Henry is planning to create two rectangular gardens.

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = -2. The y-intercept

Maru [420]

Answer:

$p(x) = - 0.7(x - 3)^{2} (x + 2)$

Step-by-step explanation:

We have that the polynomial, has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = -2.

This means the factored form of the polynomial will be.

$p(x) = a(x - 3)^{2} (x + 2)$

Also, it was given that, the y-intercept is y=-12.6.

This implies that:

$- 12.6= a(0 - 3)^{2} (0 + 2)$

$- 12.6= a(- 3)^{2} (2)$

$- 12.6= 18a$

Divide both sides by 18;

$a = \frac{ - 12.6}{18}$

$a= - 0.7$

Therefore the polynomial is

$p(x) = - 0.7(x - 3)^{2} (x + 2)$

7 0

3 years ago

What are the coordinates of the circumcenter of a triangle with vertices A(0,1) B(2,1) and C(2,5)?

yawa3891 [41]

THis is a cool question.
1) Use the point slope form to find the equation of the lines between two of the points (choose two points that when a line is drawn between them make a chord on the circle).
2) Use the midpoint of a line equation to find the midpoint of the line, then find the slope of the line that is perpendicular at that point and write an equation for it.
3) Then do the same thing for the other two points that form a chord on the circle.
4) Then set the two equations equal to each other and solve. The point where they meet is the circumcenter.

4 0

3 years ago

Write the cubic polynomial function f(x)in expanded form with zeros −6,−5,and −1, given that f(0)=60

RSB [31]

Answer:

$f(x)=2x^{3}+24x^{2}+82x+60$

Step-by-step explanation:

we know that

The roots of the polynomial are the values of x when the value of the polynomial f(x) is equal to zero

The roots of the polynomial function are

x=-6 -----> (x+6)=0

x=-5 -----> (x+5)=0

x=-1 -----> (x+1)=0

The equation of the cubic polynomial is

$f(x)=a(x+6)(x+5)(x+1)$

where

a is the leading coefficient

Remember that

f(0)=60

That means ------> For x=0 the value of f(x) is equal to 60

substitute the value of x and the value of y in the function and solve for a

$60=a(0+6)(0+5)(0+1)$

$60=a(6)(5)(1)$

$60=30a$

$a=2$

so

$f(x)=2(x+6)(x+5)(x+1)$

Applying the distributive property

Convert to expanded form

$f(x)=2(x+6)(x+5)(x+1)\\\\f(x)=2(x+6)(x^{2}+x+5x+5)\\\\f(x)=2(x+6)(x^{2}+6x+5)\\\\f(x)=2(x^{3}+6x^{2}+5x+6x^{2}+36x+30)\\\\f(x)=2x^{3}+24x^{2}+82x+60$

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B2%7D-1%7D%7B2-5a%7D%20times%20%5Cfrac%7B15a-6%7D%7Ba%5E%7B2%7D%2B5a-6%7D" id=

stepan [7]

$\bf \cfrac{a^2-1}{2-5a}\times \cfrac{15-6}{a^2+5a-6}\\\\
-----------------------------\\\\
recall\quad \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
thus\quad a^2-1\iff a^2-1^2\implies (a-1)(a+1)
\\\\\\
now\quad a^2+5a-6\implies (a+6)(a-1)\\\\
-----------------------------\\\\
thus
\\\\\\
\cfrac{a^2-1}{2-5a}\times \cfrac{15-6}{a^2+5a-6}\implies \cfrac{(a-1)(a+1)}{2-5a}\times \cfrac{3(5a-2)}{(a+6)(a-1)}\\\\
-----------------------------\\\\
$

$\bf now\quad 3(5a-2) \iff -3(2-5a)\\\\
-----------------------------\\\\
thus
\\\\\\
\cfrac{\underline{(a-1)}(a+1)}{\underline{2-5a}}\times \cfrac{-3\underline{(2-5a)}}{(a+6)\underline{(a-1)}}\implies \cfrac{-3(a+1)}{a+6}$

6 0

2 years ago

Mr. Smith wishes to retire in 16 years. When he retires he would like to have $500,000 in his bank account. Mr. Smith's bank pay

Neko [114]

The amount he should deposit is 31,250 dollars

6 0

2 years ago