Answer:
39
Step-by-step explanation:
used a calculator
Answer:
q=35
Step-by-step explanation:
x2 - 12x + q = 0
Let the two roots be r and r+2.
Factor the quadratic expression:
(x - r)[x - (r + 2)] = 0
Expand, simplify, group like terms, and get
x2 - 2(r + 1)x + r(r + 2) = 0
Compare to
x2 - 12x + q = 0
and set equal the coefficients of like terms:
Coefficient of x:
-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5
(Then the other root is r + 2 = 5 + 2 = 7)
Constant term:
r(r + 2) = q ⇒ 5(5 + 2) = q
q = 35
Test the solution:
(x - 5)(x - 7) = x2 - 12x + 35
With two roots differing by 2, you get an equation of the form
x2 - 12x + q = 0
with q = 35.
Answer:
a) cosθ = ![\frac{-2\sqrt{85} }{85}](https://tex.z-dn.net/?f=%5Cfrac%7B-2%5Csqrt%7B85%7D%20%7D%7B85%7D)
Step-by-step explanation:
<u><em> Step(i):</em></u>-
Given point ( x , y ) = ( - 2 , 3 )
We know that the polar co-ordinates
x = r cos θ and y = r sinθ
where
![r = \sqrt{(-2)^{2} +(9)^{2} } = \sqrt{4+81} = \sqrt{85}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28-2%29%5E%7B2%7D%20%2B%289%29%5E%7B2%7D%20%7D%20%3D%20%5Csqrt%7B4%2B81%7D%20%3D%20%5Csqrt%7B85%7D)
<u><em>Step(ii)</em></u>:-
x = r cos θ
cosθ ![= \frac{x}{r}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7Bx%7D%7Br%7D)
cosθ = ![\frac{-2}{\sqrt{85} } = \frac{-2}{\sqrt{85} } X \frac{\sqrt{85} }{\sqrt{85} }](https://tex.z-dn.net/?f=%5Cfrac%7B-2%7D%7B%5Csqrt%7B85%7D%20%7D%20%3D%20%5Cfrac%7B-2%7D%7B%5Csqrt%7B85%7D%20%7D%20X%20%5Cfrac%7B%5Csqrt%7B85%7D%20%7D%7B%5Csqrt%7B85%7D%20%7D)
cosθ = ![\frac{-2\sqrt{85} }{85}](https://tex.z-dn.net/?f=%5Cfrac%7B-2%5Csqrt%7B85%7D%20%7D%7B85%7D)
Hi! so what you want to do is first set up a proportion, if you know that the two triangles are congruent because abc~def you know that the proportion will work out. the proportion to set up is 54/72 from there you should know that 9 goes into both 72 and 54 so when you reduce you’d be left with 6/9 which you could further reduce to 2/3. then you can find the other sides by multiplying 92 by 2/3 and you’d get 61 and 84 by 2/3 where you’d get 56. However since you are supposed to find the perimeter, you would add all three sides together (54+56+61) and you’d be left with 171. hope this helps