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:
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<span>x² + y² + 14x − 4y − 28 = 0
x² +14x +y² - 4y =28
x²+2*7x +7² -7² + y² - 2*2y +2² - 2² = 28
(x+7)² + (y-2)² -7²-2² =28
</span>(x+7)² + (y-2)²=28+49+4
(x+7)² + (y-2)² =81 is the answer.
The sum of b and f is b+f
Three times this sum is 3(b+f)
Using the distributive property, a(b+ c) = ab + ac. In this case, b is 30, so the blank is 30.