Answer:
Option (4)
Step-by-step explanation:
Given inequality is,



x ≥ 0 [For x = 0, fraction is not defined]
(x - 6)(x + 6) ≤ 0
x - 6 ≤ 0
x ≤ 6
Or
x + 6 ≤ 0
x ≤ -6
Therefore, solution set is (-∞, -6] ∪ (0, 6]
By plotting the solution area on a number line,
Option (4) will be the answer.
Answer:
The coordinates of the center of the hyperbola are (1,-3)
Step-by-step explanation:
Equation of a hyperbola:
The equation of a hyperbola with center
is given by:

In this question, we have that:


The coordinates of the center of the hyperbola are (1,-3)
Step-by-step explanation:

Where Z is set of integer.
Answer:

Step-by-step explanation:
1) if to re-write the given equation into slope-interception form, then:

the slope of the given line is 5/2;
2) according to the rule of perpendicular, the required slope should be:
s*(5/2)=-1;
3) if to solve this equation (s*5/2=-1), then s=-2/5 or -0.4.
Answer:
2.44
Step-by-step explanation:
Given: x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6
Also, R1 + R2 = 6
in order to find the value of a:
Let p(x) = x³ + 2x² - 5ax - 7 and q(x) = x³ + ax² - 12x + 6
Using remainder theorem i.e if a polynomial p(x) is divisible by polynomial of form x - a then remainder is given by p(a).
Then,
R1 = p( -1 ) = (-1)³ + 2(-1)² - 5a(-1) - 7 = -1 + 2 + 5a - 7 = 5a - 6
R2 = q( 2 ) = 2³ + a(2)² - 12(2) + 6 = 8 + 4a - 24 + 6 = 4a - 10
Now,
R1 + R2 = 6
5a - 6 + 4a - 10 = 6
9a = 22
a=2.44
Therefore, Value of a is 2.44