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Damm [24]
3 years ago
14

Last year, your team bought 11 baseball caps for $55. This year, the cost per cap is the same. Write a

Mathematics
1 answer:
grin007 [14]3 years ago
5 0

Answer:

$75

Step-by-step explanation:

55/11=5

15*5=75

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Find a and b so that f(x) = x^3 + ax^2 + b will have a critical point at (2,3).
Digiron [165]

Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>
  • The critical points of a function are the values of x for which:

f^{\prime}(x) = 0

In this problem, the function is:

f(x) = x^3 + ax^2 + b

Hence, the derivative is:

f^{\prime}(x) = 3x^2 + 2ax

Then:

f^{\prime}(x) = 0

3x^2 + 2ax = 0

x(3x + 2a) = 0

x = 0

3x + 2a = 0

3x = -2a

x = -\frac{2a}{3}

Since the critical point is at x = 2, we have that:

-\frac{2a}{3} = 2

-2a = 6

2a = -6

a = -3

Then:

f(x) = x^3 - 3x^2 + b

Critical point at (2,3) means that when x = 2, y = 3, then:

3 = 2^3 - 3(2)^2 + b

8 - 12 + b = 3

b = 7

You can learn more about the critical point concept at brainly.com/question/2256078

4 0
2 years ago
What is the solution to the equation 9k = 40.5?<br><br> k= 4<br> k= 4.5<br> k= 5
Scilla [17]

Answer:

k=4.5

Step-by-step explanation:

40.5/9

3 0
3 years ago
Read 2 more answers
(1, 4) is a solution to the system that includes y=3x + 1 and y = -x + 5.
SIZIF [17.4K]

Answer:

yes

Step-by-step explanation:

y=3x + 1

y = -x+5

Check if (1,4) solves the first equation

4 = 3(1)+1

4 = 3+1

4=4

This is true

Check the second equation

4 = -1+5

4=4

This is true

(1,4) is a solution to the system of equations

7 0
2 years ago
Read 2 more answers
HELP RIGHT AWAY THANK YOU
Tems11 [23]

Answer:

b^{6}

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Need help ASAP homework is due and o don't get this equation
Vanyuwa [196]
(5 + x) / 6 = -1....multiply both sides by 6, cancelling out the 6 on the left side
5 + x = -1 * 6
5 + x = -6
x = -6 - 5
x = -11

6 0
3 years ago
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