Answer:
= 5n - 2
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₄ = 18 , then
a₁ + 3d = 18 , that is
3 + 3d = 18 ( subtract 3 from both sides )
3d = 15 (divide both sides by 3 )
d = 5
Then
= 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2 ← explicit rule
A. that is b^2-4ac
for
ax^2+bx+c
the deterimant (part under the radicand)
is b^2-4ac
if it is
1. less than 0 then there are no real solutions
2. eqal to 0 then there is 1 real solution
3. greater than 0, there are 2 real roots
9x^2-16x+60
b^2-4ac=(-16)^2-4*9*60=256-2160<0
no real solutions
B. grouping
ac method
4 times -5=-20
what 2 numbers multiply to get -20 and add to get 8?
-2 and 10
seperate the middle number to get that
4x^2-2x+10x-5=0
(4x^2-2x)+(10x-5)=0
2x(2x-1)+2(2x-1)=0
(2x-1)(2x+2)=0
set equal to 0
2x-1=0
2x=1
x=1/2
2x+2=0
2x=-2
x=-1
x=1/2 or -1
My apologies this is only for a reward to ask questions myself .
Answer: 1: row 3
2: Row 2
3: 6 and 10
Step-by-step explanation:I just did it
The standard form of hyperbola is:
(x-h)²/a²-(y-k)²/b²=1
center:(4,5)
Length of the horizontal transverse axis: 8-5=3=2a
thus
a=3/2
a²=9/4
b=2
b²=4
Hence the equation will be:
(x-4)²/(9/4)-(y-5)²/4=1
simplifying this we get:
[4(x-4)²]/9-(y-5)²/4=1
