MEMEG0D

107 Questions
16 Answers

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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.

MEMEG0D 30.01.2025

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5

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+448

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.

MEMEG0D 30.01.2025

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7

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+448

Algebra

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 100, Shirley runs screaming from the room. What number does Laverne say that sends mehr ..

MEMEG0D 29.01.2025

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2

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+448

Algebra

Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

MEMEG0D 29.01.2025

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7

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+448

Algebra

Let a1, a2, a3, ... be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S_5 = 1/5 and S_10 = 1/10, then find S_15.

MEMEG0D 29.01.2025

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6

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+448

Algebra

Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

MEMEG0D 28.01.2025

+1

5

1

+448

Algebra

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

MEMEG0D 27.01.2025

+1

5

2

+448

Algebra

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: mehr ..

MEMEG0D 27.01.2025

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7

0

+448

Algebra

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
PA^2 + PB^2 + PC^2 = 3PQ^2 + k.
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant mehr ..

MEMEG0D 27.01.2025

0

4

1

+448

Geometry

Let $ABC$ be a triangle. Let $X$ be a point on $\overline{AC}$ such that $\angle BXA = 90^\circ.$ If $\angle ABC = 90^\circ,$ $AX = 15,$ and $CX = 15,$ then what is $BX?$

MEMEG0D 26.01.2025

0

5

1

+448

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.

MEMEG0D 26.01.2025

0

3

2

+448

Algebra

Fill in the blanks with numbers to make a true equation.
3x^2 + 12x - 4 - 2x^2 + 6x + 7 = ___ (x + ___ )^2 + ___

Dragononweb2.0calc ●●

MEMEG0D 14.01.2025

0

7

1

+448

Algebra

The parabola y = ax^2 + bx + c is graphed below. Find a + b + c. (The grid lines are one unit apart.)
The parabola passes through (-2,8), (0,0), and (2,8).

MEMEG0D 14.01.2025

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3

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+448

Algebra

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 - 3x^2 - 14x + 25.

MEMEG0D 14.01.2025

0

7

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+448

Algebra

Let
f(x) = \left\lfloor\frac{2 - 3x}{3x + 1}\right\rfloor.
Evaluate f(1)+f(2) + f(3) + \dots + f(999)+f(1000). (This sum has 1000 terms, one for the result when we input each integer from 1 to 1000 into f.)

MEMEG0D 13.01.2025

0

7

0

+448

Algebra

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 mehr ..

MEMEG0D 13.01.2025

0

10

0

+448

Geometry

Point X is on side \overline{AC} of triangle $ABC$ such that $\angle AXB =\angle ABX + 20^\circ$, and $\angle ABC - \angle BAC = 36^\circ$. Find $\angle XBC$ in degrees.

MEMEG0D 06.01.2025