16 - 5(3t - 4) = 8(-2t + 11) <em>use distributive property</em>: <em>a(b + c) = ab + ac</em>
16 - (5)(3t) - (5)(-4) = (8)(-2t) + (8)(11)
16 - 15t + 20 = -16t + 88
36 - 15t = -16t + 88 <em>subtract 36 from both sides</em>
-15t = -16t + 52 <em>add 16t to both sides</em>
t = 52
Answer:
nth term = 523 + 24(n - 1
Step-by-step explanation:
This is modelled by an arithmetic series where first term a1 = 523 and common difference d = 24.
nth term = a1 + d(n - 1).
Here it is 523 + 24(n - 1) (answer)
Answer: 0.845
Step-by-step explanation: 1.69 divided by two is 0.845
Answer:
In 1981, the Australian humpback whale population was 350
Po = Initial population = 350
rate of increase = 14% annually
P(t) = Po*(1.14)^t
P(t) = 350*(1.14)^t
Where
t = number of years that have passed since 1981
Year 2000
2000 - 1981 = 19 years
P(19) = 350*(1.14)^19
P(19) = 350*12.055
P(19) = 4219.49
P(19) ≈ 4219
Year 2018
2018 - 1981 = 37 years
P(37) = 350*(1.14)^37
P(37) = 350*127.4909
P(37) = 44621.84
P(37) ≈ 44622
There would be about 44622 humpback whales in the year 2018
We are given : m∠WYX=(2x−1)° and m∠WYZ=(4x+1)°.
∠WYX and ∠WYZ are complementary.
We know, sum of complementary angles is = 90°.
So, we need to add ∠WYX and ∠WYZ and set it equal to 90°.
m∠WYX + m∠WYZ = 90°.
Plugging values of ∠WYX and ∠WYZ in the above equation, we get
(2x−1)° + (4x+1)° = 90°.
Removing parentheses from both sides,
2x-1 + 4x+1 =90.
Combining like terms,
2x+4x= 6x and -1+1 =0
6x +0 =90.
6x=90.
Dividing both sides by 6.
6x/6 =90/6
x= 15.
Plugging value of x=15.
m∠WYX=(2x−1)° = 2*15 -1 = 30 -1 =29
m∠WYZ=(4x+1)° = 4*15 +1 = 60+1 = 61.
Therefore, ∠WYX=29° and ∠WYZ=61°.
