Answer:
378.5 or just 378
Step-by-step explanation:
This is a linear model with x representing the number of generations that's gone by, y is the number of butterflies after x number of generations has gone by, and the 350 represents the number of butterflies initially (before any time has gone by. When x = 0, y = 350 so that's the y-intercept of our equation.)
The form for a linear equation is y = mx + b, where m is the rate of change and b is the y-intercept, the initial amount when x = 0.
Our rate of change is 1.5 and the initial amount of butterflies is 350, so filling in the equation we get a model of y = 1.5x + 350.
If we want y when x = 19, plug 19 in for x and solve for y:
y = 1.5(19) + 350
y = 378.5
Since we can't have .5 of a butterfly we will round down to 378
Simply you can substitute theta=45 degrees (or any angle,not zero) in left hand side and right hand side.
or
using a^2 - b^2 =(a+b)(a-b)
= sin(2x+x)sin(2x-x)
= sin 3x sin x
Answer:
an = 12 -7(n-1)
an = 19-7n
Step-by-step explanation:
The explicit formula for an arithmetic sequence is
an = a1 +d(n-1) where a1 is the first term and d is the common difference
a1 =12
We find d by taking the second term and subtracting the first term
d = 5-12
d = -7
an = 12 -7(n-1)
We can simplify this
an = 12 -7n+7
an = 19-7n
144/36 in lowest terms is 4.
To show my work, here.
1. Find the GCF of 144 and 36 so now we divide (144/36 = 4 and 36/36 is 1)
2. Now we have 4/1 so we simplify again so divide 4/1 and its 4
