Identify the graph and describe the solution set of this system of inequalities.
1 answer:
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9514 1404 393
Answer:
- y -9 = 2(x -1) . . . point-slope form
- y = 2x +7 . . . . slope-intercept form
- 2x -y = -7 . . . . standard form
Step-by-step explanation:
Perhaps you want the equation of the line that goes through these two points.
The slope of the line can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (9 -3)/(1 -(-2)) = 6/3 = 2
We can use one of the points to write the equation in point-slope form:
y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)
For slope 2 and point (1, 9) the equation is ...
y -9 = 2(x -1) . . . . equation in point-slope form
__
We can eliminate parentheses and get y by itself to put the equation into slope-intercept form.
y -9 = 2x -2
y = 2x +7 . . . . . . equation in slope-intercept form
__
With a little further rearranging, we can put this into standard form. We can get that by adding -7-y to both sides of the equation.
2x -y = -7 . . . . . equation in standard form
Answer:
Option (2).
Step-by-step explanation:
Let f(x) and g(x) are the two functions with domain A and B.
Then (fg)(x) will be the function with domain A∩B
(fg)(x) = f(x)g(x) Domain : A∩B
In this question two functions are,
c(x) = and d(x) = (x + 3)
Domain : (x - 2) > 0 ⇒ x > 2
and (x - 2) < 0 ⇒ x < 2
Or domain of (cd)(x) will be C = (-∞, 2)∪(2, ∞).
Similarly, d(x) = x + 3
Domain : All real numbers
: D = (-∞, ∞)
(cd)(x) = c(x)d(x)
=
Domain of (cd)(x) will be,
Domain : C∩D = (-∞, 2)∪(2, ∞) ∩ (-∞, ∞)
: (-∞, 2) ∩ (2, ∞)
Therefore, domain of (cd)(x) will be all real values except 2.
Option (2) will be the answer.