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3 years ago

15 Points!

1 answer:

6 0

$5; -3; -1 -2i$
<span>In polynomials we have not of an imaginary unit (i), therefore we have the fourth zeros -1-2i.</span>

$f(x)=(x-5)(x+3)\left[x-(-1-2i)\right]\left[x-(-1+2i)\right]\\\\=(x^2+3x-5x-15)[x^2-x(-1+2i)-x(-1-2i)+(-1)^2-(2i)^2]\\\\=(x^2-2x-15)(x^2+x-2i+x+2i+1+4)\\\\=(x^2-2x-15)(x^2+2x+5)\\\\=x^4+2x^3+5x^2-2x^3-4x^2-10x-15x^2-30x-75\\\\=x^4-14x^2-40x-75$

Answer: B)

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A sales person earns 300.50 per week plus 7% of her weekly sales. Which of the following describes the sales necessary for the s

vodomira [7]

300.50 + 0.07x > = 900.85
0.07x > = 900.85 - 300.50
0.07x > = 600.35
x > = 600.35 / 0.07
x > = 8576.43 <=== she would have to sell at least 8576.43

3 0

4 years ago

Find the polynomial of minimum degree, with real coefficients, zeros at x=4±2⋅i and x=−8, and y-intercept at −480. Write your an

valkas [14]

Answer:

The polynomial of minimum degree is $p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$ .

Step-by-step explanation:

According to the statement, we appreciate that polynomial pass through the following points:

(i) $(4 + 2\,i,0)$ , (ii) $(4 - 2\,i, 0)$ , (iii) $(-8, 0)$ , (iv) $(0, -480)$

From Algebra we know that any n-th grade polynomial can be constructed by knowing n+1 different points. Hence, the polynomial of minimum degree is a quartic function. The polynomial has the following form:

$p(x) = (x-4-2\,i)\cdot (x-4+2\,i)\cdot (x+8)\cdot (x-r_{1})$

We proceed to expand the expression until standard form is obtained:

$p(x) = (x^{2}-4\cdot x-2\,i\cdot x-4\cdot x +16+8\,i+2\,i\cdot x-8\,i+4)\cdot (x+8)\cdot (x-r_{1})$

$p(x) = (x^{2}-8\cdot x+20)\cdot (x+8)\cdot (x-r_{1})$

$p(x) = (x^{3}-8\cdot x^{2}+20\cdot x +8\cdot x^{2}-64\cdot x+160)\cdot (x-r_{1})$

$p(x) = (x^{3}-44\cdot x +160)\cdot (x-r_{1})$

If we know that $p (0) = -480$ , then:

$-480=160\cdot (-r_{1})$

$-160\cdot r_{1} = -480$

$r_{1} = 3$

Then, the polynomial is:

$p(x) = (x^{3}-44\cdot x +160)\cdot (x-3)$

$p(x) = x^{4}-44\cdot x^{2}+160\cdot x-3\cdot x^{3}+132\cdot x -480$

$p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$

The polynomial of minimum degree is $p(x) = x^{4}-3\cdot x^{3}-44\cdot x^{2}+292\cdot x-480$ .

5 0

3 years ago

How do you simplify the equation useing like terms: 8r+12p-7-3p

stiks02 [169]

Answer:

8r+9p-7

Step-by-step explanation:

12p-3p=9p

8r+9p-7

7 0

3 years ago

Find the solutions to the equation.

Kitty [74]

You can write the equation using conventional symbols as
3x^2 - 2x - 5 = 0

You can recognize that the middle coefficient is equal to the sum of the other two, so those two coefficients can be used to factor the equation.
(1/3)(3x +3)(3x -5) = 0 . . . . . put the coefficients in the form (1/a)(ax + ...)(ax + ...) (x+1)(3x-5) = 0 . . . . . simplify

The solutions are the values of x that make one or the other of the factors equal to zero.
x = -1
x = 5/3

3 0

3 years ago

1. A teenager rides his bike a distance of 54 miles in 6 hours.

pentagon [3]

9 miles!
54 divided by 6 is 9.

3 0

2 years ago

Read 2 more answers