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3 years ago

How to form a polynomial with given zeros and degree and multiplicity calculator

Mathematics

1 answer:

ohaa [14]3 years ago

3 0

Answer:

Taking P(x) = x³-12x-16 as an example

Step-by-step explanation:

For a polynomial, if

x = a is a zero of the function, then (x − a) is a factor of the function.

We have two unique zeros:

−2 and 4. However, −2 has a multiplicity of 2, which means that the factor that correlates to a zero of −2 is represented in the polynomial twice.

Following how it's constructed

zero at -2, multiplicity 2

zero at 4, multiplicity 1

p(x)=x−(−2))²(x−4)¹

Thus,p(x)=(x+2)²(x−4)

Expand: p(x)=(x²+4x+4)(x−4)

p(x) =x³−12x−16

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The base diameter and the height of a cone are both

WITCHER [35]

Answer:

11/ 42. *. X^ 2. * X = I/3 X A * h; if E = 1/3 A

Then the answer is EX

Step-by-step explanation:

Volume of cone= 1/3 * base area * height

= 1/3 * pi* (X/2)^2 * X

= 1/3. * 22/ 7 * X^3/4

= 22/ 21 * X^3 / 4

= 11/21 *. X^2/ 2. *. X

= 11/ 42. * X^3

= 11/ 42. *. X^ 2. * X

3 0

2 years ago

3х - 30 = у 7y - 6 = 3х

mars1129 [50]

Answer:

Step-by-step explanation:

This one is simple substitution... at least, substitution is the easiest method. The first equation is 3x – 30 = y and the second is 7y – 6 = 3x

As I look, I see 3 ways to use substitution to solve this:

substitute 7y – 6 for 3x
substitute 3x – 30 for y
solve 3x – 30 = y for 3x and make it equal to 7y – 6

We're going to only use 1 method for the sake of time. Try the other two on your own. Assuming you don't make any mistakes, they will work.

Method 1:

3x – 30 = y

7y – 6 = 3x — initial system of equations

7y – 6 – 30 = y — substitute 7y – 6 for 3x

7y – 6 – 30 = y — marking like terms, bold for constants, underlined for variables

7y – 36 = y — combining the constants and simplifying

Here, you could diverge into multiple paths: add 36 to both sides, subtract y from both sides, divide by 6 OR subtract 7y from both sides and divide by –6 . For the sake of time, I'm subtracting 7y, though I don't like dealing with negatives.

7y – 7y – 36 = y – 7y — subtract 7y from both sides

–36 = –6y — simplify

–36 ÷ –6 = –6y ÷ –6 — divide by –6 on both sides

y = 6 — simplify

Again, we can diverge here: substitute y into 3x – 30 = y or substitute y into 7y – 6 = 3x

I'm going to choose 3x – 30 = y but it will work either way, should you take the time (if you have it) to chase down every path this problem can take.

3x – 30 = y — initial equation

3x – 30 = 6 — substitute 6 for y

3x – 30 + 30 = 6 + 30 — add 30 to both sides to isolate 3x

3x = 36 — simplify the expression

3x ÷ 3 = 36 ÷ 3 — divide both sides by 3 to isolate x

x = 12 — simplify

So, we have x = 12 and y = 6 . We know they work for 3x – 30 = y but not if they work for 7y – 6 = 3x . Let's substitute those in to see if (12, 6) really is the solution point.

7y – 6 = 3x — original equation

7(6) – 6 ≟ 3(12) — substitute 6 for y and 12 for x

42 – 6 ≟ 36 — simplify by multiplying

36 = 36 ✔ — simplify by combining like terms on left side

Success! It works! We have found our solution!

I hope this helps increase your understanding of the concept. Have a great day!

8 0

3 years ago

Write an equation in point-slope form for the line that has a slope of 4/5 and contains the point (−5, −3).

ankoles [38]

y = mx + b, where m = slope, and b = y-intercept.

Since you are not given the y-intercept, you have to solve for it through the equation, y = (4/5)x (which is the slope you are given) + b, and replace x and y with values given, which are (-5,-3)

y = (4/5)x + b

-3 = (4/5)(-5) + b

-3 = -4 + b

1 = b

Then replace b in the first equation to get the answer

y = (4/5)x + 1

5 0

3 years ago

How do you simplify this?

lions [1.4K]

Answer:

sinA(cosA+sinA)*cosA

Step-by-step explanation:

(sinA(2cosA+sinA-cosA))/secA

sinA(cosA+sinA)/secA

sinA(cosA+sinA)*cosA

8 0

3 years ago

What is the product of 2p+q and -3q-6+1

MissTica

(2p + q)(-3q - 5)
(2p + q)(-5 -3q)
-10p -6pq -5q -3q^2
-3q^2 -5q -6pq -10p

5 0

3 years ago