Answer: $350
Step-by-step explanation:
$700 divided by 2 is 350
The value of the variable x in the equation –x + 8 + 3x = x – 6 is - 14.
<h3>How to find variable in an equation?</h3>
The variables of an equation can be found as follows:
–x + 8 + 3x = x – 6
The variable in the equation is x.
Therefore,
–x + 8 + 3x = x – 6
combine like terms on the left side
-x + 3x + 8 = x - 6
2x + 8 = x - 6
subtract x form both sides of the equation
2x - x + 8 = - 6
x + 8 = -6
subtract 8 from both sides
x = -6 - 8
x = - 14
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Answer: Choice C) 124 square cm
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Explanation:
Let's calculate the area of the trapezoid shown
b1 and b2 are the parallel bases; h is the height of the 2D trapezoid
b1 = 2
b2 = 5
h = 1.5
A = h*(b1+b2)/2
A = 1.5*(2+5)/2
A = 1.5*7/2
A = 10.5/2
A = 5.25
The area of one 2D trapezoid is 5.25 sq cm
There are two of these trapezoids that form the base faces of the trapezoidal prism. So the total base area is 2*5.25 = 10.5 sq cm
Keep this value (10.5) in mind. We'll use it later.
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Now onto the lateral surface area (LSA)
It turns out that the formula for the LSA is
LSA = p*d
where
p = perimeter of the trapezoid shown
d = depth or height of the 3D trapezoid (I'm not using h as it was used earlier)
This formula works for any polygonal base. It doesn't have to be a trapezoid.
In this case the perimeter is,
p = 1.7+2+2.65+5
p = 11.35
So
LSA = p*d
LSA = 11.35*10
LSA = 113.5
Add this LSA to the base area found earlier
10.5+113.5 = 124
The total surface area is 124 square cm
The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.
So the disk has a linear speed of
(6000 rev/min) * (12π cm/rev) = 72,000π cm/min
which is equivalent to
(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)
or approximately 135.7 km/h.
