<h2>
Answer:</h2>
The values of x for which the given vectors are basis for R³ is:
<h2>
Step-by-step explanation:</h2>
We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.
We are given three vectors as:
(-1,0,-1), (2,1,2), (1,1, x)
The matrix formed by these vectors is:
![\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%262%261%5C%5C0%261%261%5C%5C-1%262%26x%5Cend%7Barray%7D%5Cright%5D)
Now, the determinant of this matrix is:
Hence,
Answer:
y = 8x + 4
Step-by-step explanation:
y=mx+b
m=8
y = 8x + b
We just need to find b. B is where the line intersects the y- axis. On the y-axis by definition, the x-coordinate =0 but that is not helpful now...
Let's re write and try to solve for b. That means write as b = ...
y = 8x + b
b = y - (8x)
Substitute for x and y the numbers of the coordinates of the given point (3,28):
b = y - (8*x)
b = 28 - (8*3)
b = 28 - 24
b = 4
So the answer is y = 8x + 4
Answer:
x ≥-3
Step-by-step explanation:
7 − 9x − (x + 12) less than or equal to 25
7 − 9x − (x + 12) ≤ 25
Distribute the minus sign
7 − 9x − x - 12 ≤ 25
Combine like terms
− 10x −5 ≤ 25
Add 5 to each side
− 10x −5+5 ≤ 25+5
− 10x ≤ 30
Divide by -10. Remember that this flips the inequality
− 10x/-10 ≥30/-10
x ≥-3
Answer: (a)
Step-by-step explanation:
Given
The points are 
and 
The distance between two points 
is given by
Apply the distance formula
Hence, option (a) is correct.
Because 3 is not large enough to subtract 6 from.
Let's look at it this way:
I like to think of mixed number as pizzas and pizza slices. in the mixed number 7&3/12, 7 represent 7 whole pizzas, the denominator 12 represents the number of slices each pizza can be cut into, and the numerator 3 represents three slices (in the 8th pizza). when you subtract 6/12 from 7 and 3/12, since 6 is the numerator which represents slices, you are trying to take away 6 slices. but you only have 3 slices, that is not enough, so you cut one of the whole pizzas into 12 slices, now you have 6 whole pizza left and 15 slices, now you can give away 6 slices from the 15 slices.
I hope this makes sense to you.
you use this method to do addition and subtraction. when you do mixed number multiplication and division, you have to cut all the wholes into slices. well, that's a topic for another day.
