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ser-zykov [4K]
3 years ago
7

Casey has n nickels. Megan has 4 times as many nickels as Casey has. Write and expression for the total number of nickels Casey

and Megan have. Then simplify the expression.
Mathematics
1 answer:
AnnyKZ [126]3 years ago
6 0

Step-by-step explanation:

Let n be the number of nickels that Casey has.

We are told that Megan has 4 times as many nickels as Casey has, therefore, the number of nickels that Megan has will be 4*n.

Now we will add the amounts of nickels that Casey and Megan have to find the total amount of nickels.

\text{Total number of nickels Casey and Megan have}=n+4*n

Therefore, the expression n+4*n will represent the total number of nickels that Casey and Megan have .

Upon combining like terms we will get,

\text{Total number of nickels Casey and Megan have}=(1+4)n

\text{Total number of nickels Casey and Megan have}=5n

Therefore, Casey and Megan have 5n nickels.

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A BASKETBALL PLAYER MAKES A BASKET THROUGH A TEN FOOT HIGH BASKET FROM 20 FEET AWAY. IF THE SHOOTER RELEASES THE BALL FROM 8 FEE
mixas84 [53]

Answer:

The vertical velocity of the ball when released = 10.81 m/s

The vertical velocity of the ball in the basket = 8.81 m/s

Step-by-step explanation:

The given parameters are;

The height of the basket = 10 feet

The horizontal location of the shooter from the basket = 20 feet

The height from which the shooter releases the ball = 8 feet

The horizontal velocity of the ball = 10 ft/s

Therefore, we have;

Time, t = Horizontal distance/(Horizontal velocity)

t = 20/10 = 2 seconds

The vertical velocity is given as follows;

s = u·t - 1/2·g·t²

Where;

u = The vertical velocity

s = The height above the initial height from which the ball is released

s = y - y₀

Where;

y = The final height of the ball in the calculation = The height of the basket = 10 foot

y₀ = The initial height from which the ball is released = 8 feet

∴ s = 10 - 8 = 2 feet

g = The acceleration due to gravity = 9.81 m/s²

Substituting gives;

2 = u × 2 - 1/2 × 9.81× 2²

u = (2 + 1/2 × 9.81× 2²)/2 = 10.81 m/s

The vertical velocity of the ball when released = 10.81 m/s.

The vertical velocity of the ball in the basket is given by the following relation;

v² = u² - 2·g·s

v² = 10.81² - 2×9.81×2 = 77.6161

v = √(77.6161) = 8.81 m/s

The vertical velocity of the ball in the basket = 8.81 m/s

7 0
2 years ago
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VashaNatasha [74]

Answer:

17

Step-by-step explanation:

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2 years ago
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