Convert to vertex form:-
f(x) = 4(x^2 + 2x) + 7
= 4[(x + 1)^2 - 1] + 7
= 4(x + 1)^2 + 3
The axis will be the vertical line x = -1
Observe the figure below.
Statement Reason
1. AC and BD bisect each other Given
2. AE = EC and BE = ED Definition of bisection
3. Vertical angle theorem
Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".
4. SAS criterion for congruence
5. Corresponding angles of congruent triangles are congruent
6. Converse of alternate interior angle theorem
7. Vertical angle theorem
8. SAS criterion for congruence
9. Converse of alternate interior angle theorem
As, , so as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by "Converse of alternate interior angle theorem".
Answer: <u>y = -(3/7)x - (36/7)</u>
Step-by-step explanation:
Let's convert -3x - 7y = 10 to standard slope intercept form: y=mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).
-3x - 7y = 10
-7y = 3x + 10
y = -(3/7)x - (10/7)
This line has a slope of -(3/7). Any line that is parallel will have the same slope, so we can write y = -(3/7)x + b to start our new line.
We want a value of b that forces the line to go trough point (-5,-3). Use this point in the partial equation and solve for b:
y = -(3/7)x + b
-3 = -(3/7)(-5) + b
-3 = (15/7) + b
b = -3 - (15/7)
b = -(21/7) - (15/7)
b = -(36/7), or -5 1/7
y = -(3/7)x - (36/7)
The coordinates of the centroid are the average values of the - and -coordinates of the points that belong to the region. Let denote the bounded region. These averages are given by the integral expressions
The denominator is just the area of , given by
where we rewrite the integrand using the identities
Now, if
with , then
Find where this simpler sine curve crosses the -axis.
In the interval [0, 8], this happens a total of 5 times at
See the attached plots, which demonstrates the area between the two curves is the same as the area between the simpler sine wave and the -axis.
By symmetry, the areas of the middle four regions (the completely filled "lobes") are the same, so the area integral reduces to
The signs of each integral are decided by whether lies above or below axis over each interval. These integrals are totally doable, but rather tedious. You should end up with
Similarly, we compute the slightly more complicated -integral to be
and the even more complicated -integral to be
Then the centroid of is
Answer:
It is a closed circle going toward the right
Step-by-step explanation:
Since it has the line under the inequality sign that makes it so it will be equal to 5 and whatever is a greater number than 5.
I hope this helps!