All Questions ⁺⁰236009 Questions

0

4

1

+1839

Algebra

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

ABJeIIy Oct 15, 2024

0

6

1

+281

Number Theory

When expanded as a decimal, the fraction $\frac{1}{7}$ has a repetend (the repeating part of the decimal) of $142857$. The last three digits of the repetend are $857$.
When expanded as a decimal, the fraction $\frac{1}{13}$ read more ..

jaekg Oct 15, 2024

0

10

0

+281

Number Theory

When $N$ is divided by $10$, the remainder is $a$. When $N$ is divided by $2$, the remainder is $b$. What is $N$ modulo $10$, in terms of $a$ and $b$?

jaekg Oct 15, 2024

0

7

1

+281

Algebra

Let x and y be integers. If x and y satisfy 37x + 82y = -172 and x + y = -1, then find x.

jaekg Oct 15, 2024

0

5

1

+281

Number Theory

Let p be a prime. What are the possible remainders when p is divided by 17? Select all that apply.

jaekg Oct 15, 2024

0

6

1

+281

Number Theory

Find the number of bases b \ge 2 such that 144_b is prime.

jaekg Oct 15, 2024

0

8

0

+772

Algebra

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

booboo44 Oct 15, 2024

0

7

0

+772

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 $y = 5x+c?$

booboo44 Oct 15, 2024

0

7

0

+772

Algebra

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

booboo44 Oct 15, 2024

0

8

0

+772

Algebra

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

booboo44 Oct 15, 2024

Oct 14, 2024

0

7

1

+1839

Algebra

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

ABJeIIy Oct 14, 2024

0

6

0

+1839

Algebra

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

ABJeIIy Oct 14, 2024

0

8

0

+1839

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.

ABJeIIy Oct 14, 2024

0

8

0

+772

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?

booboo44 Oct 14, 2024

0

7

0

+772

Algebra

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

booboo44 Oct 14, 2024

0

5

0

+772

Algebra

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

booboo44 Oct 14, 2024

0

5

0

+606

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?

cooIcooIcooI17 Oct 14, 2024

0

5

1

+606

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2.

cooIcooIcooI17 Oct 14, 2024

0

3

1

+13

HELP

ABCD is a square. How many squares have two or more vertices in the set {A, B, C, D}?

tomorspain Oct 14, 2024

0

5

1

+510

Algebra

Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions

onyuIee Oct 14, 2024

0

6

1

+510

Algebra

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

onyuIee Oct 14, 2024

0

5

1

+510

Algebra

Real numbers a and b satisfy
a + ab = 250
a - ab = -240
Enter all possible values of a, separated by commas.

onyuIee Oct 14, 2024

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