55 kilograms of aluminum and 345 kilograms of the other metals
Answer:
Step-by-step explanation:
You just have to use the Pythagorean theorem which is A squared plus B squared = C squared. So you have A and B already so just put it in an equation
There are 61 blue marbles
<em><u>Solution:</u></em>
Let "b" be the number of blue marbles
Let "r" be the number of red marbles
Given that bag contains blue marbles and red marbles, 75 in total
number of blue marbles + number of red marbles = 75
b + r = 75 -------- eqn 1
The number of blue marbles is 5 more than 4 times the number of red marbles
number of blue marbles = 5 + 4(number of red marbles)
b = 5 + 4r ------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 2 in eqn 1
5 + 4r + r = 75
5 + 5r = 75
5r = 75 - 5
5r = 70
r = 14
From eqn 2,
b = 5 + 4(14) = 5 + 56 = 61
b = 61
Thus there are 61 blue marbles
Answer: C
<u>Step-by-step explanation:</u>
Use the multiplication rule for matrices - Multiply 1st row of first matrix with 1st column of second matrix and find their sum. Repeat for each row and column.
A x B
![\left[\begin{array}{cc}1&5\\-3&4\end{array}\right] \times \left[\begin{array}{cc}2&6\\6&-1\end{array}\right]=\left[\begin{array}{cc}1(2)+5(6)&1(6)+5(-1)\\-3(2)+4(6)&-3(6)+4(-1)\end{array}\right]\\\\\\.\qquad \qquad \qquad \qquad \qquad \quad =\left[\begin{array}{cc}32&1\\18&-22\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%265%5C%5C-3%264%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%266%5C%5C6%26-1%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%282%29%2B5%286%29%261%286%29%2B5%28-1%29%5C%5C-3%282%29%2B4%286%29%26-3%286%29%2B4%28-1%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cquad%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D32%261%5C%5C18%26-22%5Cend%7Barray%7D%5Cright%5D)
