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3 years ago

Which algebraic expression is a polynomial with a degree of 5?

Mathematics

2 answers:

anygoal [31]3 years ago

8 0

Answer:

$2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4$

Step-by-step explanation:

Since, the highest degree in a polynomial is called the degree of the polynomial,

While, the degree of each term in a polynomial with two variables is the sum of the exponents in each term.

In $3x^5 + 8x^4y^2 - 9x^3y^3 - 6y^5$ ,

Sum of exponents are 5, 6, 6, 5,

So, degree of the polynomial is 6.

In $2xy^4 + 4x^2y^3 - 6x^3y^2 - 7x^4$ ,

Sum of exponents are 5, 5, 5, 4,

So, degree of the polynomial is 5.

In $8y^6 + y^5 - 5xy^3 + 7x^2y^2 - x^3y - 6x^4$ ,

Sum of exponents are 6, 5, 4, 4, 4, 4

So, degree of the polynomial is 6.

In $-6xy^5 + 5x^2y^3 - x^3y^2 + 2x^2y^3 -3xy^5$ ,

Sum of exponents are 6, 5, 5, 5, 5

So, degree of the polynomial is 6.

Eddi Din [679]3 years ago

6 0

The degree of a polynomial is the highest exponent or sum of exponents of the variables in the individual terms of a polynomial.

Looking at each the polynomial:

3x5 + 8x4y2 – 9x3y3 – 6y5: Degree is 6 (look at the 2nd and 3rd term)

2xy4 + 4x2y3 – 6x3y2 – 7x4: Degree is 5 (look at 1st, 2nd, and 3rd term)

8y6 + y5 – 5xy3 + 7x2y2 – x3y – 6x4: Degree is 6 (look at 1st term)

–6xy5 + 5x2y3 – x3y2 + 2x2y3 – 3xy5: Degree is 6 (look at 1st and last term)

Therefore, the answer is the second option:
2xy4 + 4x2y3 – 6x3y2 – 7x4

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For the following list of data, calculate (a) the mean, (b) the median, and (c) the mode or modes (if any) 1.8, 5, 6.3, 8 ,8, 4.

disa [49]

Answer:

(a) The mean is:

The sum of the values: 1.8 + 5 + 6.3 + 8 + 8 + 4.8 + 2.8 + 4.8 = 41.5

The sum divided by the number of values: 41.5 ÷ 8 = 5.1875

(b) The median is:

The values in numerical order: 1.8, 2.8, 4.8, 4.8, 5, 6.3, 8, 8

The mean of the two middle values: (4.8 + 5) ÷ 2 = 4.9

The values in numerical order: 1.8, 2.8, 4.8, 4.8, 5, 6.3, 8, 8

The values that repeat most often: 4.8, 8 (both appear twice)

7 0

3 years ago

Check that 2b+b and 3b have the same value when b is 1,2, and 3. Do 2b+b and 3b have the same value for all values of b? Explain

Inessa [10]

Answer:

Expression 2b+b and 3b have same values for all values of b.

Step-by-step explanation:

Given the two expression $2b+b$ and $3b$ and values of b as 1, 2 and 3.

Consider first expression that is, $2b+b$ .

Substituting the value of $b=1$ ,

$2\left(1\right)+\left(1\right)=2+1=3$ ....1

Substituting the value of $b=2$ ,

$2\left(2\right)+\left(2\right)=4+2=6$ ....2

Substituting the value of $b=3$ ,

$2\left(3\right)+\left(3\right)=6+3=9$ ....3

Consider second expression that is, $3b$ .

Substituting the value of $b=1$ ,

$3\left(1\right)=3$ ....4

Substituting the value of $b=2$ ,

$3\left(2\right)=6$ ....5

Substituting the value of $b=3$ ,

$3\left(3\right)=9$ ....6

For value of b=1, equation 1 and equation 4 are same, for value of b=2, equation 2 and equation 5 are same and for value of b=3 equation 3 and equation 6 are same.

Therefore both expression are same for all values of b.

3 0

3 years ago

On a coordinate grid, which of these points would be closest to the origin?

Nimfa-mama [501]

A (2,1) is closest (0,4) is a close second but A is the closest

3 0

3 years ago

A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther

mariarad [96]

<h2>Answer:</h2>

Recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

Number of interactions for 2 children = 1

Number of interactions for 3 children = 5

Number of interaction for 4 children = 14

So,

We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

$a_{1}=0\\a_{2}=1\\a_{3}=5\\a_{4}=14\\$

Therefore, on checking, we observe that,

$a_{n}=a_{n-1}+(n-1)^{2}$

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

At,

n = 1

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

which is true.

At,

n = 2

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

At,

n = 3

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

At,

n = 4

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

Therefore, the recursive equation for the pattern followed is given by,

$a_{n}=a_{n-1}+(n-1)^{2}$

3 0

3 years ago

Eduardo mixed 5 pounds o cashews and almonds. Cashews cost $8 per pound and almonds cost $6 per pound. The total cost of the mix

NemiM [27]

Answer:

3.5 pounds of the mixture was almonds

Step-by-step explanation:

Assume that the mixture contains x pounds of cashews and y pounds of almonds

∵ x represents the amount of cashew

∵ y represents the amount of almond

∵ Eduardo mixed 5 pounds of cashews and almonds

∴ x + y = 5 ⇒ (1)

∵ Cashews cost $8 per pound

∵ Almonds cost $6 per pound

∵ The total cost of the mixture was $33

→ Multiply x by 8 and y by 6 and equate their sum by 33

∴ 8x + 6y = 33 ⇒ (2)

Now we have a system of equations to solve it

→ Multiply equation (1) by -8 to eliminate x

∵ -8(x) + -8(y) = -8(5)

∴ -8x - 8y = -40 ⇒ (3)

→ Add equations(2) and (3)

∵ (8x + -8x) + (6y + -8y) = (33 + -40)

∴ -2y = -7

→ Divide both sides by -2

∴ y = 3.5

∵ y represents the amount of almond

∴ 3.5 pounds of the mixture was almonds

7 0

3 years ago