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
The two triangles are similar, so will have a direct scale factor. We can find this by using the given measurements, 10÷8=1.25. So the scale factor from the smaller to the bigger triangle is 1.25. This means that 1.25×(x+6)=AE. We can solve this as we would with a regular linear equation:
1.25(x+6)=2x+6
1.25x+7.5=2x+6
1.5=0.75x
2=x
∴ AE is 2x+6=10
2 didved 15 times 2 see what you get that your anwers\
83.2111111111.
0.09 fits into 7.498, 83.2111111111
Set up the following equations:
x represents car A's speed, and y represents car B's speed.
We'll use elimination to solve this system of equations. Multiply the first equation by 7:
Combine both equations:
Divide both sides by 28 to get x by itself:
The speed of car A is
80 mph.Since we now know the value of one of the variables, we can plug it into the first equation:
Subtract 160 from both sides.
Divide both sides by 2 to get y by itself:
The speed of car B is
60 mph.
