She saves 8.8888888 gallons of gas every week by carpooling.
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:
When squaring a number it is essentially taking a number and multiplying it by itself. For example, 5^2 is 5×5 (=25).
Answer:
∠C (Interior) =78°
∠B (Interior) = 62°
Step-by-step explanation:
Given:
∠A (Interior) = 40°
∠C (exterior) = 102°
Computation:
∠C (Interior) = 180° - 102°
∠C (Interior) =78°
∠B (Interior) = 180° - ∠A (Interior) - ∠C (Interior)
∠B (Interior) = 180° - 78° - 40°
∠B (Interior) = 180° - 118°
∠B (Interior) = 62°
0.71 x 22 is the expression that works, because 1 AUD = 0.71USD.
