Answer:
x=4
y=4√5
Step-by-step explanation:
Set up 3 right triangles and mark their respective angles. The largest will have sides (in typical a,b,c[hypotenuse] order) y, z, and 10. The middle 8, x, and y. The smallest x, 2, and z.
Then since they are all similar triangles, using the midde and smaller triangles, set up the proportionin which both A sides when divided are equal to the B sides.
So 8/x = x/2
Cross multiply and get 16=x^2.
The square root of 16 is 4, so x is 4.
Then using the larger and middle triangles, do the same for the A and C sides.
So y/8 = 10/y.
Cross multiply and get 80=y^2.
Find the square root of it, which since it doesn't have a perfect square, you use a calculator or the whatever theorem and get √4*4*5 or simply 4√5.
So x = 4 and y = 4√5
Answer:
17
Step-by-step explanation:
QS and RS equal the same
5x - 8 = 3x + 2
-3x +8 -3x +8
2x = 10
x = 5 you would then plug x into QS
5(5) - 8
25 - 8
17
Answer:
44cm for minimum area and 0 for maximum area (circle)
Step-by-step explanation:
Let's C be the circumference of the circle and S be the circumference of the square. If we cut the string into 2 pieces the total circumferences would be the string length 100cm.
S + C = 100 or S = 100 - C
The side of square is S/4 and radius of the circle is 
So the area of the square is


Therefore the total area is

We can substitute 100 - C for S




To find the maximum and minimum of this, we can take the first derivative and set that to 0



If we take the 2nd derivative:

We can see that this is positive, so our cut at 44 cm would yield the minimum area.
The maximum area would be where you not cut anything and use the total string length to use for either square or circle
if C = 100 then 
if S = 100 then 
So to yield maximum area, you should not cut at all and use the whole string to form a circle
Answer:
105cm^2
Step-by-step explanation:
5 times 6 = 30
30 div 2 = 15
6 times 15 = 90
90 + 15 = 105
Answer: Commutative Property
Step-by-step explanation: In Picture.