The maximum value of the objective function is 31.787
<h3>How to maximize the function?</h3>
The given parameters are:
Objective function:
Max P = 4x + 5y + 21
Subject to:
y- x < 1
21x + 7y < 25
x>-2, y>-4
Rewrite the inequalities as equation
y - x = 1
21x + 7y = 25
Add x to both sides in y - x = 1
y = x + 1
Substitute y = x + 1 in 21x + 7y = 25
21x + 7x + 7 = 25
Evaluate the like terms
28x = 18
Divide both sides by 28
x = 0.643
Substitute x = 0.643 in y = x + 1
y = 0.643 + 1
y = 1.643
So, we have:
Max P = 4x + 5y + 21
This gives
P = 4 * 0.643 + 5* 1.643 + 21
Evaluate
P = 31.787
Hence, the maximum value of the objective function is 31.787
Read more about maximum functions at:
brainly.com/question/14381991
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Using a geometric sequence, it is found that:
a) The explicit formula is:
.
b) The value of her collection 9 years after she started tracking is of $94,557,148.
<h3>What is a geometric sequence?</h3>
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
![a_n = a_1q^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20a_1q%5E%7Bn-1%7D)
In which
is the first term.
Item a:
Three years ago, her collection was worth $250,000, hence the first term is
.
In two years, the collection was valued at $1,102,500, hence the common ratio is:
![q^2 = \frac{1,102,500}{250,000}](https://tex.z-dn.net/?f=q%5E2%20%3D%20%5Cfrac%7B1%2C102%2C500%7D%7B250%2C000%7D)
![q^2 = 4.41](https://tex.z-dn.net/?f=q%5E2%20%3D%204.41)
.
Hence, the explicit formula is:
![a_n = 250000(2.1)^{n-1}](https://tex.z-dn.net/?f=a_n%20%3D%20250000%282.1%29%5E%7Bn-1%7D)
Item b:
![a_9 = 250000(2.1)^{9-1} = 94557148](https://tex.z-dn.net/?f=a_9%20%3D%20250000%282.1%29%5E%7B9-1%7D%20%3D%2094557148)
The value of her collection 9 years after she started tracking is of $94,557,148.
More can be learned about geometric sequences at brainly.com/question/11847927
First you convert the hours into minutes, which is 120 and add the 10. 130 minutes in total. Then you divide the miles. 890/ 130 = 6.846..... rounding to the nearest 100 (2nd #) which would equal to 6.85
Answer:
see explanation
Step-by-step explanation:
The vertex form of f(x) is
f(x) = (x - h)² + k
where (h, k) are the coordinates of the vertex
To obtain this form use the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 14x
f(x) = x² + 2(7)x + 49 - 49 + 36
= (x + 7)² - 13
The minimum value of f(x) is the y- coordinate of the vertex
vertex = (- 7, - 13), that is minimum value = - 13