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Deffense [45]
2 years ago
6

For x=4 the functiom f(x) =x2+bx+c has the minimum value of_9.find c

Mathematics
1 answer:
shepuryov [24]2 years ago
7 0

Answer:

c = 25

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

f(x) = ax^{2} + bx + c

It's vertex is the point (x_{v}, y_{v})

In which

x_{v} = -\frac{b}{2a}

y_{v} = -\frac{\Delta}{4a}

Where

\Delta = b^2-4ac

If a>0, the vertex is a minumum point, that is, the minimum value happens at x_{v}, and it's value is y_{v}.

In this question:

a = 1

Minimum value at x = 4 means that x_v = 4. So

x_{v} = -\frac{b}{2a}

4 = -\frac{b}{2}

b = -8

So

f(x) = x^2 - 8x + c

Minimum value of 9:

y_v = 9

So

y_{v} = -\frac{\Delta}{4a}

9 = -\frac{\Delta}{4}

-\Delta = 36

\Delta = -36

b^2 - 4ac = -36

(-8)^2 - 4c = -36

-4c = -100

4c = 100

c = \frac{100}{4}

c = 25

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X = Lilys weight
x + 34 = Arthurs weight
4x - 180 = combined weight

x + x + 34 = 4x = 180
2x + 34 = 4x - 180
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     +180        + 180
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       214 = 2x
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The total weight is 248

which is the answer that you get when you do 4(107) = 180 or
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2 years ago
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6 0
2 years ago
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A(n) = -5 + 6(n - 1)a(n)=−5+6(n−1)a, left parenthesis, n, right parenthesis, equals, minus, 5, plus, 6, left parenthesis, n, min
DENIUS [597]

Answer:

The 12th term is 61

Step-by-step explanation:

I will assume that your a(n) = -5 + 6(n - 1) is correct; the rest is redundant (duplicative, unneeded).

To find the 12th term, substitute 12 for n in the above formula:

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What is the greatest common factor of 42, 56, and 112
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Step-by-step explanation:

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The length of 2 sides of a triangle are 12 inches and 4 inches. Which is the third side?
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Answer:

Let x = the third side

 

In a triangle, the sum of any 2 sides must be larger than the third side.

I believe this is called the triangle inequality theorem.

 

We can construct 3 inequalities to obtain the range of values for the third side.

 

  (Inequality #1)   12 + 4 > x

                                  16 > x

 

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So when we combine these together,  

 

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X (the third side) must be a number between 8 and 16. but not including 8 and 16

7 0
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