Answer:
The area of the rectangle is 42 units^2
Step-by-step explanation:
we know that
The area of rectangle is equal to
In this problem
AB=DC
BC=AD
see the attached figure with letters to better understand the problem
we have that
the formula to calculate the distance between two points is equal to
we have the points
<em>Find out the distance BC</em>
we have
substitute in the formula
<em>Find out the distance AB</em>
we have
substitute in the formula
<em>Find out the area</em>
we have
substitute
Well this is simple a calculator type problem...but if you are curious as the the algorithm used by simple calculators and such...
They use a Newtonian approximation until it surpasses the precision level of the calculator or computer program..
A newtonian approximation is an interative process that gets closer and closer to the actual answer to any mathematical problem...it is of the form:
x-(f(x)/(df/dx))
In a square root problem you wish to know:
x=√n where x is the root and n is the number
x^2=n
x^2-n=0
So f(x)=x^2-n and df/dx=2x so using the definition of the newton approximation you have:
x-((x^2-n)/(2x)) which simplifies further to:
(2x^2-x^2+n)/(2x)
(x^2+n)/(2x), where you can choose any starting value of x that you desire (though convergence to an exact (if possible) solution will be swifter the closer xi is to the actual value x)
In this case the number, n=95.54, so a decent starting value for x would be 10.
Using this initial x in (x^2+95.54)/(2x) will result in the following iterative sequence of x.
10, 9.777, 9.774457, 9.7744565, 9.7744565066299210578124802523397
The calculator result for my calc is: 9.7744565066299210578124802523381
So you see how accurate the newton method is in just a few iterations. :P
Answer: C. (-4, -2)
<u>Step-by-step explanation:</u>
First, eliminate one of the variables and solve for the remaining variable:
2x - 5y = 2 → 3(2x - 5y = 2) → 6x - 15y = 6
3x + 2y = -16 → -2(3x + 2y = -16) → <u> -6x - 4y = 32</u>
-19y = 38
y = -2
Next, replace "y" with -2 into either of the original equations to solve for x:
2x - 5y = 2
2x - 5(-2) = 2
2x + 10 = 2
2x = -8
x = -4
x = -4, y = -2
<u>Check:</u>
Plug in the x- and y-values into the other original equation:
3x + 2y = -16
3(-4) + 2(-2) = -16
-12 + -4 = -16
-16 = -16 
It's not rigid because dilations (scale factor not equal to 1) change the length of the segments, or the distances between the points. You'll get a similar figure but it won't be congruent. For example, if the scale factor is 3, then the distances will be three times as large; or the lengths will be 3 times as long.
To be "rigid", the lengths must be kept the same. In contrast, a reflection is rigid because the distances are kept the same. The only thing changing is the orientation (clockwise to counter-clockwise, or vice versa).
Answer:
3
Step-by-step explanation:
im not sure on this sorry i havent dont it in a LONGG time<3
here is how i got it:
3+a
a=1 n=-1
3+1-1
