Hi there!
To see if this has a solution, we can simplify it.
6x + 12 > x - 3
5x + 12 > -3
5x > -15
x > -3
Yes, there are solutions to this problem. Any number greater than -3 would match the inequality requirements.
Hope this helps!
Answer:
Step-by-step explanation:
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It's a linear program; the extrema will be at the corners.
Let's enumerate them. 4 choose 2 gives 6 possible meets of 4 lines. One pair are parallel, down to five to try.
4x-y=1 intersects x=0 at y=-1, outside the domain y≥0.
4x-y=1 intersects y=0 at x=1/4, (1/4, 0)
4x-y=1 intersects x=5 at y=19, (5,19)
(0,0) is outside the domain 4(0)-0=0 which isn't ≥1.
(5,0) is a valid corner.
It's a triangular domain. Three points to try,
C(1/4,0) = 6(1/4) + 2(0) = 3/2
C(5,19) = 6(5) + 2(19) = 68
C(5,0) = 6(5) + 2(0) = 30
Answer: Maximum C=68 at (x,y)=(5,19)
Answer:
essentially, in these problems, youre finding the square root of each number. the square root should be a decimal thats in between two other numbers, and those will be the integers that the value of the square root is between. unless the value is exactly a number and a half, it will be closer to one integer than the other. the work is below.
square root of:
59= 7.68
68= 8.246
78= 8.83
93= 9.64
104= 10.198
124= 11.14
33= 5.74
185= 13.6
215= 14.66
these are just the square roots. but, as you can see, each number is between two other whole numbers on a number line. So, just write down what those numbers are.
7.68 is between 7 and 8
8.246 is between 8 and 9
8.83 is between 8 and 9
9.64 is between 9 and 10
10.198 is between 10 and 11
11.14 is between 11 and 12
5.74 is between 5 and 6
13.6 is between 13 and 14
14.66 is between 14 and 15
so, we know thw numbers that each decimal is between, but we have to find which one each is cloest to. in order to do that, just know that if the decimal is more than .5 its closer to the larger number, and its its less than .5, its closer to thw smaller number.
7.68 is closer to 8
8.246 is closer to 8
8.83 is closer to 9
9.64 is closer to 10
10.198 is closer to 10
11.14 is closer to 11
5.74 is closer to 6
13.6 is closer to 14
14.66 is closer to 15
Answer:
angle YUT = 120
Step-by-step explanation:
in Triangle SUT
angle 70 + angle 50 + angle x = 180
70 + 50 + x = 180
120 + x = 180
x = 180 - 120
x = 60
angle SUT = 60
angle SUT + angle YUT = 180 ( straight line)
60 + x = 180
x = 120
Therefore angle YUT ( exterior angle ) = 120
