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3 years ago

Consider the following polynomial functions. f(a) = (2a - 7 + a?) and g(a) = (5 – a).

Mathematics

2 answers:

mote1985 [20]3 years ago

4 0

Answer:

1 false

2 true

3 true

4 false

5 true

Step-by-step explanation:

f(a) = (2a - 7 + a^2) and g(a) = (5 – a).

1 false f(a) is a second degree polynomial and g(a) is a first degree polynomial

When added together, they will be a second degree polynomial

2. true When we add and subtract polynomials, we still get a polynomial, so it is closed under addition and subtraction

3. true f(a) + g(a) = (2a - 7 + a^2) + (5 – a)

Combining like terms = a^2 +a -2

4. false f(a) - g(a) = (2a - 7 + a^2) - (5 – a)

Distributing the minus sign (2a - 7 + a^2) - 5 + a

Combining like terms a^2 +3a -12

5. true f(a)* g(a) = (2a - 7 + a^2) (5 – a).

Distribute

(2a - 7 + a^2) (5) – (2a - 7 + a^2) (a)

10a -35a +5a^2 -2a^2 -7a +a^3

Combining like term

-a^3 + 3 a^2 + 17 a - 35

slavikrds [6]3 years ago

4 0

Answer:

Statement 2,3 and 5

Step-by-step explanation:

The sum, difference and product of two (or more) polynomials is also a polynomial.

Statement 2 is correct

Sum:

(a² - 7 + 2a) + (5 - a)

a² + 2a - a - 7 + 5

a² + a - 2

Statement 3 is correct

This is a degree 2 polynomial so

Statement 1 is incorrect

Difference:

(a² - 7 + 2a) - (5 - a)

a² + 2a + a - 7 - 5

a² + 3a - 12

Statement 4 is incorrect

Product:

(a² + 2a - 7) × (-a + 5)

-a³ + 5a² - 2a² + 10a + 7a - 35

-a³ + 3a² + 17a - 35

Statement 5 is correct

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Vladimir [108]

Answer:

See below

Step-by-step explanation:

Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:

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Also, we have Whole numbers. Despite not having an official symbol, I usually denote the set as $\mathbb{Z}_{\ge 0}$

<u>Whole numbers less than or equal to 20</u>: $A\leq 20, A \subset \mathbb{Z}_{\ge 0} \\\implies A=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}$

<u>A. Prime numbers</u>

From the set A, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19.

Once we have 21 numbers in total and 8 prime numbers, the probability is:

$P=\frac{8}{21} \approx 40\%$

<u>B. Composite numbers</u>

From the set A, the composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20.

Once we have 21 numbers in total and 11 composite numbers, the probability is:

$P=\frac{11}{21} \approx 52\%$

<u>C. Divisible by three</u>

From the set A, the numbers divisible by three are 3, 6, 9, 12, 15, 18.

Once we have 21 numbers in total and 6 numbers divisible by three, the probability is:

$P=\frac{6}{21} \approx 30\%$

<u>D. Square of 2</u>

From the set A, the numbers square of 2 are 0, 1, 4, 9, 16.

$\sqrt{0} =0$

$\sqrt{1} =1$

$\sqrt{4} =2$

$\sqrt{9} =3$

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Once we have 21 numbers in total and 5 numbers square of 2 , the probability is:

$P=\frac{5}{21} \approx 24\%$

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The second angle is 108º

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$x\in \left(\frac{3}{4},\infty \right)$

Q4. if three fourth of a number is one tenths, what is the number?

$\frac{3}{4} x =\frac{1}{10} \implies 3x=\frac{4}{10} \implies \boxed{x = \frac{2}{15}}$

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7 0

3 years ago

PLEASE HELP!!!!!!!!!!!!!!!!

Anton [14]

Answer:

<h2>1. subtract 3x, subtract 4, divide by -4</h2><h2 /><h2>2. add x</h2>

Step-by-step explanation:

1 + 3x = -x + 4.

subtract 3x

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-3 = -4x

divide by -4

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3 years ago

How do you find the r?

astra-53 [7]

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3 years ago

A square rug measures 8 feet by 8 feet. find the diagonal distance of the rug to the nearest whole number

Tanzania [10]

This is a right angle triangle and you use the Pythagorean theorem to solve for the hypotenuse (the diagonal)

A^2 + B^2 = C^2
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3 years ago

In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are three machine tools, four p

alexandr402 [8]

Answer:

Step-by-step explanation:

As per the given question,

In a manufacturing operation, a part is produced by machining, polishing, and painting.

Number of machine tools = 3

Number of polishing tools = 4

Number of painting tools = 3

Now,

For finding the different routing consisting of machining, followed by polishing, and followed by painting, we have to simply multiply the number of machine tools, polishing tools and painting tools.

Therefore,

The different routing (consisting of machining, followed by polishing, and followed by painting) for a part are possible = 3 × 4 × 3 = 36.

Hence, the required answer is 36.

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2 years ago