BuilderBoi

For a number to be divisible by 66, it has to be divisible by all of its prime factors, which are 2, 3, and 11. 

The number is already divisible by 2.

For the number to be divisible by 3, \(a+b+18\) must equal a multiple of 3. 18 is already a multiple of 3, so \(a+b\) must equal

For the number to be divisible by 11, \(4-a+5-b+7-2\) must be a multiple of 11. 

Simplifying the equation, \(14 - (a+b)\) must be a multiple of 11. 

The only way we can do this is if \(a+b = 3\), because 11 is a multiple of 11, and 3 is a multiple of 3. 

Thus, \(a + b = \color{brown}\boxed{3}\)

The formula is \(\pi r^2h\). Subsituting, we have \(\pi \times 15^2 \times 9\). Solve and simplify for \(\pi\)

Let the 3 numbers be \(x, x+1, x+2\)

We have the equation: 

\(x(x+2)=17+3(x+1)\)

Simplifying into a quadratic:

\(x^2 - x - 20 = 0\)

Factor:

\((x+4)(x-5) = 0\)

We want x to be positive, so x must equal 5, meaning the 3 integers are \(\color{brown}\boxed{5,6,7}\)

You make a profit of 21 dollars for each dog you groom. 

You need to make 315 dollars to breakeven, and \(315 \div 21 = \color{brown}\boxed {15}\)

A. It looks suspiciously like the homework your teacher assigned. 

B. No image, so I can't help you, even if I wanted to...

wait... I spelled it wrong... It's safeshare.tv, add a youtube video and it will "unblock" it. Note: it only works on "appropriate" videos. An inappropriate video will be blocked on safershare.

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Cross multiply: 

\(c^2 - 4c = 4c+20\)

Simplify into standard form: 

\(c^2-8c+20 = 0\)

Complete the square: 

\((c - 4)^2 + 4 = 0\)

Subtract 4 from both sides: 

\((c-4)^2 = -4\)

Take the square root of both sides: 

\(c - 4 = \pm 2i\)

Add 4 to both sides: 

\(\color{brown}\boxed{ c = 4 \pm2i}\)