All Questions ⁺⁰236251 Questions

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help me!

Let x be a real number such that x^2 + 7x + 12 <= 0. Find the largest possible value of x^2 + 2x + 1.

LiIIiam0216 Jun 19, 2024

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24

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+355

Someone help

We introduced as a square root of -1. Does itself have any square roots among the complex numbers? If so, name one. If not, answer with "None."

Lilliam0216 Jun 19, 2024

-1

18

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+1839

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 ..

ABJeIIy Jun 19, 2024

-1

16

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+1839

Number Theory

Find the greatest prime divisor of the value of the arithmetic series
1 + 2 + 3 + \dots + 200

ABJeIIy Jun 19, 2024

-1

26

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+1839

Number Theory

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

ABJeIIy Jun 19, 2024

-1

23

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+1839

Number Theory

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

ABJeIIy Jun 19, 2024

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15

1

+2653

help coordinates

A line and a circle intersect at A and B. Find the coordinates of the midpoint of \overline{AB}.
The ilne is y = 3x - 2, and the circle is (x - 4)^4 + (y - 5)^2 = 68.

LiIIiam0216 Jun 19, 2024

0

19

1

+2653

need help

Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 4x + 12y.$ Find the largest possible value of $x + y.$ Give your answer in exact form using radicals, simplified as far as possible.

LiIIiam0216 Jun 19, 2024

0

15

1

+355

Math is not matching

We introduced as a square root of -1. Does itself have any square roots among the complex numbers? If so, name one. If not, answer with "None."

Lilliam0216 Jun 19, 2024

-1

20

1

+1839

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 5, it has the same three digits, in reverse order. What is N? (Express your answer in decimal.)

ABJeIIy Jun 19, 2024

-1

20

0

+1839

Number Theory

What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction \frac{2}{23} is written in base 16?
Express your answer as a five digit hexadecimal number. You do not need to include read more ..

ABJeIIy Jun 19, 2024

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20

1

+1839

Number Theory

Find the smallest positive integer B so that when we express the decimal number 250 as a base B number, we still get a 2-digit number.

ABJeIIy Jun 19, 2024

-1

23

1

+1839

Need help with number theory

Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$

ABJeIIy Jun 19, 2024

0

7

1

+948

Algebra

Let $x$ and $y$ be real numbers such that $x^2 + y^2 = 4x + 12y.$ Find the largest possible value of $x + y.$ Give your answer in exact form using radicals, simplified as far as possible.

Rangcr897 Jun 19, 2024

0

16

1

+948

Algebra

For an integer n, the inequality
x^2 + nx + 15 < -21 - 7x + x^2
has no real solutions in x. Find the number of different possible values of n.

Rangcr897 Jun 19, 2024

-3

12

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+219

Counting

There is a group of five children, where two of the children are twins. In how many ways can I distribute $8$ identical pieces of candy to the children, if the twins must get at least one piece of candy each?

BRAlNBOLT Jun 19, 2024

-3

32

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+219

Counting

In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty?

BRAlNBOLT Jun 19, 2024

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27

2

+42

Algebra Question

I found a really interesting problem with a nice solution.
Find the number of real solutions to this equation.
I may have remembered the problem wrong ;-;

Tottenham10 Jun 19, 2024

-3

10

1

+219

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

BRAlNBOLT Jun 19, 2024

-3

17

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+219

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

BRAlNBOLT Jun 19, 2024

-3

19

1

+219

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

BRAlNBOLT Jun 19, 2024

0

13

1

+1573

Geometry

Let G be the center of equilateral triangle XYZ A dilation centered at G with scale factor -1 is applied to triangle XYZ to obtain triangle X'Y'Z' Let A be the area of the region that is contained inside both triangles XYZ and X'Y'Z' Find read more ..

parmen Jun 19, 2024

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16

1

+1573

Geometry

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

parmen Jun 19, 2024

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18

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+1573

Geometry

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 12$. Find the radius of the circle.

parmen Jun 19, 2024

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14

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+1573

Geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

parmen Jun 19, 2024

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