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inna [77]
2 years ago
10

If A= and B=, find BA.

Mathematics
1 answer:
Oxana [17]2 years ago
4 0

Answer:

Option d.

Step-by-step explanation:

The given matrices are

A=\begin{bmatrix}3&2&-4\\ \:5&-5&-3\\ \:4&1&1\end{bmatrix}

B=\begin{bmatrix}2&-4&1\\ \:5&-3&2\\ \:4&4&-5\end{bmatrix}

We need to find BA.

BA=\begin{bmatrix}2&-4&1\\ \:5&-3&2\\ \:4&4&-5\end{bmatrix}\begin{bmatrix}3&2&-4\\ \:5&-5&-3\\ \:4&1&1\end{bmatrix}

BA=\begin{bmatrix}2\cdot \:3+\left(-4\right)\cdot \:5+1\cdot \:4&2\cdot \:2+\left(-4\right)\left(-5\right)+1\cdot \:1&2\left(-4\right)+\left(-4\right)\left(-3\right)+1\cdot \:1\\ 5\cdot \:3+\left(-3\right)\cdot \:5+2\cdot \:4&5\cdot \:2+\left(-3\right)\left(-5\right)+2\cdot \:1&5\left(-4\right)+\left(-3\right)\left(-3\right)+2\cdot \:1\\ 4\cdot \:3+4\cdot \:5+\left(-5\right)\cdot \:4&4\cdot \:2+4\left(-5\right)+\left(-5\right)\cdot \:1&4\left(-4\right)+4\left(-3\right)+\left(-5\right)\cdot \:1\end{bmatrix}

BA=\begin{bmatrix}-10&25&5\\ 8&27&-9\\ 12&-17&-33\end{bmatrix}

Hence, option (d) is correct.

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Answer:

There are 80 nickels, 120 dimes and 300 quarters in the piggy bank.

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Step-by-step explanation:

Please consider the complete question:

There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels there are 3 dimes. For every 2 dimes there are 5 quarters. There are 500 coins total. How many nickels, dimes, and quarters are in the piggy bank? Explain your reasoning. How much are the coins in the piggy bank worth?

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For every 2 dimes there are 5 quarters. We can represent this information in an equation as:

\frac{2}{d}=\frac{5}{q}...(2) or  

q=\frac{5d}{2}...(2)  

There are 500 coins total. We can represent this information in an equation as:

n+d+q=500...(3)

We will use substitution method to solve our given system.

Upon substituting equation (1) and equation (2) in equation (3), we will get:

\frac{2d}{3}+d+\frac{5d}{2}=500  

Multiply the equation by 6:

\frac{2d}{3}*6+d*6+\frac{5d}{2}*6=500*6  

2d*2+6d+5d*3=3000  

4d+6d+15d=3000  

25d=3000  

\frac{25d}{25}=\frac{3000}{25}  

d=120  

Therefore, there are 120 dimes in the piggy bank.

Upon substituting d=120 in equation (1), we will get:

n=\frac{2(120)}{3}

n=2(40)

n=80

Therefore, there are 80 nickels in the piggy bank.

Upon substituting d=120 in equation (2), we will get:

q=\frac{5d}{2}  

q=\frac{5(120)}{2}  

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q=300  

Therefore, there are 300 quarters in the piggy bank.

Now, we need to find the value of all coins.

We know 1 quarter is worth $0.25, so 300 quarters will be worth \$0.25\times 300=\$75.

We know 1 dime is worth $0.10, so 120 dimes will be worth \$0.10\times 120=\$12.

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\text{All coins worth}=\$75+\$12+\$4

\text{All coins worth}=\$91

Therefore, all coins in the piggy bank worth $91.

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