All Questions ⁺⁰237687 Questions

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If we write $\sqrt{5}+\frac{1}{\sqrt{5}} + \sqrt{7} + \frac{1}{\sqrt{7}}$ in the form $\dfrac{a\sqrt{5} + b\sqrt{7}}{c}$ such that $a$, $b$, and $c$ are positive integers and $c$ is as small as possible, then what is $a+b+c$?

Guest Jun 16, 2019

+5

1107

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Hello I'm having trouble on what to do first with this fractional 1 varible equation's

I'm giving the equation Solve for x: Note that 3/4 and x are rigth next to each other like this 3/4x I had some trouble with the latex this time...

x = _____ Write your answer as a fraction read more ..

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HiylinLink Jun 16, 2019

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1015

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3rd hard-ish question

Let A be the surface area of a 16 units by 1unit by 1 unit rright, rectangular prism and let B be the surface area of a 8 units by 2 units by 1 unit right rectangular prism. What is I A-B I in square units?

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NoobGuest Jun 16, 2019

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Another weird Problem...

A train traveling at 45 mph enters a tunnel that is 1 mile long. The length of the train is 1/8 of a mile. How many minutes after the front of the train enters the tunnel does the back of the train exit the tunnel? Express your answer as a decimal to the read more ..

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NoobGuest Jun 16, 2019

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Mathcounts Trainer From AOPS that I had Trouble with

A two digit, positive integer,b, is formed by reversing the digits of another two digit, positive integer, a. If both a+b and a-b are perfect squares, what is the value of a?

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NoobGuest Jun 16, 2019

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741

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Vectors and matrices

What shall I know before starting vectors and matrices? (Idk calculus but I know trigonometry)

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Guest Jun 16, 2019

+1

871

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+220

please help

An ant starts walking from the origin. During each second, it has an equal chance of moving 1 inch right, 2 inches up, 3 inches left, or 4 inches down. What is the ant's expected location after 5 seconds if it starts at the origin?

Oofrence Jun 16, 2019

Jun 15, 2019

+1

946

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help

The lengths of two sides of a triangle are 33 units and 42 units. The third side also has an integral length. What is the least possible number of units in the perimeter of the triangle?

Guest Jun 15, 2019

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906

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Help please

1. If $f(x) = x^2 - 1$ and $g(x) = x + 7,$ evaluate $f(g(7)) + g(f(3)).$
2. Suppose $f(x)=\frac{3}{2-x}$. If $g(x)=\frac{1}{f^{-1}(x)}+9$, find $g(3)$.
3. For what value of does the equation represent read more ..

Guest Jun 15, 2019

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903

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Also with this one please

Guest Jun 15, 2019

-1

846

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Please help! Do not know hot to solve

Guest Jun 15, 2019

+1

897

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Interesting property

I was thinking about this interesting property of positive integers, where if a, b, are positive integers, and a>b, then the remainder when a and b are divided by a-b seems to always the same. Is this true for all positive integers? I can't seem read more ..

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Guest Jun 15, 2019

+1

983

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+21

Help

Let $r$ and $s$ be the roots of $y^2 - 19y + 7$. Find $(r-2)(s-2)$.

Sjsjjs Jun 15, 2019

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1566

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+21

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What is the sum of the squares of the roots of $18x^2 +21x - 400$?

Sjsjjs Jun 15, 2019

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799

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+21

Help!

Rationalize the denominator of $\frac{3}{2\sqrt[3]{5}}$. The answer can be written in the form of $\frac{A\sqrt[3]{B}}{C}$, where $A$, $B$, and $C$ are integers, $C$ is positive, and $B$ is not divisible by the cube of any prime. Find $A+B+C$. read more ..

Sjsjjs Jun 15, 2019

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1165

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+21

Help?

Given that $3x + y = 10$ and $x + 3y = 14$, find $10x^2 + 12xy + 10y^2$.

Sjsjjs Jun 15, 2019

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1184

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+21

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If $(x + y)^2 = 105$ and $x^2 + y^2 = 65$, what is the value of $xy$?

Sjsjjs Jun 15, 2019

+1

908

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Rationalize the denominator of (sqrt(5)+sqrt(2))/(sqrt(5)-sqrt(2)). The answer can be written as (A+Bsqrt(C))/D, where A, B, C, and D are integers. D is positive and C is not divisible by the square of any prime. If the greatest common divisor of A, B, read more ..

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Guest Jun 15, 2019

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1098

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Simplifying Trig

The expression is (in degrees.)
I got 0, with the following strategy
using product identities and then
But when I plug it in a calculator it shows up as . read more ..

CoolStuffYT Jun 15, 2019

+1

888

2

Calculating the time it takes to heat up alcohol.

I hope it's alright if I post this here, seeing as this site seems to be mainly for math problems, but I've been struggling with this problem and this topic for a while now and I'm eager to know how to solve it so I can apply it to assignments that are read more ..

off-topic

Guest Jun 15, 2019

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