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3 years ago

Which if the following quartic functions has x = 1 and x =

Mathematics

1 answer:

Hunter-Best [27]3 years ago

5 0

<h3>Answer:</h3>

y = x⁴ +4x³ +4x² +4x +3

<h3>Step-by-step explanation:</h3>

The coefficients of the offered quartics (in order) have 1, 1, 1, and 0 sign changes, respectively. Descartes' rule of signs tells you this means the first three choices all have one (1) positive real root, so the negative real roots -1 and -3 are not the only ones.

The only possible polynomial is the last one. Synthetic division of that polynomial by roots -1 and -3 leave the remaining factor as x²+1, which has only complex zeros.

The appropriate choice is ...

... y = x⁴ +4x³ +4x² +4x +3

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-1/3 + 7/4. in simplest form plzz

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Greatest Common Factor: 12-1/3 = -4/12, 7/4 = 21/12-4/12 + 21/12 = 17/12
Answer in simplest form: 17/12

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3 years ago

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Evaluate x - y - (-z) if x = -3, y = -7, and z = -9

IceJOKER [234]

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3 years ago

Which expression is equivalent to 5+5t+3t+?

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Answer:

10t+3

Step-by-step explanation:

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3 years ago

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Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

7 0

3 years ago

6 to the power of 8 divided by 6 to the power of 4

tensa zangetsu [6.8K]

Answer:

7.716049382716049e-4‬ or 1,296

Step-by-step explanation:

If 6 is to the power of 8 and my mind is not mistaken. Then it's 6^8=1,679,616 and then divide that by 6 to the power of 4 is 6^4=1,296. In the end with the numbers set. 1,679,616 Divided by 1,296 or 1,296 divided by 1,679,616.

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4 years ago