The sequence is an arithmetic sequence with
a₁ = -4
d = a₂ - a₁
d = -1 - (-4)
d = -1 + 4
d = 3
an = x
Sn = 437
General formula in arithmetic sequence
Formula to find nth term
an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
Sn = n/2 (a₁ + an)
We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
x = 3n - 7
Second equation
Sn = n/2 (a₁ + an)
n/2 (a₁ + an) = 437
n/2 (-4 + x) = 437
n(x - 4) = 874
xn - 4n = 874
Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.
Solve for x, back to the first equatin
x = 3n - 7
x = 3(19) - 7
x = 57 - 7
x = 50
The solution is 50
Answer:
D. 7/12
Step-by-step explanation:
First, find the total number of shirts in his closet:
4 + 3 + 5
= 12
Now, find how many are green or red:
4 + 3
= 7
Since 7 out of 12 shirts are green or red, the probability that Micheal chooses green or red is D. 7/12
Answer:
(7, 46)
Step-by-step explanation:
The offered answer choices have x-values of 7, 9, 10. The corresponding upper limit of y-value is ...
x=7 : y < 8·7 -3 = 53 . . . . . 46 is in the solution set, 60 is not
x=9 : y < 8·9 -3 = 69 . . . . 82 is not in the solution set
x=10 : y < 8·10 -3 = 77 . . . . 89 is not in the solution set
Of the choices offered, only (7, 46) is in the solution set.
<span>-2x – 4 < 10
add 4 to both sides
-2x - 4 + 4 < 10 + 4
simplify
-2x < 14
divide both sides by -2
-2x/-2 < 14/-2
simplify
x < -7</span>
Answer:
25 = x
Step-by-step explanation:
The angles are vertical angles and vertical angles are equal
5x+15 = 6x -10
Subtract 5x from each side
5x-5x+15 = 6x-5x -10
15 = x - 10
Add 10 to each side
15+10 = x-10+10
25 = x
