Solve the system of equation y=1/2x-2 and 3x+y=5

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polet [3.4K]

Answer:

4 pepperoni pizzas

Step-by-step explanation:

8 0

2 years ago

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kelly makes $10 more an hour than her regular pay when she is working overtime. Yesterday, she worked 8 regular hours and 4 over

skad [1K]

C. $10 per regular hour.

5 0

3 years ago

Consider the following polynomial. - 2x * y ^ 5 + 3x ^ 7 - 10x ^ 3 * y ^ 6 + 8x ^ 6 + 4 Which of the following statements are tr

Salsk061 [2.6K]

Option a: polynomial has 5 terms.

Option c: The constant term is 4.

Explanation:

The polynomial is $-2xy^{5} +3x^{7} -10x^{3} y^{6} +8x^{6} +4$

Option a: Polynomial has 5 terms

From the polynomial, we have,

1st term = $-2 x y^{5}$

2nd term = $3 x^{7}$

3rd term = $-10 x^{3} y^{6}$

4th term = $8 x^{6}$

5th term = $4$

Hence, the polynomial has 5 terms.

Thus, Option a is the correct answer.

Option b: The leading coefficient is -2 and the degree of the polynomial is 7.

The leading coefficient is the coefficient of the variable with the largest degree.

The degree of the polynomial can be determine by the adding the powers of the variable.

degree of 1st term = $-2 x y^{5}$ = $1+5=6$

degree of 2nd term = $3 x^{7}$ $=7$

degree of 3rd term = $-10 x^{3} y^{6}$ $=3+6=9$

degree of 4th term = $8 x^{6}$ $=6$

degree of 5th term = $4$ $=0$

Thus, from these 5 terms the highest value is 9 which is the degree of the polynomial.

The polynomial $-2xy^{5} +3x^{7} -10x^{3} y^{6} +8x^{6} +4$ has a largest degree of 9 and the leading coefficient is -10.

Hence, Option b is not the correct answer.

Option c: The constant term is 4.

The constant term is a term in which variable will not occur.

From the polynomial $-2xy^{5} +3x^{7} -10x^{3} y^{6} +8x^{6} +4$ , we can see that the constant term is 4.

Hence, Option c is the correct answer.

Option d: Polynomial is in decreasing degree order

The decreasing degree order is the degree in which each term is no larger than the degree of the preceding term.

From the polynomial, we have,

degree of 1st term = $-2 x y^{5}$ = $1+5=6$

degree of 2nd term = $3 x^{7}$ $=7$

degree of 3rd term = $-10 x^{3} y^{6}$ $=3+6=9$

degree of 4th term = $8 x^{6}$ $=6$

degree of 5th term = $4$ $=0$

where the degree of the 3rd term is not less than the 4th term.

Thus, the polynomial is not in decreasing degree order.

Hence, Option d is not the correct answer.

5 0

3 years ago

Decipher this please

kotykmax [81]

Answer: I think

Step-by-step explanation: 1=e, 2=a, 3=c, 4=d

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3 years ago

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Explain how to find each root, with its multiplicity, for the polynomial y=x^5-27x^2.

Nuetrik [128]

The roots of $y = x^{5}-27\cdot x^{2}$ are 0 (multiplicity 2), -3 (multiplicity 1), $-\frac{3}{2}+i\,\frac{3\sqrt{3}}{2}$ (multiplicity 1) and $-\frac{3}{2}-i\,\frac{3\sqrt{3}}{2}$ (multiplicity 1).

The characteristics of the polynomial can be derived from algebraic techniques. Roots and multiplicity can be found by <em>factoring</em> the polynomial. The multiplicity is represented by a power binomial of the form:

$(x-r_{i})^{m},\,m \le n$ (1)

Where $n$ is the grade of the polynomial.

Now we proceed to factor the formula:

$y = x^{5}-27\cdot x^{2}$

$y = x^{2}\cdot (x^{3}-27)$

$y = x^{2}\cdot (x^{2}+3\cdot x +9)\cdot (x-3)$

Please notice that $x^{2}+3\cdot x + 9$ have two complex roots.

$y = x^{2}\cdot \left(x+\frac{3}{2}-i\,\frac{3\sqrt{3}}{2} \right)\cdot \left(x+\frac{3}{2}+i\,\frac{3\sqrt{3}}{3} \right)\cdot (x-3)$

The roots of $y = x^{5}-27\cdot x^{2}$ are 0 (multiplicity 2), -3 (multiplicity 1), $-\frac{3}{2}+i\,\frac{3\sqrt{3}}{2}$ (multiplicity 1) and $-\frac{3}{2}-i\,\frac{3\sqrt{3}}{2}$ (multiplicity 1).

We kindly invite to see this question on polynomials: brainly.com/question/1218505

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2 years ago