Answer:
b. (10, -1), (-6, -9), (2, 7)
Step-by-step explanation:
One way to solve this problem is by graphing (see attachment). In fact, that actually is the easiest way to do this.
First, graph x + y < 9 (red part on the attachment). To do this, isolate the y so that it's like a regular linear equation: y < -x + 9. Graph the line y = -x + 9 first, and then choose a point either on the left or right of the line to plug in for x and y.
Let's just choose (0, 0), which is on the left of the line: 0 < -0 + 9 ⇒ 0 < 9. Since this is a true statement, we know that we should shade the left side of the equation, and not the right side.
Now, graph x - 2y < 12 (blue part on the attachment). It's the same process here as the first inequality. For this one, we find that we also shade to the "left" of the line (it's more "up" than "left", but you get the idea).
Finally, graph y < 2x + 3 (green part on the attachment). Again, it's the same process. For this, we shade to the right.
Now look at the three points that they intersect at: they are (2, 7), (-6, -9), and (10, -1). The answer is thus B.
Answer:
k = 9
Step-by-step explanation:
Consider the pattern on the right side , that is
= k(k + 2) + 1 = k² + 2k + 1
Equating
k² + 2k + 1 = 100 ( subtract 100 from both sides )
k² + 2k - 99 = 0 ← in standard form
(k + 11)(k - 9) = 0 ← in factored form
Equate each factor to zero and solve for k
k + 11 = 0 ⇒ k = - 11
k - 9 = 0 ⇒ k = 9
But k > 0 , then k = 9
Answer:
Step-by-step explanation:
Slope of line through the three points is -3.
Slope of any perpendicular through the line is ⅓.
(0,1) is one of the points on the line, so the y-intercept is 1.
Slope-intercept equation for line of slope ⅓ and y-intercept 1:
y = ⅓x+1
