Answer:
The annual growth rate between 1985 and 2005 is 0.95%
The value of the house in the year 2010 is $152,018
Step-by-step explanation:
Let the annual growth rate = r
Value of the house in year 1985 = $120,000
Value of the house in year 2005 = $145,000
Time (t) = 2005 - 1985
= 20 years
A = P (1 + r)^t
145000 = 120000 (1 + r) ^20
(1 +r)^20 = 145000 / 120000
(1 +r)^20= 1.2083
(1 +r)^20= (1.2083)^1/20
(1 +r)^20= 1.0095
r = 1.0095 - 1
r = 0.0095
r% = 0.0095 x 100
= 0.95%
Value of the house in year 2010
=145000(1 + r)^5
=145000 (1 + 0.0095)^5
= 145000 x 1.0484
=$152,018
Answer:
x = -1/2
Step-by-step explanation:
This question can be solved by applying the laws of indices
In a^n, a - base
n - index
Given
9^x = 1/3
According to the laws of indices, a/b = b^(-a)
Hence we can write, 1/3 = 3^(-1)
9^x = 3^(2x)
Again according to the laws of indices,
a^b = a^n can be written as;
b = n
That is, if in an equation the bases are the same, the indices are also equal.
So we can write,
3^(2x) = 3^(-1)
2x = -1
Divide both sides of the equation by 2, the coefficient of x
2x/2 = -1/2
x = -1/2
Answer:
sandwich = 6.50
Step-by-step explanation:
Let s = sandwich price
d = drink price
6s + 4d = 53
4s + 6d = 47
Multiply the first equation by 3
18s + 12d = 159
Multiply the second equation by -2
-4s - 12d = -94
Add these equations together
18s + 12d = 159
-8s - 12d = -94
--------------------------
10s = 65
Divide by 10
s = 65/10
s =6.5
Step-by-step explanation:
Initial velocity(u) = 60 km/hr = 50/3 m/s
final velocity(v)= 0 (stops at rest)
acceleration(a) = -0.05 m/s²
display (s)=?
v²-u²=2as
0²- (50/3)= 2(-0.05)s
2500/9= 0.1s
s= 25000/9 m
Answer:
x = 58
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
90 = 32+x
Subtract 32 from each side
90-32 = x
58 =x
