First you'll need to find the line of symmetry using the formula x=-b/2a. In this case, you have x=-(4/3)/(2*(-1/3))=(-4/3)/(-2/3). Then take this x value and plug it into your equation to get a y-value. This will be your vertex. Now what I like to do to get the other 2 points needed to graph the parabola is pick an x value 1 unit left of the vertex x value and another x value 1 unit right of the vertex x value. That will give you two points on either side of the vertex, and connecting the three points will create your parabola.
Answer:
Step-by-step explanation:
First we need the find the set of x such as 2x + 3 >= -3
2x + 3 >= -3 [Sum -3 in both sides]
2x + 3 - 3 >= - 3 - 3
2x >= -6 [Now, divide both sides by 2]
2x / 2 >= -6/2
x >= - 3
So, for every x>= -3 we have that 2x + 3 >= -3
Now we do the same with the other ineq:
5x-2 < 3 [sum 2 in both sides]
5x - 2 + 2 < 3 + 2
5x < 5 [divide by 5 in both sides]
5x / 5 < 5 / 5
x < 1
So, for every x<1 we have 5x-2<3
Then our set it the intersection of both of the previous sects, it is:
(x<1)intersect(x>=-3):
Solution: -3 =< x < 1
The triangle's POSITION changed. The side and angle lengths did not. The angles are the same
Answer=40°
Answer:
V = 648 in^3
Step-by-step explanation:
V = lwh
V = 9 x 6 x 12
V = 648 in^3
Answer:
f1: 0.440, f2: 0.931, f3: 1.519
Step-by-step explanation:
To solve the system of equations we need to use the inverse of matrix A, as follows:
A x F = C
A^-1 x A x F = A^-1 x C
I x F = A^-1 x C
where I is the identity matrix.
The inverse of A is:
1.450 -0.392 -0.090
A^-1 = -0.074 -0.022 0.1536
-0.406 0.7122 -0.060
(computed with Excel)
The multiplication between the inverse of A and C gives:
0.440
A^-1 x C = 0.931
1.519
(computed with Excel)