Find an explicit formula for the arithmetic sequence 12, 5, -2, -9,...12,5,−2,−9,...12, comma, 5, comma, minus, 2, comma, minus,
Andrew [12]
Answer:
A(n) = 19 - 7n
Step-by-step explanation:
12, 5, -2, -9,...
First term, a = 12
Common difference, d = a2 - a1
a2 = 5
a1 = 12
Common difference, d = a2 - a1
= 5 - 12
= -7
d = -7
A(n) = a + (n - 1)d
A(n) = 12 + (n - 1) -7
= 12 + (-7n + 7)
= 12 - 7n + 7
= 12 + 7 - 7n
= 19 - 7n
A(n) = 19 - 7n
Answer:
The answer is "GK=37, GH=14, and JK=19 ".
Step-by-step explanation:
In the question, an attachment file is missing.so, please find its attached file.
Given values:
GJ=4x+2
HK=6x-1
GK =37
Find:
HJ=?
GK = GJ+JK
= GJ+(HK-HJ)
= 4x+2+((6x-1)-x)
= 4x+2+6x-1-x
=
9x+1...(a)
Solve equation (a) and put the value of x in the equation:
=9(4)+1
=36+1
=37
find GH and JK=?
Given:
GK=37
Formula:
GH = GJ-HJ
= 4x+2- x
= 3x+2....(b)
Solve equation (a):
GK= 9x+1
37=9x+1
36=9x
x=4....(c)
put the value of equation (b) in equation (c)
GH = 3x+2
= 3(4)+2
= 12+2
= 14
Formula:
JK= HK-HJ
= 6x-1- x
= 5x-1
put the value of x in the above equation:
= 5(4)-1
= 20-1
=19
Answer: y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction
or

Step-by-step explanation:
Vertex form of equation :
where (h, k) is the vertex of the parabola.

Hence, the vertex form of the equation is 
we know that
The intersection point of both graphs is a common point for both functions, for which for the same input value, both functions will have the same output value.
so
the point of intersection is 
for an input value equal to 
the output value for both functions is 
therefore
<u>the answer is the option</u>
X= 4