Answer:
Step-by-step explanation:
to find the arithmetic sequence with a4=-1 and a6=-13
first: find the difference: an=a+(n-1)d
a4=-1
that means a1+d(4-1)=-1 ( since a4 given and need to find a1)
a1+3d=-1 first equation
a1+d(6-1)=-13 ( a6 is given)
a1+5d=-13 second equation
a1+3d=-1
a1+5d=-13 ( find a and d by subtraction)
a1+3d-a1-5d=-1-(-13)
2d=12
d=-12/2=-6 ( substitute d in the equation: a1+3d=-1)
difference =-6
a1=17
a1,a2,a3,a4,a5,a6,....
the sequence is : 17,11,5,-1,-7,-13,.....
hope it works
Answer:
x = (-29)/5
Step-by-step explanation:
Solve for x:
(2 (x - 5))/3 = (3 (x + 1))/2
Multiply both sides by 6:
(6×2 (x - 5))/3 = (6×3 (x + 1))/2
6/3 = (3×2)/3 = 2:
2×2 (x - 5) = (6×3 (x + 1))/2
6/2 = (2×3)/2 = 3:
2×2 (x - 5) = 3×3 (x + 1)
2×2 = 4:
4 (x - 5) = 3×3 (x + 1)
3×3 = 9:
4 (x - 5) = 9 (x + 1)
Expand out terms of the left hand side:
4 x - 20 = 9 (x + 1)
Expand out terms of the right hand side:
4 x - 20 = 9 x + 9
Subtract 9 x from both sides:
(4 x - 9 x) - 20 = (9 x - 9 x) + 9
4 x - 9 x = -5 x:
-5 x - 20 = (9 x - 9 x) + 9
9 x - 9 x = 0:
-5 x - 20 = 9
Add 20 to both sides:
(20 - 20) - 5 x = 20 + 9
20 - 20 = 0:
-5 x = 9 + 20
9 + 20 = 29:
-5 x = 29
Divide both sides of -5 x = 29 by -5:
(-5 x)/(-5) = 29/(-5)
(-5)/(-5) = 1:
x = 29/(-5)
Multiply numerator and denominator of 29/(-5) by -1:
Answer: x = (-29)/5
Gwen has already burned 100 calories when Tristan and Keith started, and he continues to burn 10 calories per minute. The equation for Gwen is
y = 100 + 10x
Question 2)
`Tristan is burning 125 calories every 10 minutes. His burning calories rate is 12.5 calories per minute. The equation for Tristan is
y = 12.5x
Question 3)
Keith is burning 300 calories in 30 minutes. His rate per minute is 10 calories per minute. The equation for Keith is
y = 10x
