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t^2 - 9t - 36 factors to (t+3)(t-12).

The smallest value would be -3. Please correct me if I'm wrong or if I misunderstood your question 

oh sorry you already have the answer that's great 

We know that 3, 4, 5 is a Pythagorean Triple, so we can draw a dashed/dotted/faint line at the bottom, creating a triangle with the 3 and 4. 

You can then create a rectangle using the 4 on the very left and the segment with length 5 that we just created. So now we have a portion of x, which is 5. Because we drew a rectangle and there are two 4's, we can use the Pythagorean Theorem again and find that the last portion of x is 3. So x is equal to 8.

Correct me if I'm wrong 

I'm not sure if I'm supposed to find x, but that's what I'll do. I didn't really understand the question at all, but I'll answer what I think it is.

We can cross multiply to get the equation 2x^2+8x=x^2-25

Simplified, it looks like x^2+8x+25.

We can use the quadratic formula and find that x is -4+3i, -4-3i.

Please correct me if I'm wrong 

The slope in going to be (4-1)/(-6-3)=-(3/9)=-1/3

We have an equation of y=-1/3x+b

Now, we substitute one of the points, we can choose the easier one, which is (3, 1). We now have an equation of 1=-1/3(3)+b. b=2

So the final equation is y=-1/3x+2

Correct me if I'm wrong 

Start off by subtracting 2 from 10, which is 8.

Subtract 6 from 24 as two books are taken off each of the 3 shelves. 

This leaves us with 8/18, which simplifies to 4/9.

Please correct me if I'm wrong .

Solving using b

So we know that all angles in a triangle add up to 180°.

The equation we get is 50°+a+b=180°

Because there are two variables, we need to equations, and the other is already given. Which is a-b=40

We can use substitution and get 50°+(b+40°)+b=180°.

Just add and subtract a few things to get 2b=90°, and b=45°

We can take b back into the equation and get a=85°.

Solving using a

If we want to solve using a, we can substitute b=a-40 into the first equation.

We get 50°+2a-40°=180°. 2a=170° and a=85°.

There are 5! ways to put 5 journalists around the table and 2! ways to put 2 baristas around the table. Then there are ONLY 2 ways to put the sailor because the two ends are considered the same, it's just flipping another arrangement. So now we multiply 5! · 2! · 2=120 · 2 · 2=480 different arrangements.

Hope this helps!

So, we first start off by calculating C(6,3) which is 20. This is to choose 3 different rolls out of 6 to get the number of 3's. Next, we calculate C(3, 2) which is 3. Since the 3's already took 3 places, there are only three places to put our 2's. We have already placed 5 numbers so now there's only 1 spot left for 1 number, so C(1, 1) is 1. We can multiply 20 by 3 to get 60 possible sequences.

Explanation:

There are 56 ways to choose 2 girls out of 8 and there are 7 ways to choose 1 boy out of 7. 

Because we use the word "and", we multiply 56 by 7, and we get 392.

But then, there's the possibility that we choose 1 girl and 2 boys.

There are 8 ways to choose 1 girl out of 8 and there are 42 ways to choose 2 boys out of 7.

Again, we multiply due to the word "and", so we get 336

We can add 392 and 336 because we choose 2 girls and 1 boy OR 1 girl and 2 boys.

Finally, we get an answer of 728.

Solution #2:

You can choose 1 girl and 1 boy first.

There are 8 ways to choose 1 girl and 7 ways to choose 1 boy. 

Now there are 13 students left and one more student needed to help.

There are 13 ways to choose 1 more student. Gender doesn't matter now as we already have 1 girl and 1 boy.

Now we multiply as we need to choose 1 girl, 1 boy, AND another student.

Once again, we get an answer of 728.