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3 years ago

can i get some help? i tried figuring it out myself already but i must have done something wrong. please help!

Mathematics

1 answer:

zaharov [31]3 years ago

5 0

First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.

N will represent nickels

D will represent dimes

N + D = 30

---The problem tells us that there are 30 total coins

0.05N + 0.10D = 2.95

---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95

Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.

N + D = 30

N = 30 - D

Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.

0.05(30 - D) + 0.10D = 2.95

1.5 - 0.05D + 0.10D = 2.95

1.5 + 0.05D = 2.95

0.05D = 1.45

D = 29

Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.

N = 30 - D

N = 30 - 29

N = 1

Therefore, there are 29 dimes and 1 nickel.

Hope this helps!

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3 years ago

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Answer:

The equation of the plane is represented by $\frac{1}{18}\cdot x + \frac{1}{18}\cdot y + \frac{1}{18}\cdot z = 1$ .

Step-by-step explanation:

Algebraically speaking, a plane can be represented by following vectorial product:

$(a,b, c)\,\bullet\,(x,y,z) = 1$ (1)

Where:

$a$ , $b$ , $c$ - Plane coeffcients.

$x$ , $y$ , $z$ - Coordinates.

We need three distinct points to determine all coefficients. If we know that $(x_{1},y_{1},z_{1}) = (0,9,9)$ , $(x_{2},y_{2}, z_{2}) = (9,0,9)$ and $(x_{3},y_{3},z_{3}) = (9,9,0)$ , the system of equations to be solved is:

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The solution of this system is $a = \frac{1}{18}$ , $b = \frac{1}{18}$ , $c = \frac{1}{18}$ .

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3 years ago

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