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The value of x is 4.
Given that diagonals of a rectangle measure x+5 feet and 2x+1 feet as shown in the attached figure.
The diagonal of a rectangle is a line or straight line that connects the opposite corners or vertices of the rectangle.
In the given figure ABCD is a rectangle.
OA=2x+1 and OD=x+5 [Given]
AC and BD are diagonals of a rectangle.
As we know that the diagonals of a rectangle are always equal.
So, AC = BD
We can also write it as,
2×OA=2×OD
2×(2x+1) =2×(x+5)
Apply the distributive property a(b+c)=ab+ac, we get
4x+2=2x+10
Subtract 2x from both sides, we get
4x+2-2x=2x+10-2x
2x+2=10
Subtract 2 from both sides, we get
2x+2-2=10-2
2x=8
Divide both sides by 2, we get
2x/x=8/2
x=4
Hence, the value of x=4 when diagonals of a rectangle measure x+5 feet and 2x+1 feet.
Learn more about rectangles from here brainly.com/question/1549055.
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Answer option A
From the given graph is a Vertical ellipse
Center of ellipse = (-2,-3)
Vertices are (-2,3) and (-2,-9)
Co vertices are (-6,-3) and (2,-3)
The distance between center and vertices = 6, so a= 6
The distance between center and covertices = 4 , so b= 4
The general equation of vertical ellipse is
(h,k) is the center
we know center is (-2,-3)
h= -2, k = -3 , a= 6 and b = 4
The standard equation becomes
Foci are (h,k+c) and (h,k-c)
Plug in the a=6 and b=4
, we know h=-2 and k=-3
Foci are and
Option A is correct