All Questions ⁺⁰235756 Questions

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+1455

System

The system of equation
\frac{xy}{x + y} = 1, \quad \frac{xz}{x + z} = 1, \quad \frac{yz}{y + z} = 5
has exactly one solution. What is $z$ in this solution?

kittykat Mar 31, 2024

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21

1

+1455

help me

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $10$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $4$ times as much money as read more ..

kittykat Mar 31, 2024

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33

1

+1911

Constant term

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

tomtom Mar 31, 2024

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22

0

+1911

System

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

tomtom Mar 31, 2024

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24

1

+1911

Coefficient

Expand (x^2 + 1/x)*(x + x^4)^3.

tomtom Mar 31, 2024

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18

1

+1911

Expand

Expand (x^2 + 1/x)*(x + x^4)^3.

tomtom Mar 31, 2024

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18

1

+1533

Geometry

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

parmen Mar 31, 2024

Mar 30, 2024

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28

1

+1533

geometry

In triangle $ABC$, let $I$ be the incenter of triangle $ABC$. The line through $I$ parallel to $BC$ intersects $AB$ and $AC$ at $M$ and $N$, respectively. If $AB = 5$, $AC = 5$, and $BC = 8$, then find the area of triangle $AMN$.

parmen Mar 30, 2024

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20

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+1533

help geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

parmen Mar 30, 2024

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21

1

+1533

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

parmen Mar 30, 2024

0

30

1

+479

Probability

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both have read more ..

ChiIIBill Mar 30, 2024

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22

2

+34

Complex Number Arithmetic

Compute
I got 0 but it was incorrect. I think I might be doing something wrong. Thanks!

jilin73 Mar 30, 2024

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9

1

+118

Let a_1, a_2, a_3, ... be an arithmetic sequence. Let S_n denote the sum of the first n terms. If S_5=1/5 and S_10=1/10 then find S_15

Let a_1, a_2, a_3, ... be an arithmetic sequence. Let S_n denote the sum of the first n terms. If S_5=1/5 and S_10=1/10 then find S_15

SilviaJendeukie Mar 30, 2024

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25

1

+4

pls help!!!!! due soon

Let f(x)= |x| and g(x)=x^2
Find all values of x for which f(x)>g(x)

bananapants25 Mar 30, 2024

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13

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+1455

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?

kittykat Mar 30, 2024

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20

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+1455

Domain

Find the domain of the function $f(x)=\frac{2x-7}{\sqrt{x^2}} - \sqrt{5x+6-11}$.

kittykat Mar 30, 2024

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24

1

+118

Arithmetic Sequence

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 1000, Shirley runs screaming from the room. What number does Laverne say that sends Shirley screaming read more ..

SilviaJendeukie Mar 30, 2024

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23

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+279

Probability

A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile read more ..

fjeihqoO Mar 30, 2024

0

24

2

+118

Arithmetic Sequence

Let a_1, a_2, a_3, ..., a_11, a_12 be an arithmetic sequence. If and , then find a_1.

SilviaJendeukie Mar 30, 2024

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17

1

+1911

counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

tomtom Mar 30, 2024

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18

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+1911

counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

tomtom Mar 30, 2024

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18

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+279

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

fjeihqoO Mar 30, 2024

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29

0

+279

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

fjeihqoO Mar 30, 2024

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45

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+279

Algebra

All members of our painting team paint at the same rate. If $40$ members can paint a $100$ square foot wall in $50$ minutes, then how long would it take the $40$ members to paint a $480$ square foot wall, in minutes?

fjeihqoO Mar 30, 2024

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26

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+279

Painting

All members of our painting team paint at the same rate. If $45$ members can paint a specific wall in $60$ minutes, then how long would it take $12$ members to paint the same wall, in minutes?

fjeihqoO Mar 30, 2024

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