Describe the sign of the quotient of two integers when: Both integers are positive. Positive Negative

Answers

Answer 1

Answer:

The sign of the quotient of two integers depends on the signs of the integers being divided.

Both integers are positive: When both integers are positive, the quotient will also be positive. This is because dividing positive numbers will always result in a positive value.

For example, if we divide 8 by 2, the quotient is 4

Positive divided by negative: When a positive integer is divided by a negative integer, the quotient will be negative. This is because dividing a positive number by a negative number results in a negative value.

For example, if we divide 10 by -2, the quotient is -5

In summary, the sign of the quotient of two integers depends on the signs of the integers being divided. If both integers are positive, the quotient will be positive. If a positive integer is divided by a negative integer, the quotient will be negative.

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Classify the following polynomials by degree and number of terms.1. 3p^3 + 2p^2 + 19p - 5

2. 5x^4 + 12

3. n^2 - 7n - 21

4. 3

5. 2x + 7

6. -8y^2

Answers

Answer:

See below

Step-by-step explanation:

Let's classify the given polynomials by their degree and number of terms:

1. 4p³ + 2p² + 19p - 5

- Degree: 3 (the highest power of the variable, which is p, is 3)

- Number of terms: 4 (there are four terms in the expression)

2. 5x⁴ + 12

- Degree: 4 (the highest power of the variable, which is x, is 4)

- Number of terms: 2 (there are two terms in the expression)

3. n² - 7n - 21

- Degree: 2 (the highest power of the variable, which is n, is 2)

- Number of terms: 3 (there are three terms in the expression)

4. 3

- Degree: 0 (since it's a constant, it has no variable part)

- Number of terms: 1 (there is only one term, which is the constant 3)

5. 2x + 7

- Degree: 1 (the highest power of the variable, which is x, is 1)

- Number of terms: 2 (there are two terms in the expression)

6. -8y²

- Degree: 2 (the highest power of the variable, which is y, is 2)

- Number of terms: 1 (there is only one term, which is -8y²)

Answer:

3p^3 + 2p^2 + 19p - 5

Degree: The highest exponent of the variable 'p' is 3, so the degree is 3.

Number of terms: There are 4 terms in this polynomial.

5x^4 + 12

Degree: The highest exponent of the variable 'x' is 4, so the degree is 4.

Number of terms: There are 2 terms in this polynomial.

n^2 - 7n - 21

Degree: The highest exponent of the variable 'n' is 2, so the degree is 2.

Number of terms: There are 3 terms in this polynomial.

Degree: The polynomial 3 is a constant term, and constants have a degree of 0.

Number of terms: There is 1 term in this polynomial.

2x + 7 Degree: The highest exponent of the variable 'x' is 1, so the degree is 1.

Number of terms: There are 2 terms in this polynomial.

-8y^2

Degree: The highest exponent of the variable 'y' is 2, so the degree is 2.

Number of terms: There is 1 term in this polynomial.

Therefore, the classification of the given polynomials by degree and number of terms is as follows:

3p^3 + 2p^2 + 19p - 5:

Degree: 3

Number of terms: 4

5x^4 + 12:

Degree: 4

Number of terms: 2

n^2 - 7n - 21:

Degree: 2

Number of terms: 3

Degree: 0 Degree: 0

Number of terms: 1

2x + 7:

Degree: 1

Number of terms: 2

-8y^2:

Degree: 2

Number of terms: 1

Step-by-step explanation:

In algebra, a polynomial is an expression consisting of variables (such as 'x', 'y', or 'p') raised to non-negative integer powers, combined with coefficients (constants), and combined using addition and subtraction operations. The terms within a polynomial are separated by addition or subtraction signs.

The degree of a polynomial is determined by the highest exponent (power) of the variable in the polynomial. It represents the highest power to which the variable is raised. For example, in the polynomial 3p^3 + 2p^2 + 19p - 5, the highest power of the variable 'p' is 3, so the degree of the polynomial is 3.

The number of terms in a polynomial refers to the separate parts that are added or subtracted. In the polynomial 3p^3 + 2p^2 + 19p - 5, there are four terms: 3p^3, 2p^2, 19p, and -5.

Let's break down the classification of each polynomial:

3p^3 + 2p^2 + 19p - 5:

Degree: The highest exponent of the variable 'p' is 3, so the degree is 3.

Number of terms: There are four terms in this polynomial.

5x^4 + 12:Degree: The highest exponent of the variable 'x' is 4, so the degree is 4.

Number of terms: There are two terms in this polynomial.

n^2 - 7n - 21:

Degree: The highest exponent of the variable 'n' is 2, so the degree is 2.

Number of terms: There are three terms in this polynomial.

Degree: The polynomial 3 is a constant term, and constants have a degree of 0 since they have no variables.

Number of terms: There is one term in this polynomial.

2x + 7:

Degree: The highest exponent of the variable 'x' is 1, so the degree is 1.

Number of terms: There are two terms in this polynomial.

-8y^2:

Degree: The highest exponent of the variable 'y' is 2, so the degree is 2.

Number of terms: There is Number of terms: There is one term in this polynomial.

By determining the degree and number of terms in a polynomial, we can gain insights into its properties and behavior, such as its complexity, the number of solutions it may have, or its graph's share

The diameter of a Frisbee is 12 in. What is the area of the Frisbee?a. 37.68 sq. in.
b. 452.16 sq. in.
c. 18.84 sq. in.
d. 113.04 sq. in.

Answers

we know that

Area of the circle is equal to

$A=\pi r^(2)$

where

r is the radius

in this problem

$diameter=12\ in \n radius=diameter/2\n radius=12/2\n radius=6\ in$

$A=3.14* 6^(2)$

$A=113.04 in^(2)$

therefore

the answer is the option

d. 113.04 sq. in.

The area of the Frisbee is about 113 in.² ( Option D )

Further explanation

The basic formula that need to be recalled is:

Circular Area = π x R²

Circle Circumference = 2 x π x R

where:

R = radius of circle

The area of sector:

$\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} * \text{Area of Circle}$

The length of arc:

$\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} * \text{Circumference of Circle}$

Let us now tackle the problem!

Given:

Diameter of Frisbee = d = 12 in

Unknown:

Area of Frisbee = A = ?

Solution:

Area of the Frisbee could be calculated using the area of circle as follows:

$A = (1)/(4) \pi d^2$

$A = (1)/(4) * \pi * 12^2$

$A = 36 \pi ~ in.^2$

$A \approx \boxed {113.10 ~ in.^2}$

The closest option available will be option D. 113 in.²

Learn more

Calculate Angle in Triangle : brainly.com/question/12438587
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Trigonometry Formula : brainly.com/question/12668178

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse, Circle , Arc , Sector , Area, Inches , Frisbee , Diameter , Radius , Trigonometry ,

Simplify the expression (2x − 9)(x + 6).

Answers

( 2x - 9 ) ( x + 6 )

( 2x ) ( x ) + ( 2x ) ( 6 ) + ( - 9 ) ( x ) + ( - 9 ) ( 6 )

2x² + 12x - 9x - 54

2x² + 3x - 54.

(2x-9)•(x+6)

2x•x+2x•6-9•x-9•6

2x²+12x-9x-54
2x²+(12-9)•x -54
2x²+3x-54

The sum of two integers is -123.If one of them is 325 , what is the other?

Answers

Answer:

The other integer is 448

Step-by-step explanation:

Let's say the other integer is 'x'

The sum of two integers is -123.If one of them is 325

Let's set an equation to find the otherinteger. The required equation is

$-123 + other \: integer = 325$

$-123 + x = 325$

Add 123 on both sides,

$-123 + 123 + x = 325 + 123$

$x = 448$

Hence the other integer is 448

The ratio of girls to boys in Liza’s classroom is 5 to 4How many girls are in her classroom if there is a total of 27
students?

1. 12
2. 9
3. 54
4. 15

Answers

The answer is 15. There are more girls than boys. 27 divided by 2 is 13.5. As the ratio is 5:4 the number of girls must be higher than 13.5, which cancels out 12 and 9. 54 is too great so the answer is 15.

Answer:

2.9

Step-by-step explanation:

write an equation and solve for t seven less than a number t equals another number r plus 6. t = r 13 t = r - 1 t = -r 1 t = -r -13

Answers

t - 7 = r + 6 |add 7 to both sides

t = r + 13

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