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
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.
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.
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.