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3 years ago

Determine the product. (−2x2) (x2 − 3x + 4)

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

7 0

Answer:

−2x4+6x3−8x2

Explanation:

You weren't really asking for an explanation, if so let me know!

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Can the table shown below represent values of a function

Leno4ka [110]

No because there are two different outputs for the same input. (9)

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3 years ago

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Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour

UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So $C(0) = 110$

Husband

Half life of 4 hours. So

$C(4) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{4r}$

$e^{4r} = 0.5$

Applying ln to both sides

$\ln{e^{4r}} = \ln{0.5}$

$4r = \ln{0.5}$

$r = \frac{\ln{0.5}}{4}$

$r = -0.1733$

So for the husband

$C(t) = 110e^{-0.1733t}$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.1733t}$

$C(11) = 110e^{-0.1733*11} = 16.35$

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

$C(10) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{10}$

$e^{10r} = 0.5$

Applying ln to both sides

$\ln{e^{10r}} = \ln{0.5}$

$10r = \ln{0.5}$

$r = \frac{\ln{0.5}}{10}$

$r = -0.0693$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.0693t}$

$C(11) = 110e^{-0.0693*11} = 51.33$

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

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4 years ago

Which 3 dimensional figure had nine edges

vlabodo [156]

Triangular Prism is the answer

6 0

3 years ago

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Find two accurate angels that satisfy the equation sin(3x +8)=cos (x+10)

Eduardwww [97]

Answer:

the answer is 109

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3 years ago

I need help with this problem please ?

Setler79 [48]

Answer:

x² - 4x + 4

x² + 10x + 25

Step-by-step explanation:

Hello!

Trinomials are polynomials with 3 terms, hence "tri".

<u>Perfect square trinomials</u> are the result of multiplying a binomial (2 terms) by itself, making it a square of a binomial.

<h2>Finding Perfect Square Trinomials</h2>

We can easily remove the first two solutions, as they only have two terms.

We can factor in the other three and see if the binomials as the factors are the same.

x² - 4x + 4
x² - 2x - 2x + 4
x(x - 2) - 2(x - 2)
(x - 2)(x - 2)
(x - 2)²

This is a perfect square trinomial.

x² + 10x + 25
x² + 5x + 5x + 25
x(x + 5) + 5(x + 5)
(x + 5)(x + 5)
(x + 5)²

This is a perfect square trinomial.

x² + 15x + 36
x² + 3x + 12x + 36
x(x + 3) + 12(x + 3)
(x + 12)(x + 3)

This is NOT a perfect square trinomial.

<h2>Another Method...</h2>

We can also check if a trinomial is a square by using a simple checklist.

Perfect Square Trinomial: $(a + b)^2 = a^2 + 2ab + b^2$

The first term should be a perfect square
The last term should be a perfect square (don't include the sign)
The middle term is the square root of the last term, and then multiplied by 2

These rules only apply to polynomials with 3 terms.

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2 years ago

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