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rjkz [21]
3 years ago
10

Which statement is ALWAYS true?

Mathematics
1 answer:
Georgia [21]3 years ago
8 0

Answer:                                                                                                                                                                                                                                                                                                                           n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 .

Step-by-step explanation:Tell me if answer did not show it has been doing that for me

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Find the polynomial of minimum degree, with real coefficients, zeros at
drek231 [11]

Answer:

\huge\boxed{p(x)=4x^3-20x^2+4x+300}

Step-by-step explanation:

\text{If}\ x=4\pm3i\ \text{and}\ x=-3\ \text{are the zeros of a polynomial, then it has  a form:}\\\\p(x)=\bigg(x-(4-3i)\bigg)\bigg(x-(4+3i)\bigg)\bigg(x-(-3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x-4+3i)(x-4-3i)(x+3)\bigg(r(x)\bigg)\\\\p(x)=\underbrace{\bigg((x-4)+3i\bigg)\bigg((x-4)-3i\bigg)}_{\text{use}\ (a+b)(a-b)=a^2-b^2}(x+3)\bigg(r(x)\bigg)\\\\p(x)=\bigg((x-4)^2-(3i)^2\bigg)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2

p(x)=(x^2-2(x)(4)+4^2-3^2i^2)(x+3)\bigg(r(x)\bigg)\qquad\text{use}\ i^2=-1\\\\p(x)=(x^2-8x+16-9(-1))(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+16+9)(x+3)\bigg(r(x)\bigg)\\\\p(x)=(x^2-8x+25)(x+3)\bigg(r(x)\bigg)\qquad\text{use FOIL}:\ (a+b)(c+d)=ac+ad+bc+bd\\\\p(x)=\bigg((x^2)(x)+(x^2)(3)+(-8x)(x)+(-8x)(3)+(25)(x)+(25)(3)\bigg)\bigg(r(x)\bigg)\\\\p(x)=(x^3+3x^2-8x^2-24x+25x+75)\bigg(r(x)\bigg)\qquad\text{combine like terms}\\\\p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)

\text{The y-intercept is at 300}.\\\\\text{For}\ w(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+...+a_1x+a_0\\\\\text{y-intercept is}\ a_0\\\\\text{Therefore for}\ p(x)=(x^3-5x^2+x+75)\bigg(r(x)\bigg)\\\\\text{y-intercet is}\ 75\bigg(r(x)\bigg)\\\\75\bigg(r(x)\bigg)=300\qquad\text{divide both sides by 75}\\\\r(x)=4\\\\\text{Finally:}\\\\p(x)=(x^3-5x^2+x+75)(4)\qquad\text{use the distributive property}\\\\p(x)=(x^3)(4)+(-5x^2)(4)+(x)(4)+(75)(4)\\\\p(x)=4x^3-20x^2+4x+300

7 0
3 years ago
Tras una rebaja del 8%, un pantalón cuesta 17,28 euros. ¿Cuál era su precio inicial?
Sholpan [36]

Answer:

18.78

Step-by-step explanation:

x*(100%-8%)=17.28

x=18.78

3 0
2 years ago
(-8,-2) and (-4, 6) what is y?<br><br><br> HELP PLEASE THANK YOU!
Thepotemich [5.8K]

Answer:

The y’s are the numbers in the right (the second ones) -2,6.

Step-by-step explanation:

4 0
3 years ago
Brian is riding his bike. He biked a distance of 14 miles at a rate of 14 miles per hour. Rearrange the distance formula, d = rt
Mariana [72]

Answer:

60 minutes

Step-by-step explanation:

The distance formula is:

D = RT

Where

D is distance (in miles)

R is rate (in miles per hour)

T is time (in minutes)

Given,

D = 14 miles

R = 14 miles per hour

We want to find T, so we have:

D=RT\\T=\frac{D}{R}\\T=\frac{14}{14}\\T=1

So the time is 1 hour

We want in minutes, and we know 60 minutes is 1 hour, so the time (in minutes) is 60 minutes

8 0
3 years ago
Read 2 more answers
Please answer correctly !!!! Will mark brianliest !!!!!!
mr Goodwill [35]

Answer:

-3x-5 x-4 I this work good luck

6 0
3 years ago
Read 2 more answers
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