Answer:
5. -2 3/4, -2.2, 2.8, 3 1/8
6. -0.6 , 0.65 , 2/3 , 4/5
Step-by-step explanation:
Answer:
a = 3, b = 0, c = 0, d = -2
Step-by-step explanation:
<em>To find the reflection Multiply the matrices</em>
∵ The dimension of the first matrix is 2 × 2
∵ The dimension of the second matrix is 2 × 3
<em>1. Multiply the first row of the 1st matrix by each column in the second matrix add the products of each column to get the first row in the 3rd matrix.</em>
2. Multiply the second row of the 1st matrix by each column in the second matrix add the products of each column to get the second row of the 3rd matrix
![\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%26-1%5Cend%7Barray%7D%5Cright%5D)
× ![\left[\begin{array}{ccc}0&3&0\\0&0&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%263%260%5C%5C0%260%262%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}(1*0+0*0)&(1*3+0*0)&(1*0+0*2)\\(0*0+-1*0)&(0*3+-1*0)&(0*0+-1*2)\end{array}\right]=\left[\begin{array}{ccc}0&3&0\\0&0&-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%281%2A0%2B0%2A0%29%26%281%2A3%2B0%2A0%29%26%281%2A0%2B0%2A2%29%5C%5C%280%2A0%2B-1%2A0%29%26%280%2A3%2B-1%2A0%29%26%280%2A0%2B-1%2A2%29%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%263%260%5C%5C0%260%26-2%5Cend%7Barray%7D%5Cright%5D)
Compare the elements in the answer with the third matrix to find the values of a, b, c, and d
∴ a = 3
∴ b = 0
∴ c = 0
∴ d = -2
Answer:
2/9
Step-by-step explanation:
16/72 is the same thing as 2/9, just simplified. If you make 16 to 72 in a fraction you get 16/72. You divide them with their GCF which is 8. 16 divided by 8 is 2 and 72 divided by 8 is 9. Therefore the answer is 2/9.
9514 1404 393
Answer:
10
Step-by-step explanation:
Let L and T represent the initial amounts that Leo and Theo had. Let n represent the number of bills exchanged in the first exchange. Then we have ...
L -20n +50n = T -50n +20n . . . . after the first exchange, each has the same
After the second exchange, amounts trade places:
(L +30n) +6(50) = T
Substituting this into the first equation, we get ...
L +30n = ((L +30n) +300) -30n
30n = 300
n = 10
Leo gave Theo ten $20 bills.
_____
<em>Comment on the amounts</em>
Theo started with $600 more than Leo, including exactly 16 $50 bills. Leo had at least 10 $20 bills, so he could make the initial exchange. Whatever initial amount Leo had in excess of that $200 was matched in Theo's initial amount, but Theo must have had that excess in $20 bills only. For example, Leo may have started with $300 as 10×$20 +2×$50, but Theo's initial $900 would need to be 5×$20 +16×$50.
