Answer:
The formula for the nth term of this sequence is: 31 + (n-1)X6
Step-by-step explanation:
This is an arithmetic sequence (ie. each term is the last term with a fixed value added to it).
T1 =31
T2 = 37 = T1 + 6 = 31 + 6
T3 = 43 = T2 + 6 = 31 + 6 + 6 = 31 + 6X2
…
In general, the nth term is 31 + 6(n-1)
Isosceles triangle has 2 sides that are the same length. So what you have is three sides that measure: x, x, and (x-8). 70 = x + x + (x-8).
70 = x + x + x - 8
78 = 3x
x = 26.
and 26 - 8 = 18.
So two of your sides are 26 inches and the last side is 18 inches.
Answer:
89 sq meters
Step-by-step explanation:
The whole rectangle 13x8 = 104
Now subtract the white triangle
(6x5)/2 = 15
104-15 = 89
Answer:
It is found when the line starts moving up or down.
Step-by-step explanation:
Answer: second option y = 2(x + 7/2)^2 + 1/2
Explanation:
1) given:
y = (x + 3)^2 + (x + 4)^2
2) expand the binomials:
y = x^2 + 6x + 9 + x^2 + 8x + 16
3) add like terms:
y = 2x^2 + 14x + 25
4) take common factor 2 of the first two terms:
y = 2 (x^2 + 7x) + 25
5) complete squares for x^2 + 7x
x^2 + 7x = [x +(7/2)x ]^2 - 49/4
6) substitue x^2 + 7x = (x + 7/2)^2 - 49/4 in the equation for y:
y = 2 [ (x + 7/2)^2 - 49/4] + 25
7) take -49/4 out of the square brackets.
y = 2 (x + 7/2)^2 - 49/2 + 25
8) add like terms:
y = 2(x + 7/2)^2 + 1/2
And that is the vertex for of the given expression.
