Answer:
(a) This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
Step-by-step explanation:
The equation of direct variation is ...
y = kx
for some constant k. Here, we have x in hours and y in dollars. We can see if k is constant for the values given in the table.
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<h3>constant of variation</h3>
Solving the direct variation formula for k, we have ...
k = y/x
Using the table values, we can see if this is constant:
k = dollars/hour = 10/2 = 20/4 = 30/6 = 40/8 = 5
The "rate of change" is constant at $5 per hour.
The function represents direct variation because it passes through the origin and has a constant rate of change of $5 per hour.
-138 <span>≥ -6(6b - 7)
Start by multiplying everything within the parentheses by -6.
-138 </span><span>≥ -36b + 42
Now move the +42 to the other side, so you're left with -36b. (You do this by subtracting 4242)
-138 - 42 </span><span>≥ -36b
-180 </span>≥ -36b
Divide both sides by -36 to find the value of b.
-180 / -36 ≥ b
5 ≥ b.
The answer is b ≤ 5.
94,320 = 94,320 · 100% = 9,432,000%
The correct answer is option B which is the volume of the prism is 216 km³.
<h3>What is the volume of the prism?</h3>
A prism is a three-dimensional solid with a triangular base called a triangular prism. The volume of the triangular prism is equal to the product of the area of the base and the height of the prism.
The volume of the prism will be calculated by using the formula below:-
V = Area of the base x Height
Since the base is a right-angle triangle so we will calculate the area of the right-angle triangle.
V = Area of the triangle x Height
V = ( 1/2 ) x 8 x 6 x ( 9 )
V = 216 km²
Therefore the correct answer is option B which is the volume of the prism is 216 km³.
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