Answer:
The third graph is correct for the inequality 2x + 3y > -3
Step-by-step explanation:
The slope of the graph is –2/3.
The y-intercept is –1
The area above the dashed be line is shaded.
To verify, choose a coordinate in the shaded area, substitute the values for x and y. Calculate and check.
For example: (1,1)
2(1) + 3(1) > –3
2 + 3 > –3
5 > –3 True.
Answer:
<h3>
13, 15, 17</h3>
Step-by-step explanation:
x - an integer then 2x + 1 is an odd number (the smallest one)
consecutive odd numbers increase by 2
so the next odd number (the middle number) is:
2x + 1 + 2 = 2x + 3
and the third (the largest) consecutive is:
2x + 3 + 2 = 2x + 5
the sum of the the two largest numbers is:
2x + 3 + 2x + 5
3 times the smallest number is:
3(2x + 1)
the sum of the two largest is seven less than three times the smallest, so:
2x + 3 + 2x + 5 = 3(2x + 1) - 7
4x + 8 = 6x + 3 - 7
-6x -6x
-2x + 8 = -4
-8 -8
-2x = -12
÷(-2) ÷(-2)
x = 6
2x+1 = 2•6+1 = 13
2x+3 = 2•6+3 = 15
2x+5 = 2•6+5 = 17
Check:
2x+3+2x+5 = 15+3+15+5 = 38
38+7 = 45
45÷3 = 15
Answer:
x = -2/15.
Step-by-step explanation:
Finding the second derivative:
f'(x) = 15x^2 +4x - 3
f"(x) = 30x + 4
30x + 4 = 0 for a point of inflection
x = -4/30 = -2/15
So 30x + 4 is negative up to x = -2/15 and positive thereafter.
So the curve passes from concave downward to concave upward at x = -2/15.
Y - intercept is the value of y - coordinates of the point where the line intersects the y - axis, that is :
Y - intercept = 0
7.50*3= 22.50
305-22.50= 282.50
hope it helps
