Find the value of x round to the nearest degree
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a square with side length s has an area of 324 square centimeters. this equation shows the area of the square: s^2= 324. what is the side length of the square in centimeters?
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Initial number of blue marbles: 8
First pick:
p(blue marble) = 8/15
Since the marble from the first pick is returned to the bag, the bag still contains 8 blue marbles and a total of 15 marbles.
Second pick:
p(blue marble) = 8/15
Overall:
p(blue marble followed by blue marble) =
= p(blue marble) * p(blue marble)
= 8/15 * 8/15
= 64/225
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The amount of work required to stretch 9 inches beyond the natural length will be 4.5 ft-lb
Given data:
To determine the work required to stretch the spring 9 inches beyond its natural length, use the concept of Hooke's Law.
Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.
Given that stretching the spring by 2 ft requires 12 ft-lb of work, determine the constant of proportionality.
The constant of proportionality (k) represents the stiffness of the spring and can be calculated using the formula:
k = work / displacement
k = 12 ft-lb / 2 ft
k = 6 lb/ft
Now, calculate the work required to stretch the spring 9 inches (0.75 ft) beyond its natural length using the same constant of proportionality:
work = k * displacement
work = 6 lb/ft * 0.75 ft
work = 4.5 ft-lb
Hence, it would require 4.5 ft-lb of work to stretch the spring 9 inches beyond its natural length.
To learn more about Hooke's law, refer:
#SPJ12
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Answer:Randy made 64 balloon animals and his sister made 32 balloon animals.
Step-by-step explanation:
Let x represent the number of balloon animals that Randi made.
Let y represent the number of balloon animals that her sister made.
Randi and her sister made balloon animals and sold the for. $0.50 each at the school carnival. They made $48.00. This means that
0.5x + 0.5y = 48 - - - - - - - - - -1
Randi made twice as many balloons as her sister. This means that
x = 2y
Substituting x = 2y into equation 1, it becomes
0.5 × 2y + 0.5y = 48
y + 0.5y = 48
1.5y = 48
y = 48/1.5 = 32
x = 2y = 2 × 32
x = 64
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Answer:
○ C. The lines are perpendicular.
Step-by-step explanation:
In order for equations to be perpendicular,their rate of changes [slopes] must be OPPOSITEMULTIPLICATIVEINVERSES, which in this case is so:
− to +}
> OPPOSITE
+ to −}
MULTIPLICATIVE INVERSE [RECIPROCAL]
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