For squrae
area=side²
perimiter=4(side)
for circle
area=pir²
circumference=2pir
side=diameter, diameter/2=radius=side/2
find area not covered
that is areasquare-areacircle
areasquare=26²=676 sqauare inches
areaciecle, diameter=side, 26/2=13, area=pi13²=169*3.14=530.66 square inches
areanotcovered=676-530.66=145.34 square inches not coverd
ratio of perimiter to circumferece
perimiter=4*26=104
circumference=2pir=2pi13=26pi=26*3.14=81.64
circumference to perimiter is 81.64/104=0.785
Area of square = s^2
Area of Rectangle = lw
l = 2s
w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
Using distance between two points to find the lengths of the edges of the triangle, the correct option is:
b. Isosceles
The distance between two points,
and
, is given by:
![d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D)
Vertex D is translated 4 units to the right is (9,8).
The lengths of the edges are:
![DN = \sqrt{(9 - (-3))^2 + (8 - 10)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}](https://tex.z-dn.net/?f=DN%20%3D%20%5Csqrt%7B%289%20-%20%28-3%29%29%5E2%20%2B%20%288%20-%2010%29%5E2%7D%20%3D%20%5Csqrt%7B12%5E2%20%2B%202%5E2%7D%20%3D%20%5Csqrt%7B148%7D)
![DO = \sqrt{(9 - (-3))^2 + (8 - 6)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}](https://tex.z-dn.net/?f=DO%20%3D%20%5Csqrt%7B%289%20-%20%28-3%29%29%5E2%20%2B%20%288%20-%206%29%5E2%7D%20%3D%20%5Csqrt%7B12%5E2%20%2B%202%5E2%7D%20%3D%20%5Csqrt%7B148%7D)
![NO = \sqrt{(-3 - (-3))^2 + (10 - 6)^2} = \sqrt{0^2 + 4^2} = 4](https://tex.z-dn.net/?f=NO%20%3D%20%5Csqrt%7B%28-3%20-%20%28-3%29%29%5E2%20%2B%20%2810%20-%206%29%5E2%7D%20%3D%20%5Csqrt%7B0%5E2%20%2B%204%5E2%7D%20%3D%204)
<u>Two edges of the same length</u>, hence, it is an isosceles triangle, given by option b.
You can learn more about distance between two points at brainly.com/question/18345417
Answer: d) 0.9693
<u>Step-by-step explanation:</u>
refer to the z-table attached.
The table shows the percent from the MEAN. The percent below the mean is 50% so that needs to be added to the value in the table.
Look on the left side for 1.8 and the top for 0.07 (which is 1.87).
The value is 0.4693 --> add 0.5 to that value to get 0.9693.