Hello there!
n - 5 ≤ 5n - 1
Solve for n
Let's start by subtracting 5n from both sides
n - 5 - 5n ≤ 5n - 5n - 1
n - 5 - 5n ≤ -1
We need to transfer -5 on the other side, we can do that by adding 5 on both sides
n - 5 - 5n + 5 ≤ -1 + 5
n - 5n ≤ -4
-4n ≤ -4
Finally divide both sides by -4
-4n/-4 ≤ -4/-4
n ≥ -1 (This is the answer)!
Do you know why I changed the sign?
A lot of students failed to remember that rules, which is:
When you are solving an inequality, if you divide both sides by a negative sign, you MUST change the symbol as well. If it was this <, it will change to this >. Got it? Cool!
I hope the steps are clear to understand. If you have questions, feel free to let me know...
As always, I am here to help!
Answer:
The pair (0,3) is not a solution to the equation
Step-by-step explanation:
This can be proved by simply replacing the x and y variables in the equation by the x and y values of the pair, and checking if the equation renders a true statement:
By replacing x and y with their values in the pair (0,3), that is x=0 and y=3, in the equation y = 5 - 2x we get:
3 = 5 - 2 (0)
3 = 5 - 0
3 = 5
which is NOT a true statement.
On the other hand, the other two pairs (2,1) and (1,3) render true statements:
1 = 5 - 2 (2)
1 = 5 - 4
1 = 1
and
3 = 5 - 2 (1)
3 = 5 - 2
3 = 3
Answer: B
Step-by-step explanation:
Answer:
The vertex is (-3, 7)
Step-by-step explanation:
As the equation is already in 'rectangular form), to work out the vertex, we can just compare this equation to that of the standard parabola y = x^2, and in particular, consider how it has been translated:
the (x+3) part moves the graph the the left 3 (i.e in the negative direction), while the +7 moves the graph up 7.
So as the vertex of the simple parabola y = x^2 is (0,0), the vertex of this graph is just (-3,7).
Note that the -2 at the front doesn't impact this vertex - this -2 just changes the 'scale' of the parabola (i.e makes it more narrow, and also turns it upside down as it's a negative number).
