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dmitriy555 [2]
2 years ago
12

Write an equation for a quadratic function in vertex form with

Mathematics
1 answer:
il63 [147K]2 years ago
5 0

Answer:

\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6

Step-by-step explanation:

We want to write the equation for a quadratic function in vertex form with vertex at (-1, 6) that passes through the point (-3, 4).

Vertex form is given by:

\displaystyle f(x)=a(x-h)^2+k

Where (<em>h, k</em>) is the vertex and <em>a</em> is the leading coefficient.

Since our vertex is at (-1, 6), <em>h</em> = -1 and <em>k</em> = 6. Substitute:

f(x)=a(x-(-1))^2+(6)

Simplify:

f(x)=a(x+1)^2+6

Next, since the quadratic passes through the point (-3, 4), f(x) = 4 when <em>x</em> = -3. Substitute:

(4)=a(-3+1)^2+6

Solve for <em>a</em>. Simplify:

-2=a(-2)^2

Hence:

\displaystyle -2=4a\Rightarrow a=-\frac{1}{2}

Therefore, our function in vertex form is:

\displaystyle f(x)=-\frac{1}{2}(x+1)^2+6

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The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift.
garik1379 [7]

Answer:

The probability that X is less than 32 minutes is 0.736.

Step-by-step explanation:

Given : The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 24 minutes.

To find : What is the probability that X is less than 32 minutes?

Solution :

If X has an average value of 24 minutes.

i.e. \lambda=24

The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift.

The exponentially function is \frac{1}{\lambda}e^{-\frac{x}{\lambda}}

The function form according to question is

f(x)=\{\frac{1}{24}e^{-\frac{x}{24}}, x>0\}

The probability that X is less than 32 minutes is

P[x

P[x

P[x

Therefore, the probability that X is less than 32 minutes is 0.736.

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2 years ago
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Combine the like terms to make a simpler expression: 5n+6+(-7n)<br> plz hurry
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-2n + 6 is the answer to this question
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