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Vaselesa [24]
3 years ago
13

Joey decides to empty his piggy bank and count his money. His bank is filled with only nickels and dimes. Joey counted a total o

f 45 coins that added up to $3.15. How many nickels and how many dimes does Joey have in his piggy bank?
Mathematics
1 answer:
xxTIMURxx [149]3 years ago
5 0

Answer:

Joey has 18 nickles and 27 dimes in his piggy bank.

Step-by-step explanation:

1 nickle = 5 cents

1 dime = 10 cents

$1 = 100 cents

$3.15 = 135 cents

Let

n represent the number of nickles, n>=0

d represent the number of dimes, d>=0

Joey counted a total of 45 coins that added up to $3.15:

n + d = 45

5n + 10d = 315

n = 18 nickles

d = 27 dimes

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Which expression is equivalent to this: "3 multiplied by z"?
LuckyWell [14K]

Answer:

3z

Step-by-step explanation:

When you write a number followed by a variable with no operation in between them, it means multiplication.

3 multiplied by z is 3 * z, but you can write it without the multiplication sign simply as 3z.

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3 years ago
The graph of the quadratic function y = ax^2 + bx + c is given.<br> Find a + b + c.
andrey2020 [161]

Answer:

\frac{145}{24}\approx 6***

Answers may vary depending on the person reading the graph.

It is hard to tell what they think crosses nicely.

For example, I decided that the graph crossed nicely at the following points:

(0,3)

(2,8)

(6,5)

Step-by-step explanation:

I see that the graph crosses at (0,3),(2,8), and (6,5).

The equation y=ax^2+bx+c tells us the y-intercept is c since when x=0 we have y=a(0)^2+b(0)+c=0+0+c=c.

The y-intercept for our graph is 3. Therefore, c=3.

So far we have the equation:

y=ax^2+bx+3.

Let's enter the other points creating a system of linear equations to solve:

8=a(2)^2+b(2)+3

5=a(6)^2+b(6)+3

Let's simplify:

8=4a+2b+3

5=36a+6b+3

Let's subtract 3 on both sides:

5=4a+2b

2=36a+6b

I choose to solve the system by elimination.

Let's multiply the top equation by -3:

-15=-12a-6b

2=36a+6b

Now adding the equations results in:

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Divide both sides by 24:

\frac{-13}{24}=a

Now using one of the equations we can find b:

5=4a+2b with a=\frac{-13}{24}

5=4\frac{-13}{24}+2b

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5+\frac{13}{6}=2b

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\frac{43}{6}=2b

Divide both sides by 2:

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\frac{43}{12}=b

So we have the equation:

y=\frac{-13}{24}x^2+\frac{43}{12}+3

Let's evaluate a+b+c now:

\frac{-13}{24}+\frac{43}{12}+3

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\frac{73+72}{24}

\frac{145}{24}

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3 years ago
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Answer:

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