2 ≥ x ≥ -8 is how this inequality would be displayed.
Answer: 2.11cm
Step-by-step explanation:
Given the following :
The lengths of the parallel sides are (2z + 3) cm and (6z – 1) cm
The area of trapezoid is calculated using the formula:
1/2(a + b) × h
Where ;
a = Length of side 1
b = length of side 2
h = height
Take a = (2z + 3) and b = (6z – 1), h = z
Therefore ;
1/2 (2z + 3 + 6z - 1) × z
Opening the bracket
(z + 1.5 + 3z - 0.5) × z
(4z + 1 ) × z = 20cm^2
4z^2 + z = 20cm^2
Using Quadratic formula:
4z^2 + z - 20 = 0
a = 4, b = 1, c = - 20
(-b±√b^2 -4ac) / 2a
Z = 2.11 or - 2.364
z cannot be negative, therefore,
Z = 2.11 cm
Answer:
![V = \left[\begin{array}{ccc}5&-1\end{array}\right]](https://tex.z-dn.net/?f=V%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
We want to reflect this 2x1 vector on the line y = x.
To make this reflection we must use the following matrix:
![R=\left[\begin{array}{cc}0&1\\1&0\\\end{array}\right]](https://tex.z-dn.net/?f=R%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%261%5C%5C1%260%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Where R is known as the reflection matrix on the line x = y
Now perform the product of the vector <-1,5> x R.
![\left[\begin{array}{ccc}-1\\5\end{array}\right]x\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]\\\\\\\left[\begin{array}{ccc}-1(0) +5(1)&-1(1)+5(0)\end{array}\right]\\\\\\\left[\begin{array}{ccc}5&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%5C%5C5%5Cend%7Barray%7D%5Cright%5Dx%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%280%29%20%2B5%281%29%26-1%281%29%2B5%280%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%5Cend%7Barray%7D%5Cright%5D)
The vector matrix that represents the reflection of the vector <-1,5> across the line x = y is:
![V = \left[\begin{array}{ccc}5&-1\end{array}\right]](https://tex.z-dn.net/?f=V%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-1%5Cend%7Barray%7D%5Cright%5D)
Answer:
=18
Step-by-step explanation: