Answer:
See proof below
Step-by-step explanation:
We will use properties of inequalities during the proof.
Let
. then we have that
. Hence, it makes sense to define the positive number delta as
(the inequality guarantees that these numbers are positive).
Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that
, and if we prove this, we are done. To prove it, let
, then
. First,
then
hence
On the other hand,
then
hence
. Combining the inequalities, we have that
, therefore
as required.
We can write out a formula in order to solve this. Since sum represents addition, if x represents the unknown number, we can write the formula: x+51=-21. Then, to solve for x, you would subtract 51 from both sides to get x=-72 which is the final answer.
Hi so if you can put the side ac away for sec and look at sides ab bc you can see the ab is 15 In. And that Side Bc is 22 inches 15 +22 = 37 round it off to 39 that is the answer ac is 39 inches hope i helped
Note that the 2nd equation can be re-written as y=8x-10.
According to the second equation, y=x^2+12x+30.
Equate these two equations to eliminate y:
8x-10 = x^2+12x+30
Group all terms together on the right side. To do this, add -8x+10 to both sides. Then 0 = x^2 +4x +40. You must now solve this quadratic equation for x, if possible. I found that this equation has NO REAL SOLUTIONS, so we must conclude that the given system of equations has NO REAL SOLUTIONS.
If you have a graphing calculator, please graph 8x-10 and x^2+12x+30 on the same screen. You will see two separate graphs that do NOT intersect. This is another way in which to see / conclude that there is NO REAL SOLUTION to this system of equations.
Answer:

Step-by-step explanation:
we have the points
(0,-3),(2,0) and (4,3)
step 1
Find the slope
The formula to calculate the slope between two points is equal to
we take
(0,-3),(2,0)
substitute the values in the formula
step 2
Find the equation of the line in slope intercept form

we have
-----> the point (0,-3) is the y-intercept
substitute

The graph in the attached figure