All Questions ⁺⁰233097 Questions

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Number Theory

Find the smallest positive integer $N$ such that
N &\equiv 4 \pmod{6}, \\
N &\equiv 4 \pmod{10}, \\
N &\equiv 4 \pmod{15}, \\
N &\equiv 4 \pmod{24}.

Stanry Jul 4, 2024

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+257

Number Theory

Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{3}, \\
N &\equiv 2 \pmod{7}, \\
N &\equiv 2 \pmod{10}.

Stanry Jul 4, 2024

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+257

Number Theory

Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{5}, \\
N &\equiv 2 \pmod{7}.

Stanry Jul 4, 2024

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3

+636

Algebra

Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

Rangcr897 Jul 4, 2024

+1

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1

+636

Algebra

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

Rangcr897 Jul 4, 2024

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1

+636

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).

Rangcr897 Jul 4, 2024

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+636

Algebra

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

Rangcr897 Jul 4, 2024

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+529

Algebra

Find all real values of $p$ such that
(x+1)(x-2p)
has a minimum value of 0 over all real values of $x$.

magenta Jul 4, 2024

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+529

Algebra

Let $c$ be a real number. What is the maximum value of $c$ such that the graph of the parabola $y = -6x^2$ has at most one point of intersection with the line $y = 5x+c?$

magenta Jul 4, 2024

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+529

Algebra

Let $x$ and $y$ be real numbers. If $x^2 + 3y^2 = 18$, then find the maximum value of $x + y$.

magenta Jul 4, 2024

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1

+529

Algebra

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

magenta Jul 4, 2024

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1

+1292

Algebra

Find the domain of the function $f(x) = \sqrt{6-x-x^2-2x^2}$.

ABJeIIy Jul 4, 2024

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+1292

Algebra

Find the sum of all values of $k$ for which $x^2 + kx - 9x + 25 - 9$ is the square of a binomial.

ABJeIIy Jul 4, 2024

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+1292

Algebra

Find the largest real number $c$ such that $1$ is in the range of $f(x)=x^2-5x+c-3x+8$.

ABJeIIy Jul 4, 2024

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+8

Help me do the algebra question

For what values of j does the equation have exactly one real solution? Express your answer as a list of numbers, separated by commas.

Iamrockingtoday Jul 4, 2024

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+97

Help!

Eddie, Freddy and Gary had 243 game tokens altogether. After Eddie gave 3/10 of his tokens to Freddy and 1/4 of his tokens to Gary, all three boys had the same number of tokens. How many tokens did Freddy and Gary have together at first?

sugabreaddoughman Jul 4, 2024

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+97

Need help

Raju, Sam, and Tristan had 435$. Raju spent 4/5 of his money. Sam spent 2/3 of his money and Tristan spent 3/4 of his money. In the end, Raju has 55$ more than Sam. Tristan has $10 more than Sam. How much money Tristan has at first?

sugabreaddoughman Jul 4, 2024

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+635

Algebra

For what values of $j$ does the equation $(2x + 7)(x - 4) = -31 + jx$ have exactly one real solution? Express your answer as a list of numbers, separated by commas.

Hi6942O Jul 4, 2024

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+635

Algebra

The entries in a certain row of Pascal's triangle are
1, n, \dots, n, 1.
The average of the entries in this row is 2. Find $n$.

Hi6942O Jul 4, 2024

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+635

Algebra

The system of equations \frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 1 has exactly one solution. What is $z$ in this solution?

Hi6942O Jul 4, 2024

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+635

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{12}.

Hi6942O Jul 4, 2024

+1

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2

+23

word problem

In Mr. Patterson's class, the average score among students who studied for an exam was 78. The average among students who did not study was 54. The overall class average was 70. What portion of the class did not study? Express your answer as a common read more ..

onyulee Jul 4, 2024

Jul 3, 2024

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+516

Algebra

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

RedDragonl Jul 3, 2024

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+516

Algebra

The roots of Ax^2+Bx+1 are the same as the roots of x^2- 3x + 5 + x^2 - 2x + 1. What is A+B?

RedDragonl Jul 3, 2024

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+4

Something I randomly thought about

Hello, I'm interested in finding a general way to solve equations like the one below;
x+y+z=17,
xy+xz+yz=94,
xyz=168 read more ..

Halprt Jul 3, 2024

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