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Anestetic [448]
3 years ago
11

A ruler is 12 inches long. What is the of this ruler

Mathematics
1 answer:
Nuetrik [128]3 years ago
7 0

Can you please clarify what you want to ask? Thanks!

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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
Whats a quadratic equation that has the roots of 6 and negative 9
Komok [63]

Answer:

x^2-3x-54

Step-by-step explanation:

(x+6)(x-9)     Setup the roots

x^2-9x+6x-54   FOIL out the terms

x^2-3x-54    Add like terms together

5 0
3 years ago
$14.65 plus what equals $65.00?
ziro4ka [17]

79.65

I used a calculator

5 0
2 years ago
Read 2 more answers
Find "both answers.
amid [387]
Sorry yo i just need points :/
5 0
3 years ago
Brett is 75 feet from the base of a building. he measures the angle of elevation to the top of the building and records it as 80
SashulF [63]
This is the concept of trigonometry, we are required to calculate the number of floors the building has given the information above;
# floors=[height of the building]/[height of each floor]
height of each floor=17 ft
let the height of the building be,h.
h is given by;
tan theta=opposite/adjacent
theta=80
opposite=h
adjacent=75 ft
thus
tan 80=h/75
h=75 tan 80
h=425.35 ft
thus the number of floors will be:
425.35/17
=25.020≈25 floors


8 0
3 years ago
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