Which of the following best defines a function?

Use synthetic division to find the quotient and remainder. Express your answer as a polynomial.

OLEGan [10]

1. 2x³ - 11x² + 13x - 21 ÷ x - 3

x - 3 = 0 ⇒ x = 3

3 | 2 -11 13 -21

2 -5 -2 -27

1. Answer: 2x² - 5x - 2 - $\frac{27}{x - 3}$

*************************************************************

2. 3x³ + 7x² - 13x + 10 ÷ x + 2

x + 2 = 0 ⇒ x = -2

-2 | 3 7 -13 10

3 1 -15 40

2. Answer: 3x² + x - 15 + $\frac{40}{x + 2}$

3. 2x³ + 13x² - 21x + 9 ÷ x - 1

x - 1 = 0 ⇒ x = 1

1 | 2 13 -21 9

2 15 -6 3

3. Answer: 2x² + 15x - 6 + $\frac{3}{x - 1}$

4. 7x³ + 0x² - 8x + 16 ÷ x - 2

x - 2 = 0 ⇒ x = 2

2 | 7 0 -8 16

7 14 20 56

4. Answer: 7x² + 14x + 20 + $\frac{56}{x - 2}$

5. 8x⁴ - 14x³ - 71x² - 10x + 24 ÷ x - 4

x - 4 = 0 ⇒ x = 4

4 | 8 -14 -71 -10 24

8 18 1 -6 0

5. Answer: 8x³ + 18x² + x - 6

8 0

3 years ago

5)Find two square numbers that add up to 20

Wittaler [7]

The square of 4 and 2 adds up to 20!
4 square is 16.
2 square is 4
So 16+4=20

8 0

3 years ago

Is the equation true, false or open <br><br> 9p+8=10p+7

kifflom [539]

9p + 8 = 10p + 7
- 9p - 9p
   8 = p + 7
   - 7 - 7
   1 = p

5 0

4 years ago

Two containers, X and Y, are each filled by an ideal gas at the same temperature. The volume of Y is half the volume of X. The n

-Dominant- [34]

Answer:

The answer to the question is

The ratio of the two gas pressures $\frac{P_{x} }{P_{y} }$ , that is Px to Py = 1/6

Step-by-step explanation:

Let the gases Volumes be V₁ and V₂

Where volume of X = V₁ and

volume of Y = V₂

The volume of Y is half the volume of X

∴ V₂ = $\frac{1}{2}$ × V₁

Let the number of moles be n₁ and n₂ in X and Y respectively

therefore n₂ = 3 × n₁

The pressure of the gas in X is Pₓ and the pressure of the gas in Y is $P_{y}$ then we have

P₁ × V₁ = n₁ × R × T₁ , and P₂ × V₂ = n₂ × R × T₂

(P₁ × V₁)/(n₁ × T₁) = (P₂ × V₂)/(n₂ × T₂)

but T₁ = T₂

Therefore

(P₁ × V₁)/n₁ = (P₂ × V₂)/n₂. However n₂ = 3 × n₁ and V₂ = $\frac{1}{2}$ × V₁ therefore substituting in the equation we have

(P₁ × V₁)/n₁ = (P₂ × $\frac{1}{2}$ × V₁ )/(3 × n₁) from where

P₁ /P₂ = ( $\frac{1}{2}$ × V₁ × n₁)/(V₁×3 × n₁) =0.5/3 = 1/6

The ratio of $\frac{P_{x} }{P_{y} }$ = 1/6

6 0

4 years ago

20 POINTS

RUDIKE [14]

<em>The correct expressions are as follows:</em>

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$ Equivalent $343$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$ Not Equivalent $49$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$ Equivalent $7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$ Not Equivalent $49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}$

$\texttt{ }$

<h3>Further explanation</h3>

Let's recall following formula about Exponents and Surds:

$\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }$

$\boxed { (a ^ b) ^ c = a ^ { b . c } }$

$\boxed {a ^ b \div a ^ c = a ^ { b - c } }$

$\boxed {\log a + \log b = \log (a \times b) }$

$\boxed {\log a - \log b = \log (a \div b) }$

<em>Let us tackle the problem!</em>

$\texttt{ }$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7^2)^{\frac{7}{5}}$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7)^{2\times \frac{7}{5}}$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}}$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5} + \frac{14}{5}}$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{15}{5}}$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{3}$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{343}$

$\texttt{ }$

<em>From the results above, it can be concluded that the correct statements are:</em>

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$ Equivalent $343$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$ Not Equivalent $49$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$ Equivalent $7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}$

$7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}$ Not Equivalent $49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}$

$\texttt{ }$

<h3>Learn more</h3>

Coefficient of A Square Root : brainly.com/question/11337634
The Order of Operations : brainly.com/question/10821615
Write 100,000 Using Exponents : brainly.com/question/2032116

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Exponents and Surds

Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent , Perfect , Square , Factor.

4 0

4 years ago

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