Answer:
<u>The table shows that:</u>
- The value of y decreases when the value of x decreases or vice versa, the value of y increases as x increases.
Therefore the line has a positive slope
Answer:
Length: 139 feet
Width: 104 feet
Step-by-step explanation:
The formula for the perimeter of a rectangle can be given by
. We are given the perimeter of the pool along with the width.


From here, all we have to do is plug back into the original formula:

Which can be further simplified as:


From here, all we have to do is add 70 to both sides of the equation and divide by four:


To make sure that this answer is accurate, we can find that the width of the rectangle should then be 104 (given by 139 - 35). All we have to do is plug back into the original equation:




And the substitution works, so the length of the rectangle would be 139 feet and the width would be 104 feet.
Answer:
<u><em>y = 63</em></u>
Step-by-step explanation:
<em>y is directly proportional to x²</em>
<em>As given,</em>
<em>when y = 3 => x = 2</em>
<em>So, 3 = 4 - 1</em>
<em>Which means the relation can be written as :-</em>
<em>y = x² - 1</em>
<em></em>
<em>Substituting x = 8</em>
<em>y = (8)² - 1</em>
<em>y = 64 - 1</em>
<u><em>y = 63</em></u>
Answer:
C.(3|-4)
Step-by-step explanation:
Given the vector:
![\left[\begin{array}{ccc}4\\3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C3%5Cend%7Barray%7D%5Cright%5D)
The transformation Matrix is:
![\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C-1%260%5Cend%7Barray%7D%5Cright%5D)
The image of the vector after applying the transformation will be:
![\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\left[\begin{array}{ccc}4\\3\end{array}\right]\\\\=\left[\begin{array}{ccc}0*4+1*3\\-1*4+0*3\end{array}\right]\\\\=\left[\begin{array}{ccc}3\\-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C-1%260%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C3%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%2A4%2B1%2A3%5C%5C-1%2A4%2B0%2A3%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C-4%5Cend%7Barray%7D%5Cright%5D)
The correct option is C