Can someone help me please

Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+11x+21=0

IgorLugansk [536]

We must graph y=x^3-9x^2+11x+21. Please, see the attached file.
Then we see were the graph cuts the x-axis, and these values of x are the real solutions of the given equation:

The real solutions of the given equation are:x = -1, 3, and 7

7 0

3 years ago

Factor the polynomial function over the complex numbers. f(x)=x^4-x^3-2x−4 Enter your answer in the box. f(x) = The answer is: (

Vladimir79 [104]

Answer:

Factors: $(x+i\sqrt2)(x-i\sqrt2)(x+1)(x-2)=0$

Step-by-step explanation:

We are given a polynomial:

$f(x)=x^4-x^3-2x-4$

We have to factor the given polynomial into its complex factors.

The factorization can be done as follows:

$f(x)=x^4-x^3-2x-4 = 0\\x^4-x^3-2x-4 = 0\\x^4-4-x^3-2x=0\\\text{Identity: }a^2-b^2 = (a+b)(a-b)\\(x^4-4)-(x^3+2x) = 0\\(x^2+2)(x^2-2)-x(x^2+2) = 0\\(x^2+2)(x^2-2-x) = 0\\(x^2+2)(x^2-x-2) = 0\\(x^2+2)(x^2-2x-+x-2) = 0\\(x^2+2)((x(x-2)+1(x-2))=0\\(x^2+2)(x+1)(x-2)=0\\\text{Identity: }a^2-b^2 = (a+b)(a-b)\\(x^2-(\sqrt{-2})^2)(x+1)(x-2)=0\\(x+i\sqrt2)(x-i\sqrt2)(x+1)(x-2)=0$

8 0

3 years ago

Which ratio is equivalent to the ratio 33:36

xenn [34]

Answer:

Step-by-step explanation:

33/3 = 11

36/3 =13

11 :13

5 0

3 years ago

Hey need some help with this problem, its trigonometry with right triangles using SohCahToa if you can give me a hand it would b

Firlakuza [10]

For the given triangle, the value of x equals 30.9892 units.

Step-by-step explanation:

Step 1:

In the triangle, the angle is 40°, the opposite side has a length of 26 units, the adjacent side has a length of x units while the hypotenuse is not given.

To determine the value of x, we determine the value of the tan of the given triangle.

To calculate the tan of angle A we divide the opposite side's length by the the adjacent side's length.

$tan A = \frac{oppositeside}{adjacent side}.$

Step 2:

The length of the opposite side = 26 units.

The length of the adjacent side = x units.

$tan A = \frac{oppositeside}{adjacent side}, tan 40 = 0.8390, tan A = \frac{26}{x} .$

$0.8390 = \frac{26}{x} , x = \frac{26}{0.8390} = 30.9892.$

So x measures 30.9892 units.

6 0

3 years ago

Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square increasing when the area of the

abruzzese [7]

The area of the square is increasing at the rate of 36(3/2)^(1/2).btw,i forget to add ^2 to `cm`

3 0

3 years ago