all possible values of a/b.

Stanry Sep 14, 2024

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3

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Algebra

The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a. read more ..

Stanry Sep 7, 2024

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Algebra

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

Stanry Aug 18, 2024

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Algebra

For certain values of k and m, the system
3a + 2b = 2
a + 2b = k - 8a - mb
has infinitely many solutions (a,b). What are k and m? read more ..

Stanry Aug 18, 2024

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8

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+279

Algebra

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

Stanry Aug 14, 2024

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5

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+279

Algebra

If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?

Stanry Aug 14, 2024

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10

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+279

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.

Stanry Aug 13, 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.

Stanry Aug 13, 2024