<span>Inductive reasoning is that when two lines intersect you will always have a pair of congruent angles considering an exception when all the angles are congruent. According to this,
1) Vertical angles (or opposite angles) are congruent. In this case, vertical angles could be acute or obtuse depending on the position of the lines.
2) The second case is the exception when all the angles are equal. It means that the lines are perpendicular.
3) Again back to the first case, vertical angles are equal or congruent in other words.
4) And again back to the second case when the lines are perpendicular, then all the angles that formed are equal to each other.
You can observe all the cases in the picture attached below.</span>
Answer:
y = -56
Step-by-step explanation:
The equation for direct variation is
y = kx where k is the constant of variation
y = -8 x
We know x =7
y = -8*7
y = -56
Funtion ! in vertex form is given by
<span>f(x) = 4x^2 + 8x + 1</span> = 4(x^2 + 2x + 1/4) = 4(x^2 + 2x + 1 + 1/4 - 1) = 4(x + 1)^2 + 4(-3/4) = 4(x + 1)^2 - 3
Thus, the least minimun value is (-1, -3)
Also, the least minimum value of function 2 is (-1, 0)
Therefore, function 1 has the least minimum value at (-1, -3)
Essentially when people ask you find the solution to system of equation, there asking at what x value do these to graphs intersect. The easiest way to do this is to get a graphing calculator, or desmos and type in the equation and find where they intersect. Heck, even the question says to solve it with a graph, but I'll demonstrate it algebraically.
One way you can do this is set the equation equal to each other. This is because you want to know at what x-value has the same y-value. So we get:
x^2 + 6x + 8 = x + 4
We can then combine like terms, or move everything to one side. So we get:
x^2 + 5x + 4 = 0.
Then we can use the quadratic formula to solve for x.
x=(-5 +/- sqrt(5^2 - 4(1)(4)))/(2(1)
This simplifies into:
(-5 +/- 3)/2
Finally we add and subtract:
(-5 + 3)/2 = x = -1
(-5 - 3)/2 = x = -4
And our solution is x = -1, x = -4