Assuming that each square is one unit, the first one is \(2*1+5*2+1*1=13\) units

2. This is two equal triangles. So \((4*2)/2+(4*2)/2\)=4

3. There are two pentagons of equal area. So the area would be \(7.5*2=15\)

4. Make a 4x5 square around it. Subtract 4 from one of the outside triangles. Subract 2 from another. Finally subtract 5 from the last. So \(20-4-5-2=9\).

A solution exists if and only if 8 is invertible modulo p. In other words, \(\gcd(8,p)=1\). Since \(8=2^3\) is a power of 2, 8 is invertible modulo q if and only if q is an odd integer. All primes except for 2 are odd, so the number we are looking for is 2.

Those aren't consecutive!

Numbers that digits sum to 8: 8, 17, 26, 35, 44, 53, 62, 71, 80.

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

The answer is 71 and 72.

Hope this helps,

~Mosspelt6

\(527_{10}\) means 527 in base 10.

The answer would be \(20033_4\)

-Mosspelt6

8 players are taking biology, so 20-8=12 players are not taking biology, which means 12 players are taking chemistry alone. Since 4 are taking both, there are 12+4=16 players taking chemistry.

it doesn't work for me either

yeah i've seen this problem before, but it was with mothers and daughters

Use the standard method for solving "working together" problems: make an equation showing the fractions of the job that each worker does in a fixed amount of time. Let x be the number of hours required by the slower machine; then x-1 is the number of hours required by the faster machine. Then the fractions of the job each does in 1 hour are 1/x and 1/x-1. And the fraction of the job they do together in 1 hour is 1/2. So 1/x + 1/(x-1) = 1/2

Multiply both sides of the equation by the least common denominator to clear fractions. You will end up with a quadratic equation that does not factor; so you will need to get your irrational answer using the quadratic formula or something like a graphing calculator.

Does this help?

\(\)For a positive number N which is not a perfect square, exactly half of the positive factors will be less than \(\sqrt{n}\). Since 60 is not a perfect square, half of the positive factors of 60 will be less than \(\sqrt{60}\), or about 7.746.

Clearly, there are no positive factors of between 7 and \(\sqrt{60}\).

Therefore half of the positive factors will be less than 7.

So the answer is 1/2.

Using the formula (1/a)*b= b/a we get

\(\frac{1}{3}*30 = \frac{30}{3} = 10.0\)