9514 1404 393
Answer:
10
Step-by-step explanation:
The n-th triangular number is given by ...
t(n) = n(n+1)/2
We went to find n when t(n) = 55.
55 = n(n+1)/2
110 = n(n+1)
Adding 1/4 completes the square.
110.25 = (n +0.5)^2
√110.25 = n+0.5 . . . . . we are interested in the positive value of n
n = 10.5 -0.5 = 10
The triangular number that has 55 dots in its shape is the 10-th number.
__
<em>Additional comment</em>
Here, we have gone to the trouble to formally complete the square to find the value of n. You may realize that it isn't really necessary to go to that trouble.
A reasonable estimate of the value of n is possible by considering that the product n(n+1) is a little more than n², so the value of n will be a little less than √110 ≈ 10.49. The nearest integer is 10, which is the answer we're looking for.
Slope is rise/ run, or change in y/ change in x. the error was that the person out run/rise, so the correct answer is 4/6.
Each sweater is $35
B/c in total it was $160
And we know that the skirt is $20
So we do 160-20 which is equal to 140
There are 4 sweaters so 140 divided by 4 which is
$35. !!!! Yayayayay
Answer: 
Step-by-step explanation:
For this exercise you need to remember that a Square is defined as a Quadrilateral whose sides are equal in lenght and all its interios angles measure 90 degrees.
Based on that definition, and observing the squarE given in the picture attached, you can write the following equation:
Then, you need to solve for the variable "x" in order to find its value. You get that this is:
Now, knowing the value of "x" you can susbstitute it into any expression that represents the side of the square, and then you must evaluate in order to find the lenght of the side.
You get:
