Find the distance between the two points rounding to the nearest tenth (if necessary).

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

what is the equation of the line that is perpendicular to the line y=3/5x+10 and passes through the point (15,-5)

riadik2000 [5.3K]

Answer:

$y = -\frac53x + 20$

Step-by-step explanation:

Hello!

A line that is perpendicular to another has an opposite-reciprocal slope.

Meaning:

Flip the sign (+/-)
Flip the fraction

The slope perpendicular to 3/5 would be -5/3.

We can solve for the y-intercept by plugging in the x and y values given from the coordinate into the equation with out new slope.

<h3 /><h3>Solve for B</h3>

$y = -\frac53x + b$
$-5 = -\frac53(15) + b$
$-5 = -25 + b$
$20 = b$

The y-intercept of the new line is 20.

The equation is $y = -\frac53x + 20$

6 0

2 years ago

a garden is in the shape of a square with a perimeter of 60 feet. the garden is surrounded by two fences. one fence is around th

Anon25 [30]

Answer: The total cost of the fences=$165.6

Step-by-step explanation:

Let a = the length of the side if the square.

The perimeter of the square is 60 ft

4a = 60ft

divide both sides by

4a = 60/4

a = 15 ft

The garden is surrounded by two fences, one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside

Expand to get:

4*a + 4(a + 2*3)

Replace a with 15 to get:

= 4*15 + 4(15 + 6) 60 + 4(21) 60+84

= 144ft

The cost of the fence is $1.15 per foot

The cost of 144 ft fence will be:

= 144*1.15

= $165.6

Learn more about event correlation here: brainly.com/question/1333555

#21165

7 0

1 year ago

A bag of marbles has 6 red marbles and 7 green marbles in it. What is the percent probability of pulling a green marble out of t

soldi70 [24.7K]

Answer:

If a bag contains 4 red marbles, 3 blue marbles, and 7 green marbles and a marble is randomly selected from the bag, what is the probability that it is blue? P=3/(3+4+7)=3/14 because each of 14 marbles is equally likely to be drawn.

Step-by-step explanation:

7 0

3 years ago

Starting at sea level, a submarine descended at a constant rate to a depth of − 4/5 mile relative to sea level in 3 minutes.

Jobisdone [24]

If it were 4 then it would be 1 1/3 for one minute

5 0

3 years ago

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