All Questions ⁺⁰237293 Questions

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Area of a Circle from Equation

Find the area of the region enclosed by the graph of x^2+y^2 = 2x-6y+6+8x-2y+1.

Vihan23 Jul 2, 2024

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32

1

+949

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

gnistory Jul 2, 2024

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37

1

+949

Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/9 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

gnistory Jul 2, 2024

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31

1

+949

Algebra

Seven years ago, Grogg's dad was $9$ times as old as Grogg. Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?

gnistory Jul 2, 2024

0

38

0

+949

Algebra

Let a and b be the solutions to 7x^2 + x - 5 = -3x^2 - 9x - 4. Compute (a - 4)/(b - 4) + (b - 4)/(a - 4).

gnistory Jul 2, 2024

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28

1

+949

Algebra

Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 11x - 6. Find u/v^2 + v/u^2.

gnistory Jul 2, 2024

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24

3

+949

Algebra

Let a and b be the solutions to 5x^2 - 11x + 4 = 4x^2 - 17x + 6. Find 1/a^3 + 1/b^3.

gnistory Jul 2, 2024

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16

1

+2729

Number Theory

Let $m$ and $n$ be non-negative integers. If $m = 6n + 2$, then what integer between $0$ and $m$ is the inverse of $5$ modulo $m$? Answer in terms of $n$.

LiIIiam0216 Jul 2, 2024

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30

2

+2729

Number Theory

Find the remainder when 40^{13} is divided by 81.

LiIIiam0216 Jul 2, 2024

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25

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+157

Need some help

There were red, blue, white and green stickers in a bag. After the percentage of red stickers was increased by 60%, the percentage of blue stickers was decreased by 30% and 2/7 of the white stickers were coloured green, the number of each colour of read more ..

sugabreaddoughman Jul 2, 2024

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26

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+157

Kindly assist. Thanks.

Eric bought some hats and bags for $191 altogether. Each hat cost $12.80 and each bag cost $23.30. 2/5 of the hats and bags that Eric bought were hats. How many bags did Eric buy?

sugabreaddoughman Jul 2, 2024

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30

1

+2729

Number Theory

How many of the 1000 smallest positive integers are congruent to 7 modulo 29?

NotThatSmart ●

LiIIiam0216 Jul 2, 2024

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33

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+2729

Number Theory

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 2, 2024

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31

1

+2729

Number Theory

A school orders $99$ textbooks, all for the same price. When the bill for the total order comes, the first and last digits are obscured. What are the missing digits?
_18,486.7_

LiIIiam0216 Jul 2, 2024

0

20

1

+2729

Number Theory

The number $N$ is a multiple of $7$. The base $2$ representation of $N$ is
101010010101000101A10001B001010C100011_2.
Compute $A,$ $B,$ and $C$.

LiIIiam0216 Jul 2, 2024

0

19

1

+2729

Number Theory

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

NotThatSmart ●

LiIIiam0216 Jul 2, 2024

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34

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+1855

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

NotThatSmart ●

ABJeIIy Jul 2, 2024

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46

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+1855

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 in both triangles $XYZ$ and $X'Y'Z'.$ Find read more ..

ABJeIIy Jul 2, 2024

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36

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+1855

Geometry

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

ABJeIIy Jul 2, 2024

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35

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+1855

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

ABJeIIy Jul 2, 2024

+1

24

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+280

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 ..

ABJelly Jul 2, 2024

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51

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+2729

Number Theory

Find the inverse of $15$ modulo $25$.

LiIIiam0216 Jul 2, 2024

0

45

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+2729

Number Theory

Find the inverse of $3$ modulo $100$.

LiIIiam0216 Jul 2, 2024

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38

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+2729

Number Theory

Find the inverse of $8$ modulo $38.$

LiIIiam0216 Jul 2, 2024

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