Answer:
10 terms
Step-by-step explanation:
equate the sum formula to 55 and solve for n
n(n + 1) = 55 ( multiply both sides by 2 to clear the fraction )
n(n + 1) = 110 ← distribute parenthesis on left side
n² + n = 110 ( subtract 110 from both sides )
n² + n - 110 = 0 ← in standard form
Consider the factors of the constant term (- 110) which sum to give the coefficient of the n- term (+ 1)
the factors are + 11 and - 10 , since
11 × - 10 = - 110 and 11 - 10 = + 1 , then
(n + 11)(n - 10) = 0 ← in factored form
equate each factor to zero and solve for n
n + 11 = 0 ⇒ n = - 11
n - 10 = 0 ⇒ n = 10
However, n > 0 , then n = 10
number of terms which sum to 55 is 10
Answer:
one number= x = 44
the other number= (x-4)= 40
Step-by-step explanation:
one number= x
the other number= (x-4)
x + (x-4) = 84
2x= 84+4
2x= 88
x= 88/2= 44
one number= x = 44
the other number= (x-4)= 40
Answer: The height of the telephone pole = $15.046
Step-by-step explanation:
Given: Angle of elevation= 62 degrees.
Distance of Ben from the base of the pole = 8 feet
According to trigonometry, we have
i.e.
Hence, The height of the telephone pole = $15.046
Answer:
g(x)= x+1
Step-by-step explanation:
Given ![f(x)= \sqrt[3]{x+2}](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Csqrt%5B3%5D%7Bx%2B2%7D)
, ![f(x)= \sqrt[3]{x+3}](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Csqrt%5B3%5D%7Bx%2B3%7D)
![f(g(x))= \sqrt[3]{x+3}](https://tex.z-dn.net/?f=f%28g%28x%29%29%3D%20%5Csqrt%5B3%5D%7Bx%2B3%7D)
Replace x with g(x)
![f(g(x))= \sqrt[3]{g(x)+2}](https://tex.z-dn.net/?f=f%28g%28x%29%29%3D%20%5Csqrt%5B3%5D%7Bg%28x%29%2B2%7D)
Now we need to find out what we plug in for g(X) to get x+3 under the radical
g(x) +2 is under the radical. we need x+3 , so we replace g(x) with x+`
So g(x)+2 becomes x+1+2 is x+3
Hence g(x) is x+1
Hello there!
It would be 11x² - 3x - 3.
Hope This Helps You!
Good Luck :)
