All Questions ⁺⁰236048 Questions

-1

13

1

+1839

Algebra

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

ABJeIIy Jul 16, 2024

-1

15

1

+1839

Algebra

Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5}

ABJeIIy Jul 16, 2024

-1

20

0

+1839

Algebra

The solutions to
2x^2 - 10x + 13 = -6x^2 - 18x - 15
are a+bi and a-bi, where a and b are positive. What is a\cdot b?

ABJeIIy Jul 16, 2024

-1

25

0

+1839

Algebra

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

ABJeIIy Jul 16, 2024

+1

10

2

+280

Geometry

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

ABJelly Jul 16, 2024

0

10

0

+1911

Geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 15$, and $PR = 20$, read more ..

tomtom Jul 16, 2024

0

15

1

+893

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).

AnswerscorrectIy Jul 16, 2024

+1

7

2

+893

Algebra

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

AnswerscorrectIy Jul 16, 2024

0

10

1

+893

Algebra

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

AnswerscorrectIy Jul 16, 2024

0

11

1

+1310

Number Theory

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

learnmgcat Jul 16, 2024

+1

12

3

+36

May someone give me a hint on this question?

A Senate committee has Democrats and Republicans. In how many ways can they sit around a circular table if each member sits next to two members of the other party? (Two seatings are the same if one is a rotation of the other.) read more ..

Answerscorrectly Jul 16, 2024

0

9

1

+1310

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}.

learnmgcat Jul 16, 2024

0

10

1

+1310

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}.

learnmgcat Jul 16, 2024

Jul 15, 2024

0

13

3

+893

Counting

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if each scientist must sit next to a mathematician? (Two seatings are considered equivalent read more ..

AnswerscorrectIy Jul 15, 2024

0

9

1

+893

Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

AnswerscorrectIy Jul 15, 2024

0

6

1

+893

Counting

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

AnswerscorrectIy Jul 15, 2024

0

8

1

+1557

Algebra

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

parmen Jul 15, 2024

0

14

0

+1557

Algebra

Find all values of t such that floor(t) = 3t + 4 - t^2. If you find more than one value, then list the values you find in increasing order, separated by commas.

parmen Jul 15, 2024

0

16

0

+1557

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.)

parmen Jul 15, 2024

0

8

1

+4

Complex Number Proof (plz help)

Let z and w be complex numbers such that |z| = |w| = 1 and zw is not equal to -1.
(a) Prove that conjugate {z} = 1/z and conjugate{w} = 1/w
(b) Prove that ={z + w}/{zw + 1} is a real number.

Maurya Jul 15, 2024

+1

14

2

+280

Counting Problem

In a certain game, Players 1 through 5 take turns rolling a standard six-sided die, beginning with Player 1 If a six is rolled, that player wins. If any other number is rolled, the die is given to the player whose number corresponds to the number read more ..

BRAINBOLT Jul 15, 2024

+1

20

0

+280

Impossible

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$

BRAINBOLT Jul 15, 2024

+1

8

1

+280

Number Theory

Let $a$ be an integer such that $a \equiv 5 \pmod{7}$. Find the value of $a + 1 \pmod{7}$. Express your answer as a residue between $0$ and the modulus.

BRAINBOLT Jul 15, 2024

0

9

1

+2653

Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
0.\overline{0121}_3 = 0.01210121 \dots,
which is repeating.

When read more ..

LiIIiam0216 Jul 15, 2024

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