All Questions ⁺⁰236007 Questions

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Geometry

Simon has built a gazebo, whose shape is a regular heptagon, with a side length of 3 units. He has also built a walkway around the gazebo, of constant width 2 units. (Every point on the ground that is within 2 units of the gazebo and outside the gazebo read more ..

ABJelly Aug 2, 2024

Aug 1, 2024

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8

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help number theory

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

LiIIiam0216 Aug 1, 2024

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14

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+46

Number Theory problem:

What is the arithmetic mean of all of the positive two-digit integers with the property that the integer is equal to the sum of its first digit plus its second digit plus the product of its two digits?

Umeko1.0 Aug 1, 2024

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7

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+2653

plz help

Find the greatest prime divisor of the value of the arithmetic series
1 + 2 + 3 + \dots + 135 + 136 + 137 + 138 + 139 + 140.

LiIIiam0216 Aug 1, 2024

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11

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+2653

help help

Express 2.\overline{57} as a base 10 fraction in reduced form.

LiIIiam0216 Aug 1, 2024

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7

1

+2653

need help

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.

LiIIiam0216 Aug 1, 2024

0

16

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+2653

help me

Let $a$ be an integer such that $0 \le a \le 7$ and $a^2 \equiv a \pmod{8}$. If $a \neq 0,$ then find the value of $a$.

LiIIiam0216 Aug 1, 2024

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15

3

+2653

plz help

Find a six-digit multiple of $64$ that consists only of the digits $2$ and $4$.

LiIIiam0216 Aug 1, 2024

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10

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+2653

help need help

The number $N$ is a multiple of $7$. The base $2$ representation of $N$ is
10011010011ABC110_2.
Compute the ordered triple of digits $(A,B,C)$.

LiIIiam0216 Aug 1, 2024

Jul 31, 2024

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11

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+2653

need help help

The Fibonacci sequence is defined by F_1 = F_2 = 1 and F_{n + 2} = F_{n + 1} + F_n. Find the remainder when F_{1000} is divided by 17.

LiIIiam0216 Jul 31, 2024

0

6

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+2653

help me

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

LiIIiam0216 Jul 31, 2024

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20

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+2653

plz help

What is 100000_{16} * E21A8_{16} in base 16?

LiIIiam0216 Jul 31, 2024

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6

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+355

Find the number of solutions to in the interval

Find the number of solutions to
in the interval

Lilliam0216 Jul 31, 2024

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20

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+598

Algebra

Solve the inequality $4t^2 \le -9t + 12 - 14t + 36.$ Write your answer in interval notation.

cooIcooIcooI17 Jul 31, 2024

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12

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+598

Inequality

Solve the inequality $x(x + 6) > 16 - 5x + 33.$ Write your answer in interval notation.

cooIcooIcooI17 Jul 31, 2024

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14

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+598

system

For a certain value of k, the system
x + y + 3z = 10 - x + 5y,
4x + 2y + 5z = 7 + 11y + 19z,
kx + z = 3 + 5y
has no solutions. What is this value of k?

cooIcooIcooI17 Jul 31, 2024

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14

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+2653

need help now

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

LiIIiam0216 Jul 31, 2024

0

6

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+551

help me help

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

Pythagorearn Jul 31, 2024

-2

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help me plz

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

Stanry Jul 31, 2024

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+842

need help

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

RedDragonl Jul 31, 2024

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11

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+310

geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

MEMEG0D Jul 31, 2024

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help geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

eramsby1O1O Jul 31, 2024

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geometry help

In triangle PQR, M is the midpoint of PQ .Let X be the point on QR such that PX bisects QPR and let the perpendicular bisector of PQ intersect PX at Y. If PQ=28,PR=16 and MY=5 then find the area of triangle PYR</ read more ..

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CosmicKing Jul 31, 2024

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