The square root of 1764 using perfect factors is 42
<h3>How to determine the
square root using
perfect factors?</h3>
The number is given as:
1764
Rewrite as
x^2 = 1764
Express 1764 as the product of its factors
x^2 = 2 * 2 * 3 * 3 * 7 * 7
Express as squares
x^2 = 2^2 * 3^2 * 7^2
Take the square root of both sides
x = 2 * 3 * 7
Evaluate the product
x = 42
Hence, the square root of 1764 using perfect factors is 42
Read more about perfect factors at
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Answer:
32 units^2
Step-by-step explanation:
Finding the width and the length:
One side = √[(-1 - (-1)^2 + (5 - (-3))^2]
= √(0 + 64)
= 8.
The adjacent side = √(9-9)^2 + (-3-5)^2
= 8.
Perimeter - 4 *8 = 32 units^2.
We are choosing 2
2
r
shoes. How many ways are there to avoid a pair? The pairs represented in our sample can be chosen in (2)
(
n
2
r
)
ways. From each chosen pair, we can choose the left shoe or the right shoe. There are 22
2
2
r
ways to do this. So of the (22)
(
2
n
2
r
)
equally likely ways to choose 2
2
r
shoes, (2)22
(
n
2
r
)
2
2
r
are "favourable."
Another way: A perhaps more natural way to attack the problem is to imagine choosing the shoes one at a time. The probability that the second shoe chosen does not match the first is 2−22−1
2
n
−
2
2
n
−
1
. Given that this has happened, the probability the next shoe does not match either of the first two is 2−42−2
2
n
−
4
2
n
−
2
. Given that there is no match so far, the probability the next shoe does not match any of the first three is 2−62−3
2
n
−
6
2
n
−
3
. Continue. We get a product, which looks a little nicer if we start it with the term 22
2
n
2
n
. So an answer is
22⋅2−22−1⋅2−42−2⋅2−62−3⋯2−4+22−2+1.
2
n
2
n
⋅
2
n
−
2
2
n
−
1
⋅
2
n
−
4
2
n
−
2
⋅
2
n
−
6
2
n
−
3
⋯
2
n
−
4
r
+
2
2
n
−
2
r
+
1
.
This can be expressed more compactly in various ways.
Answer:
f(x) = 2x+1
Step-by-step explanation:
Equation in slope intercept form y = mx + b where m = slope b = y-intercept
To find slope ,
m = (y2-y1)/(x2 - x1)
m = (3 - 1) / (1 - 0)
m = 32/1
m = 2
y-intercept b = 1
In this case y = 2x + 1 or f(x) = 2x+1
