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enyata [817]
3 years ago
7

State the degree and leading coefficient of each polynomial in one variable.if it is not a polynomial in one variable explain wh

y. number 2,4,6 please I'm stuck ​

Mathematics
1 answer:
valina [46]3 years ago
7 0

Answer:

  2. degree 3; leading coefficient 8

  4. degree 6; leading coefficient 7

  6. not a polynomial

Step-by-step explanation:

The "leading coefficient" is the coefficient of the highest-degree term in the sum of terms that makes up a polynomial.

These expressions all have one variable, so the number of variables in not an issue in any case. All of the exponents are positive integers, so that is not an issue in any case. However, the variable appears in the denominator in the expression of problem 6, so that sum is not a polynomial.

__

2. In order to put this into the form we recognize as a polynomial, the expression must be "simplified' by performing the multiplication of the two factors:

 = 8x³ -4x² +6x -3

The leading coefficient is the coefficient of the highest-degree term, which is the product of the highest-degree terms of the factors. That product is ...

  (2x)(4x²) = 8x³

so the leading coefficient is 8. The variable is to the 3rd power, so the degree is 3.

You don't actually have to do the rest of the multiplication in order to find the required answer.

__

4. The expression is already written as a sum, so we only need to find the term of highest degree. That is the last one: 7y^6. Its degree is 6 and its leading coefficient is 7.

__

6. Variables are not allowed in the denominator of a polynomial. This expression is not a polynomial.

_____

<em>Comment on degree</em>

The degree of a term is the exponent of the variable. If there is more than one variable, the degree of the term is the sum of their exponents. For example, the polynomial ...

  x² +xy +y²

has three terms, each of degree 2.

If this example were one of your problems, it would be rejected as "not a polynomial in one variable," since two variables are involved.

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Solve the system of equations by substitution y=5x-13 and 5x+2y=19
castortr0y [4]
Y = 5x - 13 ----------- (1)
5x + 2y = 19 --------- (2)

Sub (1) into (2):

5x + 2(5x -13) = 19
5x + 10x - 26 = 19
15x = 19 + 26
15x = 45
x = 3 -------- sub back into (1)
y = 5(3) - 13
y = 15 - 13
 y = 2

Ans: x = 3, y = 2
6 0
3 years ago
The sum of the dibits of a two digit number is 15. The number obtained by interchanging its digits exceeds the given number by 9
QveST [7]

Answer:

  78

Step-by-step explanation:

Interchanging the digits of a 2-digit number changes the value by a multiple of 9. The multiple is the difference between the digits of the number.

So, we have two digits that add to 15, and have a difference of 9/9 = 1. Since you're familiar with your addition facts, you know that the two digits are 7 and 8. Since the number we're looking for is the smallest of the numbers you can make with those digits, ...

  the original number is 78.

_____

More formally, let t and o represent the tens and ones digits of the original number.

  t + o = 15 . . . . . . the sum of digits is 15

  (10o +t) - (10t +o) = 9 . . . . swapping digits increases the value by 9

The latter equation simplifies to ...

  9o -9t = 9 . . . . collect terms

  o - t = 1 . . . . . . divide by 9 . . . (note the difference of digits is 9/9=1)

Adding this to the first equation gives ...

  (t +o) +(o -t) = (15) +(1)

  2o = 16

  o = 8

  t = o -1 = 7

The tens digit is 7 and the ones digit is 8: 78.

3 0
2 years ago
How many full glasses of water will be needed to fill the jug ? Jug= 2.8 litres, Cup= 200ml​
igomit [66]

Answer:

14 cups

Step-by-step explanation:

1 l = 1000ml

to filled the jug we need 2.8 litres

2.8 l to ml

2.8 × 1000

= 2800ml

how many cup would give us 2800ml

2800 ÷ 200

=14 cups

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Veronika [31]

Answer:

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Step-by-step explanation:

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Answer:

c) d is greater than or equal to 530

Step-by-step explanation:

Hope this helps!

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