Answer:-2
Step-by-step explanation:
whatever the number attachted to x is, is the slope
Answer:
B.
Step-by-step explanation:
a function is continuous, if the functional values are the same at the "connection" points of the various segments (and the segments themselves are continuous).
"continuous" simply means that the graph of the function is a continuous line without any "rips". it can have corners and such, but no "interruptions".
specifically it means : for every possible y value in the defined range of the function there is an x value that causes this y.
all defined segments are continuous functions.
so, let's look at
A. the first connection point is x=-2.
-2 + 6 = 0.5×(-2)²
4 = 0.5×4 = 2
4 = 2 is wrong. => here, at this point, the function "rips" apart and is not continuous.
B. x=-2
-2 + 4 = 0.5×(-2)²
2 = 2 is correct. continuous at this point.
second connection point x=4
0.5×4² = 20 - 3×4
0.5×16 = 20 - 12
8 = 8 is correct. continuous at this point
C. x=-2
-2 - 2 = 0.5×(-2)²
-4 = 2 is wrong. not continuous
D. x=-2
-2 + 4 = 0.5×(-2)²
2 = 2 is correct. continuous here.
now for x=4
4 + 4 = 25 - 3×4
8 = 25 - 12 = 13
8 = 13 is wrong. not continuous.
A U B is the set of elements which are in A, in B, or in both A.
Since,
A = {2, 3, 6}
B = {2, 4, 5, 7}
To find A U B, we have to write all numbers that are in A and/or in B. The number that are in both sets must not be written again.
A U B = {2, 3, 6, 4, 5, 7}
Writing then in acending order:
A U B = {2, 3, 4, 5, 6, 7}
Answer: A U B = {2, 3, 4, 5, 6, 7}.
In order to find GCF, you will need more than just 1 number
Solution
Let take boat speed = x
Current speed = 4
Upstream = x - 4
Downstream = x + 4
Distance = 9
Time upstream + Time downstream = 10
Time = Distance/Speed
9/(x + 4) + 9/(x - 4) = 10
Solving this equation 9(x-4)+9(x+4) = 10(x^2 -16)
9x - 36 + 9x + 36 = 10x^2 - 160
18x = 10x^2 -160
10x^2 -18x - 160 = 0
Now solving the above quadratic equation, we get
x = 5 or x = -16/5
We ignore the negative value.
The answer is 5.
The speed of the boat in still water is 5mph.
Thank you.