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3 years ago

Find a quadratic function that includes the set of values below. (0,9). (2,15) (3,12)

Mathematics

1 answer:

nlexa [21]3 years ago

3 0

Answer:

$f(x) = -2x^2 + 7x + 9$

Step-by-step explanation:

$f(x) = ax^2 + bx + c\\f(0) = 9 => c = 9;\\f(2) = 15 = 4a + 2b + 9 2a + b = 3\\f(3) = 9a + 3b + 9 = 12 3a + b = 1\\Subtract the second equation from the first:\\-a = 2 => a = -2; b = 7; c = 9\\f(x) = -2x^2 + 7x + 9$

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Simplify using the laws of exponents (4^3)^-2 × (2^3)^4 ×(8/15)^-2

katrin2010 [14]

Answer:

$\dfrac{225}{64}$

Step-by-step explanation:

$(4^3)^{-2} \times (2^3)^4 \times (\dfrac{8}{15})^{-2} =$

$= (2^2)^{-6} \times 2^{12} \times (\dfrac{15}{8})^{2}$

$= 2^{-12} \times 2^{12} \times \dfrac{225}{64}$

$= \dfrac{225}{64}$

8 0

3 years ago

Let r(d) represent the monthly revenue, in dollars, from selling skateboards when the price of a skateboard has been decreased b

vodka [1.7K]

Answer:

A.\ \ r(d)=-100(d-25)^2+122,500

Hope this helps!

3 0

3 years ago

G(n) = 4n+5 f(n)= n^3+3n^2 find (g+f)(n)

Tpy6a [65]

Given:

The two functions are:

$g(n)=4n+5$

$f(n)=n^3+3n^2$

To find:

The function $(f+g)(n)$ .

Solution:

We have,

$g(n)=4n+5$

$f(n)=n^3+3n^2$

Now,

$(f+g)(n)=f(n)+g(n)$

$(f+g)(n)=n^3+3n^2+4n+5$

Therefore, the correct option is B.

7 0

3 years ago

(a) A lamp has two bulbs, each of a type with average lifetime 1400 hours. Assuming that we can model the probability of failure

Temka [501]

Answer:

For first lamp ; The resultant probability is 0.703

For both lamps; The resultant probability is 0.3614

Step-by-step explanation:

Let X be the lifetime hours of two bulbs

X∼exp(1/1400)

f(x)=1/1400e−1/1400x

P(X<x)=1−e−1/1400x

X∼exp⁡(1/1400)

f(x)=1/1400 e−1/1400x

P(X<x)=1−e−1/1400x

The probability that both of the lamp bulbs fail within 1700 hours is calculated below,

P(X≤1700)=1−e−1/1400×1700

=1−e−1.21=0.703

The resultant probability is 0.703

Let Y be a lifetime of another lamp two bulbs

Then the Z = X + Y will follow gamma distribution that is,

X+Y=Z∼gamma(2,1/1400)

2λZ∼

X+Y=Z∼gamma(2,1/1400)

2λZ∼χ2α2

The probability that both of the lamp bulbs fail within a total of 1700 hours is calculated below,

P(Z≤1700)=P(1/700Z≤1.67)=

P(χ24≤1.67)=0.3614

The resultant probability is 0.3614

8 0

3 years ago

Is -4 a solution to the equation ?

Novosadov [1.4K]

9514 1404 393

Answer:

Step-by-step explanation:

Put the value where the variable is and see if you get a true statement.

2(-4) -8 = -15

-8 -8 = -15 . . . . . . . false

-4 is <em>not a solution</em> to the equation

3 0

3 years ago

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