Interval notation uses parenthesis and brackets, while inequality notation uses inequality symbols.
a)
Interval notation: [-4, 8)
Inequality notation: 
x >= -4, x < 8
---For inequality notation, it can also be written as two separate inequalities. I am not sure what your teacher is looking for, so I will provide both the compound and separate formats.
b)
Interval notation: (-infinity, 7)
Inequality notation: x < 7
c)
Interval notation: (-infinity, -6) U (0, infinity)
Inequality notation: 
x < -6, x >= 0
Hope this helps!
Answer:
Step-by-step explanation:
So, as balloon reaches its maximum height i.e. 11 m , its velocity become 0.
Therefore, 
.
It is given that acceleration due to gravity should be taken as , 
.(because it direction is down)
Now it is also given that upward direction is positive and downward direction is negative. So velocity should be negative.
Using equation of motion,
.....eqn 1.
where , displacement = -11 m(because it displace towards down) and 
Putting these values in eqn 1 .
But as we know direction of velocity is downward.
Therefore,
where negative sign indicates its direction is downward.
Answer:
AB = ![\left[\begin{array}{ccc}-3&4&6\\-6&3&5\\5&0&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%264%266%5C%5C-6%263%265%5C%5C5%260%26-4%5Cend%7Barray%7D%5Cright%5D)
Each column of AB is written as a linear combination of columns of Matrix A in the explanation below.
Step-by-step explanation:
A = ![\left[\begin{array}{ccc}-2&2&1\\-3&1&1\\2&0&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%262%261%5C%5C-3%261%261%5C%5C2%260%26-1%5Cend%7Barray%7D%5Cright%5D)
B= ![\left[\begin{array}{ccc}2&-1&0\\1&2&1\\-1&-2&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-1%260%5C%5C1%262%261%5C%5C-1%26-2%264%5Cend%7Barray%7D%5Cright%5D)
We need to write each column of AB as a linear combination of the columns of A so we will multiply each column of A with each column element of B to get the column of AB. So,
AB Column 1 = 2 * ![\left[\begin{array}{ccc}-2\\-3\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%5C%5C-3%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
+ 1 ![\left[\begin{array}{ccc}2\\1\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%5C%5C1%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
+ (-1) ![\left[\begin{array}{ccc}1\\1\\-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C1%5C%5C-1%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}-3\\-6\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%5C%5C-6%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
AB Column 2 = (-1) + 2 + (-2) = ![\left[\begin{array}{ccc}4\\3\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C3%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
AB Column 3 = (0) + (1) + 4 = ![\left[\begin{array}{ccc}6\\5\\-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%5C%5C5%5C%5C-4%5Cend%7Barray%7D%5Cright%5D)
Finally, we can combine all three columns of AB to form the 3x3 matrix AB.
AB =
We know the width of the first picture, is 4
we know the ratio from smaller to larger is 1.5:2
thus
solve for "w".
we know the length of the first picture, 6
solve for "L".
Answer:
y=4x+7
Step-by-step explanation:
You can find the slope of the line by using the formula of change and y over change in x. ∆y/∆x OR (y2-y1)/(x2-x1)
11-3=8
1--1=2
8/2=4
Let's plug in a y value 3.
3=4*-1+b
b=7
Once you found b rewrite your equation in slope intercept form.
y=4x+7
You can check this equation by plugging in the unused coordinate (1,11) and find it balances.
