Answer:
Step-by-step explanation:
Number of nickels = $1 * 1 nickel/$0.05 = 20 nickels
Thickness of 20 nickels = 20 nickels * 1.95 mm = 39 mm
Let's do the same for the quarters. Each quarter is worth $0.25.
Number of quarters = $1 * 1 quarter/$0.25 = 4 quarters
Thickness of 4 quarters = 4 quarters * 1.75 mm = 7 mm
Find the ratio of the two:
39 mm/7 mm = 5.57
1 pair of sides are parallel in a trapezoid
<u>Option A)</u> when y=6 and w= 2, <u>Option B)</u> when y=4 and w=-1 are the TWO correct choices.
Step-by-step explanation:
The given inequality is w<x<y and x>2.
<u>step 1</u>: let us <u>assume that x=3</u>, since it is given that x>2.
<u>step 2</u>: substitute the value of x=3 and each options in the inequality
<u>step 3</u>: option A) w=2, y=6. Then w<x<y = 2<3<6 (the condition satisfies).
option B) w= -1, y=4. Then w<x<y = -1<3<4 (the condition satisfies).
option C) w= 0, y=2. then w<x<y ≠ 0<2<2 (does not satisfies).
option D) w= -2, y=0. then w<x<y ≠ -2<2<0 (does not satisfies).
option E) w= -4, y= -1. then w<x<y ≠ -4<2<-1 (does not satisfies).
Answer:
Let a = side length of a cube
Let S = surface area of a cube
Area of a square = a²
Since a cube has 6 square sides: S = 6a²
To make a the subject:
S = 6a²
Divide both sides by 6:

Square root both sides:

(positive square root only as distance is positive)
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![\sf x=-3-\sqrt{2} \implies (x+[3+\sqrt{2}])=0](https://tex.z-dn.net/?f=%5Csf%20%20x%3D-3-%5Csqrt%7B2%7D%20%5Cimplies%20%28x%2B%5B3%2B%5Csqrt%7B2%7D%5D%29%3D0)
![\sf x=-3+\sqrt{2} \implies (x+[3-\sqrt{2}])=0](https://tex.z-dn.net/?f=%5Csf%20%20x%3D-3%2B%5Csqrt%7B2%7D%20%5Cimplies%20%28x%2B%5B3-%5Csqrt%7B2%7D%5D%29%3D0)
Therefore,
for some constant a
Given the y-intercept is at (0, -5)





Substituting found value of a into the equation and simplifying:
![\sf y=-\dfrac57(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])](https://tex.z-dn.net/?f=%5Csf%20y%3D-%5Cdfrac57%28x%2B%5B3%2B%5Csqrt%7B2%7D%5D%29%20%28x%2B%5B3-%5Csqrt%7B2%7D%5D%29)

