Answer:
c
Step-by-step explanation:
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:
-10.5
Step-by-step explanation:
Greater a negative number the smaller it is.
Answer:
(3/2,10)
Step-by-step explanation:
Mid point is ((10-7)/2,(13+7)/2)=(1.5,10)
Answer:The number of days it will take to sell the same amount of cookies is 3 and the number of tubs that will be sold is 27
Step-by-step explanation:
Let x represent the number of days it will take either of them to sell the same number of tubs.
Let y represent the total number of tubs that that Joseph will sell in x days.
Let z represent the total number of tubs that that Dwayne will sell in x days.
Joseph has already sold 3 tubs. If Joseph starts selling 8 tubs per day, it means that in x days, the number of tubs that he will sell will be
y = 8x + 3
Dwayne hasn't sold any yet. If Dwayne begins selling 9 tubs per day, it means that in x days, the number of tubs that he will sell will be
z = 9x
To determine the number of days it will take to sell the same amount of cookies, we will equate y to z. It becomes
8x + 3 = 9x
9x - 8x = 3
x = 3
The number of tubs that each will sell will be 9x = 9×3 = 27
