Answer:
4 trips
Step-by-step explanation:
there are 892 bales of hay
each one weighs about 62.5 pounds
892 * 62.5 = 55,750
George's truck can only carry 8 tons
1 ton = 2,000 pounds
2,000 * 8 = 16,000 pounds
So,
55,750 / 16,000 = 3.484375
But since you can't make 3.484375 trips in a truck, round it up.
3.484375 rounded up equals 4
George has to take 4 trips
The given matrix equation is,
![1.5\left[\begin{array}{cc}x&6\\8&4\end{array}\right] +y\left[\begin{array}{cc}1&4\\3&2\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right]](https://tex.z-dn.net/?f=%201.5%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%266%5C%5C8%264%5Cend%7Barray%7D%5Cright%5D%20%2By%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%264%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20)
.
Multiplying the matrices with the scalars, the given equation becomes,
![\left[\begin{array}{cc}1.5x&9\\12&6\end{array}\right] +\left[\begin{array}{cc}y&4y\\3y&2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%269%5C%5C12%266%5Cend%7Barray%7D%5Cright%5D%20%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dy%264y%5C%5C3y%262y%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20%20)
Adding the matrices,
![\left[\begin{array}{cc}1.5x+y&9+4y\\12+3y&6+2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%2By%269%2B4y%5C%5C12%2B3y%266%2B2y%5Cend%7Barray%7D%5Cright%5D%20%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20)
Matrix equality gives,
Solving the equations together,
We can see that the equations are not consistent.
There is no solution.
Let’s find the area of the rectangular cake and the square pieces.
I’m going to turn the fractions into decimals since it’s easier for me.
13.5•9
121.5
Now find the area of the square pieces.
2.25•2.25
5.0625
Now divide the area of the cake by the pieces to find how many can fit.
121.5/5.0625
24
So, 24 square pieces can be cut out of the rectangular cake.
GCF(9; 15) = 3
9 = 3 · 3
15 = 3 · 5
9 + 15 = 3 · 3 + 3 · 5 = 3·(3 + 5)
Used distributive property: a(b + c) = ab + ac
(x2-y1)²+(2xy)1 =
x⁴-2x²y²+y⁴+4x²y² =
x⁴+2x²y²+y⁴=
(x²+y²)²
