All Questions ⁺⁰237293 Questions

0

25

0

+2729

Number Theory

Find the inverse of $7$ modulo $21$.

LiIIiam0216 Jul 2, 2024

+1

20

2

+59

Let be the twenty (complex) roots of the equation Calculate Note that the addition formula for cotangent is still valid when working

Let be the twenty (complex) roots of the equation
Calculate Note that the addition formula for cotangent is still valid when working with complex numbers.

Yeetww Jul 2, 2024

0

37

0

+2729

Number Theory

Which of the residues 0, 1, 2, 3, 4 satisfy the congruence x^5 = 0 mod 5?

LiIIiam0216 Jul 2, 2024

0

38

0

+2729

Number Theory

Which of the residues 0, 1, 2, ..., 11 satisfy the congruence 3x = 1 mod 12?

LiIIiam0216 Jul 2, 2024

Jul 1, 2024

0

19

2

+2729

Number Theory

The numbers $24^2 = 576$ and $56^2 = 3136$ are examples of perfect squares that have a units digits of $6.$
If the units digit of a perfect square is $5,$ then what are the possible values of the tens digit?

LiIIiam0216 Jul 1, 2024

0

30

1

+2729

Number Theory

A four-digit hexadecimal integer is written on a napkin such that the units digit is illegible. The first three digits are 2, $F$, and 1. If the integer is a multiple of $19_{10}$, what is the units digit?

LiIIiam0216 Jul 1, 2024

0

39

1

+2729

Number Theory

If n = 43 mod 60, what is the residue of n modulo 7?

LiIIiam0216 Jul 1, 2024

0

37

1

+2729

Algebra

Determine all of the following for $f(x) \cdot g(x)$, where $f(x) = -x^2+ 8x - 5$ and $g(x) = x^3 - 11x^2 + 2x$.
Leading term
Leading coefficient
Degree read more ..

LiIIiam0216 Jul 1, 2024

+1

25

2

+35

Interval Notation

For what real values of x is -4 < x^4 + 4x^2 < 21 satisfied? Express your answer in interval notation.

NotThatSmart ●●

AHGSIGMA Jul 1, 2024

0

26

1

+363

Number theory

How many of the 1000 smallest positive integers are congruent to 1 modulo 9? Can you also explain what a modulo is?

Lilliam0216 Jul 1, 2024

-1

38

1

+216

Coordinates

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

BRAlNBOLT Jul 1, 2024

-1

27

1

+216

Coordinates

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

BRAlNBOLT Jul 1, 2024

0

25

1

+216

Coordinates

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
PA^2 + PB^2 + PC^2 = 3PQ^2 + k.
If $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant read more ..

NotThatSmart ●

BRAlNBOLT Jul 1, 2024

0

19

3

+921

Algebra

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

booboo44 Jul 1, 2024

0

38

1

+864

Geometry

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

NotThatSmart ●

RedDragonl Jul 1, 2024

0

28

2

+864

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

RedDragonl Jul 1, 2024

0

18

3

+22

Help

A packet of chocolates contains pieces of milk, dark and orange chocolates. 25% of the chocolates are dark chocolates. The ratio of the number of dark chocolates to the number of milk chocolates is 5:7. There are 78 pieces of dark and orange chocolates. read more ..

NotThatSmart ●●●

derpmcfearson Jul 1, 2024

0

24

1

+789

Number Theory

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

bingboy Jul 1, 2024

0

33

1

+1766

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

blackpanther Jul 1, 2024

0

25

0

+864

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

RedDragonl Jul 1, 2024

0

27

1

+864

Geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

RedDragonl Jul 1, 2024

0

42

0

+900

Number Theory

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

eramsby1O1O Jul 1, 2024

0

26

1

+900

Number Theory

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

eramsby1O1O Jul 1, 2024

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