All Questions ⁺⁰235710 Questions

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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 $XZ = 5$ and $YZ = 2,$ find $WX.$

AUnVerifedTaxPayer Sep 7, 2024

0

4

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+176

Geometry

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $AB = 2$, then find $AC.$

AUnVerifedTaxPayer Sep 7, 2024

+1

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2

+176

need help

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $3$ from one wall, and a distance of $3$ from the other wall. Find the radius read more ..

AUnVerifedTaxPayer Sep 7, 2024

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+176

help geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{PA}$ is $5,$ and $AB$ has a length of 6. Find the radius of the circle.</ read more ..

AUnVerifedTaxPayer Sep 7, 2024

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2

+1246

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

Akhain1 Sep 7, 2024

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7

1

+1246

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?

Akhain1 Sep 7, 2024

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8

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+337

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?

MeIdHunter Sep 7, 2024

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10

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+337

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?

MeIdHunter Sep 7, 2024

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3

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+337

Algebra

The solutions to
2x^2 - 10x + 13 = -6x^2 - 18x - 15
are a+bi and a-bi, where a and b are positive. What is a\cdot b?

MeIdHunter Sep 7, 2024

+1

4

1

+544

Algebra

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator read more ..

cooIcooIcooI17 Sep 7, 2024

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6

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+544

Algebra

Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.

cooIcooIcooI17 Sep 7, 2024

0

5

1

+544

Algebra

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

cooIcooIcooI17 Sep 7, 2024

0

2

1

+2669

Algebra

Find the largest integer k such that the equation 5x^2 - kx + 8 - 2x^2 + 25 =0 has no real solutions

LiIIiam0216 Sep 7, 2024

0

10

1

+834

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2.

gnistory Sep 7, 2024

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8

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+263

Geometry

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

bIueb3rry Sep 7, 2024

-1

3

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+331

Algebra

The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a. read more ..

Stanry Sep 7, 2024

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7

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+306

Algebra

Let $A$, $B$, and $C$ be constants so that
\frac{1}{x^3-2x^2-5x+9}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}
holds for all real numbers $x$ other than $-5$ and $3.$ What is $A$?

nathanl6656 Sep 7, 2024

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2

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+207

Algebra

Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$). If the graphs of $y=f(x)$ and $y=f(1/x)$ are drawn, at how many points do they intersect?

BRAlNBOLT Sep 7, 2024

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4

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+838

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?

magenta Sep 7, 2024

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+50

How do I ask an off topic question?

Help please. Also, here is a problem for you people
Points T and U lie on a circle centered at O, and point P is outside the circle such that PT and PU are tangent to the circle. If , then what is the measure of read more ..

AUnVerifiedTaxPayer Sep 7, 2024

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5

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+279

Number Theory

How many positive four-digit integers $N$ have the property that the three-digit number obtained by removing the leftmost digit is equal to $\frac{N}{24}?$

fjeihqoO Sep 7, 2024

0

3

1

+279

Number Theory

The product of a set of distinct positive integers is $630$. If one of the numbers is 42, what are the other two numbers?

fjeihqoO Sep 7, 2024

0

11

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+834

Number Theory

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

gnistory Sep 7, 2024

0

7

0

+834

Number Theory

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

gnistory Sep 7, 2024

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