All Questions ⁺⁰236092 Questions

0

23

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+2653

Geometry

The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XY = 8$ and $WX = 8,$ find $XY.$

LiIIiam0216 Jun 11, 2024

0

22

1

+1557

Number Theory

Find the smallest positive integer B so that when we express the decimal number 301 as a base B number, we still get a 2-digit number.

parmen Jun 11, 2024

0

23

0

+1557

Number Theory

Convert 3132_4 to base 3 without first converting to decimal.

parmen Jun 11, 2024

0

23

2

+1310

Numbers

Convert 35 from base 10 to base 8.

learnmgcat Jun 11, 2024

0

24

1

+1310

Numbers

Convert 987_{16} to decimal.

learnmgcat Jun 11, 2024

0

12

1

+1310

Numbers

Convert 60329_12 to decimal.

learnmgcat Jun 11, 2024

0

16

1

+1310

Numbers

Convert 11012_9 to decimal.

learnmgcat Jun 11, 2024

-4

16

1

+219

Decimals

Convert 0.031\overline{4}$ to a fraction in simplest form.

BRAlNBOLT Jun 11, 2024

-4

13

1

+219

Decimal

Convert 0.29\overline{6} to a fraction in simplest form.

BRAlNBOLT Jun 11, 2024

-4

24

1

+219

Decimal

Find the six-digit number abcdef such that
0.\overline{abcdef} = \frac{2}{17},
without a calculator.

BRAlNBOLT Jun 11, 2024

-4

19

0

+219

Decimal

Find the first ten digits after the decimal point in the decimal expansion of \frac{13}{29}=0.abcdefghij\ldots without a calculator.
(Express your answer as a ten digit number.)

BRAlNBOLT Jun 11, 2024

0

16

1

+68

precalc help

Given a square matrix $\mathbf{A}$, the characteristic polynomial of $\mathbf{A}$ is defined as \[P_{\mathbf A}(t) = \det (t \mathbf{I} - \mathbf{A}),\]
where $\mathbf{I}$ is the identity matrix. For example, read more ..

LearningCat Jun 11, 2024

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16

0

+1310

Conic

The ellipse x^2 + 4y^2 = 4 and the hyperbola x^2 - my^2 = 1 are tangent. Compute m.

learnmgcat Jun 11, 2024

+1

24

1

+9

math

Aishah poured 17 litres of water into 3 containers. Container A had 3 times as much water as Container B. Container C had 2.5 litres of water fewer than Container B. Find the amount of water in Container B in litres.
Aishah poured 17 litres of water read more ..

studywithme513524 Jun 11, 2024

0

25

1

+1839

Geometry

All the sides of a triangle are integers. If the perimeter of the triangle is $3,$ then how many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are co read more ..

ABJeIIy Jun 11, 2024

0

12

1

+1839

Geometry

There are four cities: Capital City, Little Village, Mytown, and Yourtown. The distance from Capital City to Little Village is $5$ miles. The distance from Capital City to Mytown is $2$ miles. The distance from Mytown to Yourtown is $3$ read more ..

ABJeIIy Jun 11, 2024

0

18

0

+1839

Geometry

Triangle $ABC$ has altitudes $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ If $AD = 12,$ $BE = 20,$ and $CF$ is a positive integer, then find the largest possible value of $CF.$

ABJeIIy Jun 11, 2024

0

16

1

+667

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{36} + \sqrt{45}} + \frac{1}{\sqrt{39} +\sqrt{96}}

siIviajendeukie Jun 11, 2024

0

25

0

+667

Geometry

The circles $x^2 + y^2 = 4$ and $(x - 5)^2 + (y - 8)^2 = 60$ intersect in two points $A$ and $B.$ Find the distance $AB$.

siIviajendeukie Jun 11, 2024

0

24

0

+667

Algebra

Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
f(p) = f(q) = f(r) = f(s) = 1
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$

siIviajendeukie Jun 11, 2024

0

22

0

+667

Algebra

Let $f(x) = x^2 + bx + 12 - 3x + 10$ for all real numbers $x$. Find the greatest integer value of $b$ such that $-4$ is not in the range of $f(x)$.

siIviajendeukie Jun 11, 2024

0

20

0

+667

Math problem

Let S be the set of all real numbers of the form
a1/3 + a2/3^2 + a3/3^3 + ....
where a_i \in {0, 1, 2} for all i.
(a) Is the number 1/7 in the set S?
(b) Is the number 1/4 in the set S? read more ..

siIviajendeukie Jun 11, 2024

0

15

1

+667

Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

siIviajendeukie Jun 11, 2024

0

26

0

+667

Geometry

Let \alpha and \beta be acute angles whose sum is also acute, such that $\angle BAC = \alpha,$ $\angle DAB = \beta,$ and $AB = 1$. Let $E$ be the foot of the perpendicular from $A$ to $BC$, and $F$ be the foot of the perpendicular from $E$ to $AB$, as shown read more ..

siIviajendeukie Jun 11, 2024

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