siIviajendeukie

147 Questions
11 Answers

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Algebra

Find all c such that |c + 5| - 3c = 10 - 5|c - 1| + 7|c + 8|.

siIviajendeukie 2 hours ago

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Algebra

Assume that $f(3) = 4$. Name a point that must be on the graph of y= f(2/5*x + 4) + f(3x - 1) .

siIviajendeukie 3 hours ago

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Algebra

Let a(x) and b(x) be functions. Find (a\circ b)(3) - (b\circ a)(3) if $a(x) = 2x + 5$ and $b(x) = 4 - x^2$.

siIviajendeukie 4 hours ago

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Number Theory

Find the largest positive integer n for which there exist positive integers a, b, and c such that
\gcd(a + 3b, b + 3c, c + 3a) = nabc

siIviajendeukie 29 oct 2024

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Number Theory

Let N be the number of ordered 6-tuples (a_1, a_2, a_3, a_4, a_5, a_6) of positive integers that satisfy
\frac{1}{a_1} + \frac{1}{a_2} + \frac{1}{a_3} + \frac{1}{a_4} + \frac{1}{a_5} + \frac{1}{a_6} = 6.
Find the remainder when N is divided lee mas ..

siIviajendeukie 29 oct 2024

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Number Theory

Let a, b, and c be integers such that 7a + 4b = 3c. Find the largest integer that always divides $abc$.

siIviajendeukie 29 oct 2024

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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 lee mas ..

siIviajendeukie 21 oct 2024

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Algebra

The parabola $y = ax^2 + bx + c$ is graphed below. Find $a+b+c$. (The grid lines are one unit apart.)
The parabola goes through (-5,0), (0,3), and (4,0).

siIviajendeukie 21 oct 2024

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Algebra

Find the vertex of the graph of the equation x - y^2 + 8y = 13 + 2y - 4x + 15y + 3y^2.

siIviajendeukie 21 oct 2024

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Algebra

Find the vertex of the graph of the equation y = -2x^2 + 8x - 15 + 6x^2 + 14x + 28.

siIviajendeukie 21 oct 2024

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Algebra

Find the area of the region enclosed by the graph of x^2 + y^2 = 2x - 6y + 6 + 8x - 2y - 5x + 8y + 208.

siIviajendeukie 21 oct 2024

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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 lee mas ..

siIviajendeukie 7 oct 2024

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Algebra

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

siIviajendeukie 7 oct 2024

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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.

siIviajendeukie 7 oct 2024

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Number Theory

Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $15$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim lee mas ..

siIviajendeukie 3 oct 2024

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Number Theory

What are the first $5$ digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{3}$ is written in base $16$?

siIviajendeukie 3 oct 2024

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Geometry

Let \alpha and \beta be acute angles whose sum is also acute, such that $\angle BAC = \alpha,$ $\angle DAB = \beta,$ and $AB = 1$. Let $E$ be the foot of the perpendicular from $A$ to $BC$, and $F$ be the foot of the perpendicular from $E$ to $AB$, as shown lee mas ..

siIviajendeukie 1 oct 2024