Answer:
an = 1/2 (n) (n+1)
Step-by-step explanation:
1,3,6,10,.........
3-1=2
6-3=3
Each term is different so there is no common difference. It is not an arithmetic sequence
3/1=3
6/3 =2
Each term is different so there is no common ratio. It is not a geometric sequence
1 3 6 10
+2 +3 +4
a1 = 1
a2 = 3
a3 = 6 = 2*3
a4 = 10 = 2*5
Answer:
b) i) Curve A
ii) - 1.75
iii) x = 1 - √5 or x = 1 + √5
Step-by-step explanation:
b) i) We are given a function y = x² - 2x - 3 and the graph of this function is also shown in the side diagram.
The equation can be rearranged to y = (x - 1)² - 4
⇒ (x - 1)² = y + 4
Therefore, this is an equation of a parabola having the vertex at (1,-4) point and its axis is parallel to the positive y-axis.
So, the curve A represents the equation given. (Answer)
ii) Now, at x = 2.5, f(x) = 2.5² - 2 × 2.5 - 3 = - 1.75 (Answer)
iii) When y = 1, then x² -2x - 3 = 1
⇒ x² - 2x - 4 = 0
⇒ (x - 1)² - 5 = 0
⇒ (x - 1)² - (√5)² = 0
⇒ (x - 1 + √5)(x - 1 - √5) = 0
⇒ x = 1 - √5 or x = 1 + √5 (Answer)
Answer:
23 should have been subtracted from, not added to, both sides of the equation.
Answer:
The lenght of the first piece is 6 feet.
The lenght of the second piece is 18 feet.
The lenght of the third piece is 30 feet.
Step-by-step explanation:
Let be:
the lenght of the first piece (in feet).
the lenght of the second piece (in feet).
the lenght of the third piece (in feet).
You know that the total lenght of the piece of siding is 54 feet. This means that:

Having this expression, you can solve for "x":

Therefore, the lenght of the first piece is 6 feet.
Then:
(The lenght of the second piece is 18 feet)
(The lenght of the third piece is 30 feet)