Answer:
x = 3
Step-by-step explanation:
3(x + 2) = 6(x - 1) + 3
Divide both sides by 3.
x + 2 = 2(x - 1) + 1
Distribute the 2 on the right side.
x + 2 = 2x - 2 + 1
Combine like terms on the right side.
x + 2 = 2x - 1
Add 1 to both sides. Subtract x from both sides.
3 = x
x = 3
Answer: The answers are
(i) The local maximum and local minimum always occur at a turning point.
(iii) The ends of an even-degree polynomial either both approach positive infinity or both approach negative infinity.
Step-by-step explanation: We are given three statements and we are to check which of these are true about the graphs of polynomial functions.
In the attached figure (A), the graph of the polynomial function
is drawn. We can see that the local maximum occurs at the turning point P and local minimum occurs at the turning point Q. Also, the local maximum is not equal to the x-value of the coordinate at that point
Thus, the first statement is true. and second statement is false.
Again, in the attached figure (B), the graph of the even degree polynomial
is drawn. We can see that both the ends approaches to positive infinity and in case of
, both the ends approch to negative infinity.
Thus, the third statement is true.
Hence, the correct statements are first and third.
Answer: f(x) = 1.2(x/2) if 120 ≤ x ≤ 240
Step-by-step explanation:
Let, she made f(x) sundaes in x minutes.
Then according to the question,
She just makes sundaes for a single shift of at most 4 hours and at least 2 hours,
⇒ She can make sundaes for a single shift of at most 240 minutes and at least 120 minutes,
That is, 120 ≤ x ≤ 240
Now, She can prepare 1 sundae every 2 minutes,
⇒ She can prepare 1/2 sundae every 1 minutes,
⇒ She can prepare x/2 sundae every x minutes,
Also, she earns $1.20 for each sundae she makes.
Thus, her total earning in x minutes,

⇒ 
Where, 120 ≤ x ≤ 240
Which is the required function related her earnings to the number of minutes she works.
Answer: 7/8
Step-by-step explanation:
If the ratio is vanilla to chocolate, it would be
42:48
Dividing by 2
= 21:24
Dividing by 3
= 7:8