All Questions ⁺⁰236111 Questions

0

19

1

+551

Algebra

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

Pythagorearn Jul 3, 2024

0

8

1

+551

Algebra

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

Pythagorearn Jul 3, 2024

0

11

1

+551

Algebra

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

Pythagorearn Jul 3, 2024

0

19

1

+948

Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $5$ pieces of candy per scoop to the vat, and another machine that can remove exactly $3$ pieces of candy with a different scoop from read more ..

Rangcr897 Jul 3, 2024

0

26

0

+948

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

Rangcr897 Jul 3, 2024

0

10

0

+948

Number Theory

A positive integer is called nice if it is a multiple of $8.$
A certain nice positive integer $n$ has exactly $9$ positive divisors. How many prime numbers are divisors of $n?$

Rangcr897 Jul 3, 2024

0

17

0

+948

Number Theory

A positive integer is called nice if it is a multiple of $8.$
A certain nice positive integer $n$ has exactly $9$ positive divisors. What is the smallest possible value of $n?$

Rangcr897 Jul 3, 2024

0

10

0

+1337

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 $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim read more ..

learnmgcat Jul 3, 2024

0

10

2

+948

Number Theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$.
Be sure to include complete explanations with your answer, using complete sentences. Imagine you were going to show your solution to a classmate, read more ..

Rangcr897 Jul 3, 2024

+2

13

2

+35

Quadratics

The equation y = -16^2 + 26t + 105 describes the height (in feet) of a ball tossed up in the air at 26 feet per second from a height of 105 above the ground. In how many seconds will the ball hit the ground? express your answer as a decimal rounded to the read more ..

AHGSIGMA Jul 3, 2024

0

9

2

+1489

Number Theory

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(1200)$?

kittykat Jul 3, 2024

0

19

2

+1489

Number Theory

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(191)$?

kittykat Jul 3, 2024

0

17

0

+1489

Number Theory

The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$
What is the smallest positive integer that has exactly $2$ perfect square divisors?

kittykat Jul 3, 2024

0

17

0

+1489

Number Theory

A terminal zero is a $0$ that appears at the end of a number. For example, the number $3,800$ has two terminal zeros.
How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?

kittykat Jul 3, 2024

0

13

1

+1337

Number Theory

How many bases $b \ge 2$ are there such that $100_b + 1_b$ is prime?

learnmgcat Jul 3, 2024

0

15

0

+1337

Number Theory

What is the smallest prime divisor of $5^{19} + 7^{13} + 23$?

learnmgcat Jul 3, 2024

0

12

0

+1337

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 ..

learnmgcat Jul 3, 2024

0

9

2

+40

elimination

Find the ordered pair if:

onyulee Jul 3, 2024

0

12

0

+1489

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.)

kittykat Jul 3, 2024

0

15

0

+1489

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.

kittykat Jul 3, 2024

Jul 2, 2024

0

15

3

+46

Please Help! Thank you!

An equilateral triangle of side centimeters is rotated completely about a side to form a solid. What is the number of cubic centimeters in the volume of the solid?
I got

greenplanet2050 Jul 2, 2024

0

22

0

+1489

Algebra

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

kittykat Jul 2, 2024

0

27

0

+1839

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 ..

ABJeIIy Jul 2, 2024

0

8

1

+1839

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 ..

ABJeIIy Jul 2, 2024

0

22

1

+1839

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 ..

ABJeIIy Jul 2, 2024

1 Online Users