Answer:
see explanation
Step-by-step explanation:
If A +B = 45° then tan(A+B) = tan45° = 1
Expanding (1 + tanA)(1 + tanB)
= 1 + tanA + tanB + tanAtanB → (1)
Using the Addition formula for tan(A + B)
tan(A+B) = 
= 1 ← from above
Hence
tanA + tanB = 1 - tanAtanB ( add tanAtanB to both sides )
tanA + tanB + tanAtanB = 1 ( add 1 to both sides )
1 + tanA + tanB + tanAtanB = 2
Then from (1)
(1 + tanA)(1 + tanB) = 2 ⇒ proven
2x + y = 10 is y = -2x + 10
4x + 7 = 40
-7 -7
4x = 33
4 4
x = 8.25
y = -2(8.25) + 10
y = -6.5 and x = 8.25
Hope this helps :)
Answer: H. 139.50
Step-by-step explanation:
Multiply 9 by 8 first and you get 72. Then multiply 9 by 7.5 and you get 67.5 then add 72 and 67.5 and you get 139.5 or 139.50
OK first let's check the x=1.5.
Oh my, that's called a depressed cubic, no
term. There's a formula for these very much like the quadratic formula but you're probably not quite old enough for that. Anyway,
is a solution, but that's not what they're asking. They are asking us to compare
with
and conclude
It turns out we did need all the rest of it. Save those brain cells, there's lots more math coming.
~~~~~~~~~~~~~~
I love it when the student asks for more. Here's the formula for a depressed cubic. I won't derive it here (though I did earlier today, coincidentally, but I'm probably not allowed to link to my Quora answer "what led to the discovery of complex numbers" from here). We use the trick of putting coefficients on the coefficients to avoid fractions.
has solutions
![x = \sqrt[3] { q - \sqrt{p^3 + q^2} } + \sqrt[3] {q + \sqrt{p^3 + q^2} } ](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%20%7B%20q%20-%20%5Csqrt%7Bp%5E3%20%2B%20q%5E2%7D%20%7D%20%2B%20%5Csqrt%5B3%5D%20%7Bq%20%2B%20%5Csqrt%7Bp%5E3%20%2B%20q%5E2%7D%20%7D%20%0A%0A)
That's pretty simple, though sometimes we end up having to take the cube roots of complex numbers, which isn't that helpful. Let's try it out on
That's 
so
![x = \sqrt[3] { 3 - \sqrt{(2/3)^3+9} } + \sqrt[3] {3 + \sqrt{(2/3)^3+9} }](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%20%7B%203%20-%20%5Csqrt%7B%282%2F3%29%5E3%2B9%7D%20%7D%20%2B%20%5Csqrt%5B3%5D%20%7B3%20%2B%20%5Csqrt%7B%282%2F3%29%5E3%2B9%7D%20%7D%20)
![x = \sqrt[3] { 3 - \sqrt{753}/9 } +\sqrt[3]{3 + \sqrt{753}/9 }](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%20%7B%203%20-%20%5Csqrt%7B753%7D%2F9%20%7D%20%2B%5Csqrt%5B3%5D%7B3%20%2B%20%5Csqrt%7B753%7D%2F9%20%7D)
Answer:
9/20 also 45%
Step-by-step explanation:
well if 20 of them 9 are brown so 9 out of 20 of them are brown/45% of them because out of 20 each thing right or each person is 5%
