Jyrgernry

26 Questions
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In the diagram, $\triangle PQR$ is right-angled at $Q$, $PQ$ is horizontal and $QR$ is vertical. What are the coordinates of $Q$? Type your answer in the form (a,b) (no spaces) where a and b are real numbers.

Jyrgernry Apr 22, 2026

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What is the circumference of the circle with center at P and passing through Q? Express your answer in terms of \pi.
P = (0,0) and Q = (1,1).

Jyrgernry Apr 22, 2026

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Algebra

The graph of f(x)=ax^3+bx^2+cx+d is shown below. What is the value of 8a-14b+6c-5d?

Jyrgernry Apr 22, 2026

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Algebra

Let f(x) and g(x) be two linear functions. The graphs of $f(x)$ and $g(x)$ are shown below.
Evaluate f(1) + g(1) + f(g(1)) + g(f(1)).

Jyrgernry Apr 22, 2026

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Algebra

The graph of y = f(x) is shown below.
For a constant a, let g(x) = f(x + a). Find the constant a so that $g(x)$ and $g^{-1}(x)$ are the same function.

Jyrgernry Apr 22, 2026

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Algebra

The graph of the invertible function y = f(x) is shown below.
If f(a)=b and f(b)=4, then what is the value of $a-b$?

Jyrgernry Apr 22, 2026

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Two chords with length r are drawn on a circle of radius r. What is the maximum possible distance between their endpoints?

Jyrgernry Apr 21, 2026

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William writes the integers from 2 through 15 from left to right on a piece of paper, then does the following:

* He begins by circling the leftmost uncircled integer, then circles all its powers. Afterwards, he repeats this process until every read more ..

Jyrgernry Apr 21, 2026

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Given regular heptagon ABCDEFG, a circle can be drawn that is tangent to DC at C and to EF at F. What is radius of the circle if the side length of the heptagon is 1?

Jyrgernry Apr 21, 2026

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In the diagram, a semicircle is centered at $O,$ and $\overline{AB}$ is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

Jyrgernry Apr 21, 2026