I think the answer is third one. Hoped this helped!
Answer:
The perpendicular line 4x − 5y = 20 has a slope of 4/5 and as such, the slope of the required line = -5/4
(y - 3)/(x + 4) = -5/4 simplify to get the required equation: 5x + 4y + 8 = 0
Answer:
a²+1/a² = 7
Step-by-step explanation:
Given, a = (3+√5)/2
We have to find the value of a² + 1/a².
1/a = 1/((3+√5)/2) = 2/(3+√5)
By taking conjugate,
2/(3+√5) = 2/(3+√5) × (3-√5)/(3-√5)
= 2(3-√5) / (3+√5)(3-√5)
By using algebraic identity,
(a - b)(a + b) = a² - b²
(3+√5)(3-√5) = (3)² - (√5)²
= 9 - 5
= 4
2(3-√5) / (3+√5)(3-√5) = 2(3-√5) / 4
So, 1/a = (3-√5)/2
Now, a² = [(3+√5)/2]²
= (3+√5)²/4
By using algebraic identity,
(a + b)² = a² + 2ab + b²
(3+√5)² = (3)² + 2(3)(√5) + (√5)²
= 9 + 6√5 + 5
= 14 + 6√5
a² = (14+6√5)/4
= 2(7+3√5)/4
a² = (7+3√5)/2
Now, 1/a² = [(3-√5)/2]²
= (3-√5)²/4
By using algebraic identity,
(a - b)² = a² - 2ab + b²
(3-√5)² = (3)² - 2(3)(√5) + (√5)²
= 9 - 6√5 + 5
= 14 - 6√5
1/a² = (14-6√5)/4
1/a² = (7-3√5)/2
a²+1/a² = (7+3√5)/2 + (7-3√5)/2
= 7/2 + 3√5/2 + 7/2 - 3√5/2
= 7/2 + 7/2
= 7
Therefore, a²+1/a² = 7
1(x)+3=total cost
x=the number of rides you go on
Answer:
y=45000(1-0.03)^x
Step-by-step explanation:
1) the exponential decay formula is
y=c(1-r)^x
where c= starting amount
r=rate of change
x=time
so
y=45000(1-0.03)^x
y=45000-1350x
