Answer:
a) $800+$300+$249.99=$1,349.99
b) 5.55% * 1349.99= $74.92
c) $74.92 + $1,349.99 = $1,424.91
Any arithmetic sequence can be expressed as:
a(n)=a+d(n-1), a=initial term, d=common difference, n=term number.
We are told that a=4 and d=6 so we have:
a(n)=4+6(n-1), so the 39th term is:
a(39)=4+6(38)
a(39)=4+228
a(39)=232
Answer:
y = 60
Step-by-step explanation:
<h3>Step 1: Make sense of the given</h3>
"The ratio of y to x is 3"
This means that, ![y\div x=3](https://tex.z-dn.net/?f=y%5Cdiv%20x%3D3)
"The sum of y and x is 80"
This means, ![x+y=80](https://tex.z-dn.net/?f=x%2By%3D80)
<h3>Step 2: Make use of the facts</h3>
If
, then
.
We can plug this into the other equation by substitution:
![x + (3 * x)=80](https://tex.z-dn.net/?f=x%20%2B%20%283%20%2A%20x%29%3D80)
This simplifies to:
![4x = 80](https://tex.z-dn.net/?f=4x%20%3D%2080)
Which we can solve out and get:
.
<h3>Step 3: Plug and Chug</h3>
We solved for x, but we need the value of y.
So, we go back to the equation we first derived: "
".
And now we substitute the value of x, into this.
![y = (3 * (20))](https://tex.z-dn.net/?f=y%20%3D%20%283%20%2A%20%2820%29%29)
By solving this out, we get:
![y=60](https://tex.z-dn.net/?f=y%3D60)
So, the value of y is 60.
Let l and w be the length and width of the rectangle. We are given the proportion 2l=4w, which implies l=2w.
The perimeter of a rectangle is given by 2(l+w). We know that the perimeter is 80, and we can plug l=2w to get
![2(l+w)=80 \iff 2(2w+w)=80 \iff 3w=40 \iff w=\dfrac{40}{3}](https://tex.z-dn.net/?f=2%28l%2Bw%29%3D80%20%5Ciff%202%282w%2Bw%29%3D80%20%5Ciff%203w%3D40%20%5Ciff%20w%3D%5Cdfrac%7B40%7D%7B3%7D)
Which, in turn, implies that
![l=2w=\dfrac{80}{3}](https://tex.z-dn.net/?f=l%3D2w%3D%5Cdfrac%7B80%7D%7B3%7D)
Answer:
Segment GD is half the length of segment HC.
Step-by-step explanation: