What is x? 5x - 1 = - 8, №18010280, 19.10.2021 13:15

Mathematics

What is x? 5x - 1 = - 8

Step-by-step answer

P Answered by Specialist

x = -1.4, -7/5, or -1 2/5 (all same answer, just in different forms)

Step-by-step explanation:

Step 1: Add 1 to both sides.

Step 2: Divide both sides by 5.

x = -1.4, -7/5, or -1 2/5.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Mathematics

Relationship B has a lesser rate than Relationship A. This graph represents Relationship A. - Which equations could represent Relationship B? - Select each correct answer. y = 3/2 x y = 4x y = 5x y = x 10 - 9 - 8 - 7 - 6 - . (2, 6) 5 - 4 - 3 - . (1, 3) 2 - 1 - 0 - 1 2 3 4 5 6 7 8 9 10

Step-by-step answer

P Answered by Specialist

4

I think the answer is C and D..searched it up

Mathematics

Relationship B has a lesser rate than Relationship A. This graph represents Relationship A. - Which equations could represent Relationship B? - Select each correct answer. y = 3/2 x y = 4x y = 5x y = x 10 - 9 - 8 - 7 - 6 - . (2, 6) 5 - 4 - 3 - . (1, 3) 2 - 1 - 0 - 1 2 3 4 5 6 7 8 9 10

Step-by-step answer

P Answered by Specialist

4

I think the answer is C and D..searched it up

Mathematics

12)write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 5, -3, and -1 + 3i f(x) = x4 + 12.5x2 - 50x - 150 f(x) = x4 - 4x3 + 15x2 + 25x + 150 f(x) = x4 - 4x3 - 15x2 - 25x - 150 f(x) = x4 - 9x2 - 50x - 150question 13(multiple choice worth 5 points)use the rational zeros theorem to write a list of all potential rational zeros. f(x) = x3 - 7x2 + 9x - 24 ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 ±1, ±2, ±3, ±4, ±24 ±1, ±one divided by two, ±2, ±3, ±4, ±6, ±8, ±12, ±24 ±1,

Step-by-step answer

P Answered by Master

Solved.

Step-by-step explanation: The calculations are as follows -

(12) Given zeroes are 5, -3 and -1 + 3i. So, the other conjugate of -1 + 3i, i.e., -1 - 3i will also be a root of the polynomial. So the polynomial f(x) will be of degree 4 and is given by

$f(x)=(x-5)(x+3)(x+1-3i)(x+1+3i)\\\\\Rightarrow f(x)=(x^2-2x-15)(x^2+2x+1-9i^2)\\\\\Rightarrow f(x)=(x^2-2x-15)(x^2+2x+10)\\\\\Rightarrow f(x)=x^4-9x^2-50x-150.$

(13) Given polynomial is

f(x)=x^3-7x^2+9x-24.

Now, we will substitute the rational numbers in place of 'x' and check whether the value of f(x) becomes zero or not.

We will see that

$f(-1)\neq 0,~~f(1)\neq 0,~~f(2)\neq 0,~~f(-2)\neq 0, ~~f(3)\neq 0, ~~f(-3)\neq 0,~~etc$

Also, the polynomial is not zero for any rational number.

(14) Given, $f(x)=7x+6~~\textup{and}~~g(x) = 4x^2.$

So,

(f+g)(x)=f(x)+g(x)=7x+6+4x^2.

Thus, the problems are solved.

Mathematics

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 5, -3, and -1 + 3i f(x) = x4 + 12.5x2 - 50x - 150 f(x) = x4 - 4x3 + 15x2 + 25x + 150 f(x) = x4 - 4x3 - 15x2 - 25x - 150 f(x) = x4 - 9x2 - 50x - 150 question 13(multiple choice worth 5 points) use the rational zeros theorem to write a list of all potential rational zeros. f(x) = x3 - 7x2 + 9x - 24 ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 ±1, ±2, ±3, ±4, ±24 ±1, ±one divided by two, ±2, ±3, ±4, ±6, ±8, ±12, ±24 ±1,

Step-by-step answer

P Answered by Specialist

Q1 - D. f(x) = x^4-9x^2-50x-150

Q13 - A. ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

Q14 - A. $7x+6+4x^{2}$

Step-by-step explanation:

Question 1:

We know that rational roots always occurs in pairs. So, the zeros of the function will be 5, -3, -1+3i, -1-3i

So, the factored form is (x-5)(x+3)(x+1-3i)(x+1+3i)=0

i.e. (x^2-2x-15)(x+1-3i)(x+1+3i)=0

i.e. (x^3-x^2-3ix^2-17x+6ix-15+45i)(x+1+3i)=0

i.e. x^4-9x^2-50x-150=0

Hence, the polynomial function is f(x)=x^4-9x^2-50x-150 .

Question 13:

Rational Zeros Theorem states that 'If p(x) is a polynomial with integer coefficients and if $\frac{p}{q}$ is a zero of p(x) = 0. Then, p is a factor of the constant term of p(x) and q is a factor of the leading coefficient of p(x)'.

Let, $\frac{p}{q}$ is a zero of x^3-7x^2+9x-24=0 . Then, p is a factor of -24 and q is a factor of 1.

Thus, possible values of p = ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 and q = ±1

This gives, possible values of $\frac{p}{q}$ are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

Question 14:

We have, f(x) = 7x + 6 and g(x) = $4x^{2}$

Then, (f+g)(x) = f(x) + g(x) = 7x + 6 + $4x^{2}$

So, (f+g)(x) = $7x+6+4x^{2}$

Mathematics

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 5, -3, and -1 + 3i f(x) = x4 + 12.5x2 - 50x - 150 f(x) = x4 - 4x3 + 15x2 + 25x + 150 f(x) = x4 - 4x3 - 15x2 - 25x - 150 f(x) = x4 - 9x2 - 50x - 150 question 13(multiple choice worth 5 points) use the rational zeros theorem to write a list of all potential rational zeros. f(x) = x3 - 7x2 + 9x - 24 ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 ±1, ±2, ±3, ±4, ±24 ±1, ±one divided by two, ±2, ±3, ±4, ±6, ±8, ±12, ±24 ±1,

Step-by-step answer

P Answered by Specialist

Q1 - D. f(x) = x^4-9x^2-50x-150

Q13 - A. ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

Q14 - A. $7x+6+4x^{2}$

Step-by-step explanation:

Question 1:

We know that rational roots always occurs in pairs. So, the zeros of the function will be 5, -3, -1+3i, -1-3i

So, the factored form is (x-5)(x+3)(x+1-3i)(x+1+3i)=0

i.e. (x^2-2x-15)(x+1-3i)(x+1+3i)=0

i.e. (x^3-x^2-3ix^2-17x+6ix-15+45i)(x+1+3i)=0

i.e. x^4-9x^2-50x-150=0

Hence, the polynomial function is f(x)=x^4-9x^2-50x-150 .

Question 13:

Rational Zeros Theorem states that 'If p(x) is a polynomial with integer coefficients and if $\frac{p}{q}$ is a zero of p(x) = 0. Then, p is a factor of the constant term of p(x) and q is a factor of the leading coefficient of p(x)'.

Let, $\frac{p}{q}$ is a zero of x^3-7x^2+9x-24=0 . Then, p is a factor of -24 and q is a factor of 1.

Thus, possible values of p = ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 and q = ±1

This gives, possible values of $\frac{p}{q}$ are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

Question 14:

We have, f(x) = 7x + 6 and g(x) = $4x^{2}$

Then, (f+g)(x) = f(x) + g(x) = 7x + 6 + $4x^{2}$

So, (f+g)(x) = $7x+6+4x^{2}$

Mathematics

12)write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 5, -3, and -1 + 3i f(x) = x4 + 12.5x2 - 50x - 150 f(x) = x4 - 4x3 + 15x2 + 25x + 150 f(x) = x4 - 4x3 - 15x2 - 25x - 150 f(x) = x4 - 9x2 - 50x - 150question 13(multiple choice worth 5 points)use the rational zeros theorem to write a list of all potential rational zeros. f(x) = x3 - 7x2 + 9x - 24 ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24 ±1, ±2, ±3, ±4, ±24 ±1, ±one divided by two, ±2, ±3, ±4, ±6, ±8, ±12, ±24 ±1,

Step-by-step answer

P Answered by Specialist

Solved.

Step-by-step explanation: The calculations are as follows -

(12) Given zeroes are 5, -3 and -1 + 3i. So, the other conjugate of -1 + 3i, i.e., -1 - 3i will also be a root of the polynomial. So the polynomial f(x) will be of degree 4 and is given by

$f(x)=(x-5)(x+3)(x+1-3i)(x+1+3i)\\\\\Rightarrow f(x)=(x^2-2x-15)(x^2+2x+1-9i^2)\\\\\Rightarrow f(x)=(x^2-2x-15)(x^2+2x+10)\\\\\Rightarrow f(x)=x^4-9x^2-50x-150.$

(13) Given polynomial is

f(x)=x^3-7x^2+9x-24.

Now, we will substitute the rational numbers in place of 'x' and check whether the value of f(x) becomes zero or not.

We will see that

$f(-1)\neq 0,~~f(1)\neq 0,~~f(2)\neq 0,~~f(-2)\neq 0, ~~f(3)\neq 0, ~~f(-3)\neq 0,~~etc$

Also, the polynomial is not zero for any rational number.

(14) Given, $f(x)=7x+6~~\textup{and}~~g(x) = 4x^2.$

So,

(f+g)(x)=f(x)+g(x)=7x+6+4x^2.

Thus, the problems are solved.

Mathematics

Which of these polynomial equations is of least degree and has -1, 2, and 4 as three of its roots? a) 5x^2 + 2x + 8 = 0 b) (x + 2)(x - 1)(x + 4) = 0 c) x^3 - 5x2 + 2x + 8 = 0 d) x^4 - x^3 - 5x^2 + 2x + 8 = 0

Step-by-step answer

P Answered by PhD

12

If it has the roots -1,2, and 4 it is:

(x+1)(x-2)(x-4)

(x^2-x-2)(x-4)

x^3-4x^2-x^2+4x-2x+8

x^3-5x^2_2x+8

Only C is equal to the equation with the roots provided and it is of degree 3

Mathematics

Which of these polynomial equations is of least degree and has -1, 2, and 4 as three of its roots? a) 5x^2 + 2x + 8 = 0 b) (x + 2)(x - 1)(x + 4) = 0 c) x^3 - 5x2 + 2x + 8 = 0 d) x^4 - x^3 - 5x^2 + 2x + 8 = 0

Step-by-step answer

P Answered by PhD

12

If it has the roots -1,2, and 4 it is:

(x+1)(x-2)(x-4)

(x^2-x-2)(x-4)

x^3-4x^2-x^2+4x-2x+8

x^3-5x^2_2x+8

Only C is equal to the equation with the roots provided and it is of degree 3

Mathematics

99 points, need with algebra 1. use the parabola tool to graph the quadratic function f(x)=x^2 + 10x + 16. 2. let f(x) = x^2 - 2x - 4 what is the average rate of change for the quadratic function from x = -1 to x = 4? 3. use the parabola tool to graph the quadratic function f(x) = -5x^2 - 2 4. use the parabola tool to graph the quadratic function f(x) = 2x^2 + 24x + 70 5. select the statements that are true for the graph of y = (x + 2)^2 + 4 a. the vertex is (-2, 4) b. the graph has a minimum c. the vertex is (2, 4) d. the graph has a maximum.

Step-by-step answer

P Answered by Master

15

1 is in picture above.

2.

$average \: rate = \frac{f(4) - f(1)}{4 - ( - 1)} = \frac{5}{4 - ( - 1)} = 1$