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ser-zykov [4K]
3 years ago
6

My pigg y bank has only pennies and nicklels in it , and 2/7 of the coins are nickel If i remove 84 pennies then 1/3 of the reme

ning are pennies 1} suppose there are initially p pennies and n nickels in the pigy bank write an equation using the fact that 2/7 of the coins initially in the
Mathematics
1 answer:
zubka84 [21]3 years ago
4 0

Answer:

There are 105 pennies in the piggy bank.

There are 42 nickels in the piggy bank.

Step-by-step explanation:

there are:

p pennies in the piggy bank

n nickels in the piggy bank

Then we can define T, the total number of coins, as:

T = p + n

We know that 2/7 of the total number of coins are nickels.

This can be written as:

n = (2/7)*T = (2/7)*(n + p)

And if we remove 84 pennies, 1/3 of the remaining coins are pennies.

This can be written as:

p - 84 = (1/3)*(n + p - 84)

Then we have a system of two equations:

n = (2/7)*(n + p)

p - 84 = (1/3)*(n + p - 84)

Let's solve the system, to do it, we first need to isolate one of the variables in one of the equations.

We can isolate n in the first one, to get:

n = (2/7)*(n + p) = (2/7)*n + (2/7)*p

n - (2/7)*n = (2/7)*p

n*(5/7) = (2/7)*p

n = (7/5)*(2/7)*p = (2/5)*p

n = (2/5)*p

Now we can replace this in the other equation:

p - 84 = (1/3)*(n + p - 84)

p - 84 = (1/3)*( (2/5)*p + p - 84)

Let's solve this for p

p - 84 = (1/3)*( (7/5)*p - 84)

3*(p - 84) = (7/5)*p - 84

3p - 252 = (7/5)*p - 84

3*p - (7/5)*p = 252 - 84

(15/5)*p - (7/5)*p = 168

(8/5)*p = 168

p = (5/8)*168 = 105

There are 105 pennies in the piggy bank.

And we know that:

n = (2/5)*p = (2/5)*105 = 42

There are 42 nickels in the piggy bank.

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Answer: D.) g(x) = 6(3)^{-x}


Step-by-step explanation: We are given an exponential function f(x).

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According to rules of transformations y=f(-x).

That is variable x is being multiplied by a negative sign.

In the given options g(x) = 6(3)^{-x}, the variable x is being multiplied by a negative sign.

Therefore, correct option is D option.


4 0
3 years ago
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Kathy needs money for a trip to Europe if she has US$300 in the bank but wants to withdraw half of it In British pounds and half
Aleks [24]

Answer: She has 21.63 more euros than pounds and has 1.23 times more euros than pounds.

Step-by-step explanation:

She has US$300, and she will withdraw half of it on pounds, and half of it in euros.

(half of US$300 is US$150)

We know that:

1 pound = US$1.6

(1 pound/US$1.6) = 1

Then US$150 = US$150*(1 pound/US$1.6) = (150/1.6) pounds = 93.75 pounds.

And we also know that:

1 euro = US$ 1.3

then:

(1 euro/US$ 1.3) = 1

This means that:

US$150 = US$150*(1 euro/US$ 1.3) = (150/1.3) euros = 115.38 euros.

This means that:

115.38 - 93.75 = 21.63

This means that she has 21.63 more euros than pounds.

and:

115.38/93.75 = 1.23

She has 1.23 times more euros than pounds.

6 0
2 years ago
How do you find out a Pythagorean triple?
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3 years ago
A raft travels down river at a rate of 6 miles per hour. The total distance d in miles that the raft travels is equal to the rat
Fudgin [204]

Answer:

d=6h

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Speed of the raft= 6 miles per hour

Total distance (d) of the raft= rate × number of hours

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Dependent variable is the distance (d)

Equation for the situation

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h=number of hours

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d=r*h

d=6*h

d=6h

8 0
3 years ago
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katovenus [111]
Volume ratio = 1331/729 which is the cube of the linear scale factor.
To find the linear scale factor, let find the cubic root of the numerator & the denominator:

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&  ∛729 = ∛9³  = 9

So the linear scale is 11/9 ==> then the ratio of their surface area will be:

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