Answer:
a=6 b=4 z=2
Step-by-step explanation:
Answer:
6 ft and 8 ft
Step-by-step explanation:
let x be the length of one leg then (x + 2) is the other leg.
Using Pythagoras' identity in the right triangle, that is
x² + (x + 2)² = 10² ← expand left side and simplify
x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )
2x² + 4x - 96 = 0 ( divide all terms by 2 )
x² + 2x - 48 = 0 ← in standard form
(x + 8)(x - 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x - 6 = 0 ⇒ x = 6
But x > 0 ⇒ x = 6
Thus the 2 sides are 6 ft and x + 2 = 6 + 2 = 8 ft
Comment
There are 4 terms in this series
That's because the summation (Sigma) goes from 3 to 6 inclusive. So k takes on values of 3,4,5,6
You could use this summation formula
Formula
Sum = (a + L)n/2
Substitution
a is the first term.
k = 3 for the first term
a = -5k + 20
a = -5(3) + 20
a = -15 + 20
a = 5
For the last term k = 6
L = -5(6) + 20
L = -30 + 20
L = - 10
Sum
Sum = (5 - 10)*4/2
Sum = -5 * 2
Sum = -10
Comment
You may wonder how come the last term and the sum are the same. The reason to be found by figuring out the 4 terms and adding them together.
When k = 3, -5k + 20 = -15 + 20 = 5
When k = 4, -5k + 20 = -20 + 20 = 0
When k = 5, -5k + 20 = -25 + 20 = -5
When k = 6, -5k + 20 = -30 + 20 = -10
Sum = 5 + 0 - 5 - 10 = - 10
Conclusion.
It is an accident of the numbers.
Answer: - 10 = the Sum
(2y + 5)° = 4y °
- 4y + 2y° = -5°
-2y° = -5°
y =5/2
There are only two numbers that are 10 away from 0 it would be 10 and -10
