Vertices (3,0),(-3,0) co-vertices (0,-5),(0,5)
transverse axis (line passing vertices) is on(or parallel to) x-axis then formula is
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
..notice.. x^2 is on positive / y^2 is on negative
center (h,k) is midway between vertices = (0,0)
we have h = k = 0 and now formula is
x^2/a^2 - y^2/b^2 = 1
a is the distance from a vertex to center = 3
b is the distance from a co-vertex to center = 5
the formula is
x^2/3^2 - y^2/5^2 = 1 ... answer is the 1st
You can use the distributive property and multiply this out.
2x(3x² +9x -3) -2(3x² +9x -3)
= 6x³ +18x²-6x -6x² -18x +6
= 6x³ +12x² -24x +6
The coefficient of the x² term is 12.
_____
You can do this in your head using the techniques of Vedic mathematics. Write the coefficients of the two expressions, putting 0 for the x² coefficient in the first factor.
0 2 -2
3 9 -3
The x² term of the product will be the sum of the products of terms whose degrees add to 2. That is, the first term of the first row times the last term of the second row, plus the product of the middle two numbers in each row, plus the product of the first term in the second row times the last term in the first row.
Here's a more visual representation of the products that get added to get the coefficient of the x² term.
0 2 -2
3 9 -3 . . . . product is 0
0 2 -2
3 9 -3 . . . . product is 18
0 2 -2
3 9 -3 . . . . product is -6
The sum, of course, is 0 +18 -6 = 12
Answer:
For x ≥ 2, the graph will be a straight line parallel to x-axis and having equation y = - 3
And for x < 2 will be a straight line having equation y = x i.e. the graph makes 45° angle with the positive x-axis and passing through the origin.
Step-by-step explanation:
The piece wise function g(x) is given by
g(x) = x if x < 2 and g(x) = - 3 if x ≥ 2.
Now, the graph has two parts, one for x ≥ 2 and another for x < 2.
Here, for x ≥ 2, the graph will be a straight line parallel to the x-axis and having equation y = - 3
Again, the graph for x < 2 will be a straight line having equation y = x i.e. the graph makes 45° angle with the positive x-axis and passing through the origin. (Answer)
D. Rigid transformations were applied therefore not changing any of the shapes values.
The formula is 2(wl+hl+hw) to calculate surface area fo a rectangular prism.
