Answer:
p = 5/7
Step-by-step explanation:
The given function is:
for -4 ≦ x < 1
for 1 ≦ x ≦ 5
Part a)
A continuous function has no breaks, jumps or holes in it. So, in order for g(x) to be continuous, the point where g(x) stops during the first interval -4 ≦ x < 1 must be equal to the point where g(x) starts in the second interval 1 ≦ x ≦ 5
The point where, g(x) stops during the first interval is at x = 1, which will be:
The point where g(x) starts during the second interval is:
For the function to be continuous, these two points must be equal. Setting them equal, we get:
3 = 7p - 2
3 + 2 = 7p
p = 
Thus the value of p for which g(x) will be continuous is .
Part b)
We have to find p by setting the two pieces equal to each other. So, we get the equation as:
Substituting the point identified in part (a) i.e. x=1, we get:
This value agrees with the answer found in previous part.
Answer:
y = 1/x+2 + 3
Step-by-step explanation:
x = -2
y = 3
Explanation:
6(2x + 5) = 2(3x – 2)
[given]
6(2x) + 6(5) = 2(3x) + 2(-2)
12x + 30 = 6x – 4
[distributive property of equality; individually multiply each addend inside the parenthesis and simplify (distribute the terms) ]
12x + 30 = 6x – 4
–6x –6x
6x + 30 = -4
[subtraction property of equality; subtract both sides by 6x in order to keep the x term on the left side]
6x + 30 = -4
–30 –30
6x = -34
[subtraction property of equality; subtract both sides by 30 in order to keep the constant term on the right side]
6x = -34
÷6 ÷6
x = -34/6
[division property of equality; divide both sides by 6 to eliminate the coefficient of 6 in 6x in order to obtain the variable x]
x = -17/3
[GCF(greatest common factor); divide both sides by the greatest common factor until both numbers are prime (only divisible by 1 and itself]
Divide 309 by 3. You should get 103 (hamburgers). if you multiply that by 2 you will get 206 (cheeseburgers). Add the two together you get the total which was 309 originally.
103 hamburgers and 206 cheeseburgers.
Answer:
the answers are A D and E
