Mathematics High School

What are the zeros of the polynomial function f(x) = x3 − x2 − 12x?

a. 0, −4, −3
b. 0, −4, 3
c. 0, 4, −3
d. 0, 4, 3

Legit answer plz
this is important

Answers

Answer 1
x^3-x^2-12x=0  factor out x

x(x^2-x-12)=0  factor parenthetical expression

x(x^2-4x+3x-12)=0

x(x(x-4)+3(x-4))=0

x(x+3)(x-4)=0

So x=-3, 0, 4

So c) 0, 4, -3
Answer 2

Answer:

The correct option is c.

Step-by-step explanation:

The given function is

[tex]f(x)=x^3-x^2-12x[/tex]

Taking out the common factors.

[tex]f(x)=x(x^2-x-12)[/tex]

Now, factorize the parenthesis.

[tex]f(x)=x(x^2-4x+3x-12)[/tex]

[tex]f(x)=x(x(x-4)+3(x-4))[/tex]

[tex]f(x)=x(x-4)(x+3)[/tex]

Equate the function equal to 0, to find the zeros of the polynomial function f(x).

[tex]f(x)=0[/tex]

[tex]x(x-4)(x+3)=0[/tex]

Using zero product property, we get

[tex]x=0[/tex]

[tex]x-4=0\Rightarrow x=4[/tex]

[tex]x+3=0\Rightarrow x=-3[/tex]

The zeros of the polynomial function f(x) are 0,4,-3. Therefore the correct option is c.

Related Questions

The teen club had a cupcake sale. they started with 126 cupcakes. they sold 2/3 of their cupcakes in the morning. how many were left for them to sell in the afternoon?

Answers

126 ÷ 3= 42
42×2= 84 (number of cupcakes sold)
126-84= 42 (number of cupcakes left)

HELP QUICK!!!
An ellipse has foci F1(9, 0) and F2(11, 6), and the point (1, 6) is on the ellipse. Identify the constant sum for the ellipse.
a 20
b 10
c 0
d 100

Answers

The first step is to find the distance from the given point to each of the two foci as follows:
Distance D1:
(D1)^2 = (9-1)^2 + (0-6)^2 = 100
D1 = 10
Distance D2:
(D2)^2 = (11-1)^2 + (6-6)^2 = 100
D2 = 10

The constant sum is the summation of the two distances as follows:
constant sum = D1 + D2 = 10 + 10 = 20

The correct choice is:
a) 20

Answer:   20

Step-by-step explanation:

Please help me !!!!!!!!

Answers

It's C the missing side is 9 units long so since cosine is adjacent divided by hypotenuse it would be 9/41
41^2 - 40^2 = 1681 - 1600 = 81

side xy = square root 81 = 9

cosine(X) = Adj / Hypo
cosine(X) = 9/41
answer
C. 9/41

From 75 campsites to 120 campsites

Answers

subtract 75 from 120

120-75 =45 more campsites

1. Evaluate 6.314 - 9.77.

3.456
-3.464
-3.456
-16.084

2. Evaluate -5.118 - (-4.1).

-9.218
-1.018
1.018
9.218

3. Find the value of x + y for x = 75.9 and y = 2.65.

10.24
102.4
78.55
79.55

4. Find the value of -x + y for x = 75.9 and y = 2.65.

-78.55
78.55
73.25
-73.25

Answers

Evaluate 6.314 - 9.77.

3.456
-3.464
-3.456 ☆
-16.084

2. Evaluate -5.118 - (-4.1).

-9.218
-1.018 ☆
1.018
9.218

3. Find the value of x + y for x = 75.9 and y = 2.65.

10.24
102.4
78.55 ☆
79.55

4. Find the value of -x + y for x = 75.9 and y = 2.65.

-78.55
78.55
73.25
-73.25☆

Answer:

1. -3.456

2. -1.018

3. 78.55

4. -73.25

Step-by-step explanation:

In Algebra, the following notations have to be considered.

Algebra is a branch of mathematics that deals with the computation of numbers irrespective of the signs involved.

- × - = +

+ × - = -

- × + = -

+ × + = +

Therefore,

1. 6.314 - 9.77 = -3.456

2.  -5.118 - (-4.1) =  -5.118 + 4.1 = -1.018

3. x + y for x = 75.9 and y = 2.65.

This requires substitution

75.9 + 2.65 = 78.55

4. -x + y for x = 75.9 and y = 2.65

= -75.9 + 2.65

= -73.25


A bag contains 30 red tiles, 15 green tiles, and 5 yellow tiles. One tile is drawn and then replaced. Then a second tile is drawn. What is the probability that the first tile is yellow and the second tile is green?
A.
1%
B.
3%
C.
6%
D.
18%

Answers

Allright we know that the total number of tiles is 50 so we can assume that if you pick the first tile and its yellow ther is a (5/50) chance to pick it up and then REPLACED meaning that it is put back so you have still 50 tiles to choose from, if then you choose a green tile you have a (15/50) chance of picking it up

(5/50)*(15/50)=0.03 YOU HAVE A 3 PERCENT CHANCE!!!:D
^This is to calculate the probability of picking it in that order)^

What is the precise definition of an angle? question 1 options:?

Answers

In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Webassign find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at the point (6, 36), and the x-axis.

Answers

first find the tangent line

dy/dx=2x
at x=6, the slope is 2(6)=12
so
use point slope form
y-y1=m(x-x1)
point is (6,36)
so
y-36=12(x-6)
y-36=12x-72
y=12x-36

alright, so we know they intersect at x=6
and y=12x-36 is below y=x^2

so we do [tex] \int\limits^6_0 {x^2} \, dx - \int\limits^6_0 {12x-36} \, dx = \int\limits^6_0 {x^2-(12x-36)} \, dx = \int\limits^6_0 {x^2-12x+36} \, dx =[/tex]
[tex][\frac{x^3}{3}-6x^2+36x]\limits^6_0=(\frac{6^3}{3}-6(6)^2+36(6))-(0)=\frac{216}{3}-216+216=[/tex] [tex]72+0=72[/tex]

the area under the curve bounded by the lines and the x axis is 72 square units

solve the equation by completing the square. round to the nearest hundredth if necessary. x^2-6x=20

Answers

x^2 - 6x = 20
x^2 - 6x + 9 = 20 + 9
(x - 3)^2 = 29
x - 3 = (+-) sqrt 29
x = 3 (+-) sqrt 29
x = 3 (+-) 5.39

x = 3 + 5.39 = 8.39 <=
x = 3 - 5.39 = - 2.39 <=
x^2-6x+(b/2)^2=20+(b/2)^2
x^2-6x+(6/2)^2=20+(6/2)^2
x^2-6x+(3)^2=20+(3)^2
x^2-6x+9=20+9
(x-3)^2=29
x-3=5.38 or -5.38
x=5.38+3 or -5.38+3
x=8.38 or -2.38




























My sister is 15 years older than i am. the sum of our ages is 41. find our ages

Answers

x = you, and y = ur sis

x + y = 41
y = x + 15

x + (x + 15) = 41
2x + 15 = 41
2x = 41 - 15
2x = 26
x = 26/2
x = 13 <== u r 13

y = x + 15
y = 13 + 15
y = 28 <== ur sis

Rectangular prisms A and B are similar.
The edge of prism B is 3 times that of prism A. How many times the volume of prism A is the volume of prism B?

Answers

27 times smaller or 1/27 because 3^3 equals to 27.
[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{let's say the edge of A is \underline{k} long, then B's is \underline{3k}} \\\\\\ \cfrac{A}{B}\qquad \cfrac{k}{3k}\implies \cfrac{1}{3}\implies \cfrac{s}{s}\qquad thus \\\\\\ \cfrac{A}{B}\qquad \cfrac{1}{3}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{1}{3}=\sqrt[3]{\cfrac{s^3}{s^3}}\implies \left( \cfrac{1}{3} \right)^3=\cfrac{s^3}{s^3}\implies \cfrac{1^3}{3^3}=\cfrac{s^3}{s^3} \\\\\\ \cfrac{1}{27}=\cfrac{s^3}{s^3}[/tex]

The sum of two numbers is 33. Twice the first number minus the second number equals 18. Find both numbers.

Answers

We can call the two numbers x and y. Then, x + y = 33, and 2x - y = 18. We can use substitution to solve this problem:

y = 33 - x 

SO

2x - 33 + x = 18

3x = 51

x = 17

Now, we know x. We can use this to find y:

x + y = 33

17 + y = 33

y = 16

So, the numbers are 16 and 17. 

The both numbers are = 17 and 16

Solving for the unknown numbers

The sum of two numbers = 33

Let the two numbers be X and y.

therefore X + y = 33 ----> equation 1

Twice the first number minus the second number= 18.

That is,

2x - y = 18 -----> equation 2

From equation 1 make X the subject of formula;

X = 33 – y

substitute X into equation 2,

2(33 – y) - y = 18

66 – 2y – y = 18

66 – 3y = 18

66 – 18 = 3y

48 = 3y

y = 48/3

y = 16

Substitute y = 16 into equation 1

Therefore, X +16 = 33

X = 33 –16

X = 17

Therefore, he both numbers are = 17 and 16

Learn more about summation here:

https://brainly.com/question/14322177

20 POINTS, PLEASE HELP ASAP!!!!

Answers

Question b)

17 minutes ⇒ 1 revolution = 2π
1 minute ⇒ 2π/17

Angle of rotation is 2π/17 per minute

Question c)

The period of the rotation is 2π/17 

The wheel starts rotating from the height of 5 meters from the ground and the maximum height is 125 meter from the ground.
The amplitude is 125 - 5 = 120 ÷ 2 = 60

The midline of the rotation is at 125 - 5= 120 ÷2 = 60 + 5 = 65 (this is the location of the centre of the wheel). This value is a shift of 65 from the zero midlines (which in this case would be the ground)

Question C

The movement of the wheel can be described as starting from 0° then reaching its peak at 180° and come back to its original position as it stops and it makes a complete circular turn 360°.

If we sketch this on a graph, we will obtain a curve of -cos(x)

We need to apply the period, the amplitude and the shift produced by this rotation into the equation [tex]y = -cos(x)[/tex]

The period is [tex] \frac{2 \pi }{7} [/tex] ⇒ [tex]f(t)=-cos( \frac{2 \pi }{7}t) [/tex]
The amplitude of 60 ⇒ [tex]f(t)=-60cos( \frac{2 \pi }{7}t) [/tex]
The shift of the midline by 65 units upwards ⇒ [tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]

The final equation is
[tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]

and the graph is shown in the third picture below

5/14 divided by 3/4, what's the answer

Answers

Rule:  (a/b)/(c/d)=(a/b)*(d/c)

(5/14)/(3/4)

(5/14)(4/3)

(5*4)/(14*3)

20/42

10/21
Answer: 10/21 or 0.47619...

This can be calculated by finding the reciprocal of 3/4, which is 4/3.
 
Next, you multiply 5/14 by 4/3. To multiply fractions, you multiply the two numerators and set it as the new numerator and multiply the two denominators and set it as the new denominator.

5 * 4 = 20
14 * 3 = 42

To simplify, you can divide each by 2 since it goes into both values.

20/2 = 10
42/2 = 21

Answer: 10/21

If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?

Answers

52/2 = 26 ounces of cereal in 1 box
26 * 5 = 130 ounces of cereal in 5 boxes

Answer:

If there are 52 ounces of cereal in 2 boxes, how many ounces are there in 5 boxes?

Step-by-step explanation:

If we have 52 ounces in 2 boxes, in 1 box we have: 52/2 = 26 ounces.

If we have 5 boxes and 26 ounces in each, we have: 5 x 26 = 130 ounces in total.

Find the area of a sector that has a central angle of 40 and a radius of 2 cm. Round your answer to the nearest 100th. Use 3.14=

Answers

I think the answer is around 1.4 as you need to multiply the area by 1/9 after finding the real area. 

Find the area of the triangle

Answers

The area of a triangle is equal to bh/2.
The base here is 8 and the height is 3.
8*3=24
24/2=12
The answer is B, 12 yd^2

Find the product.

(n + 7)(n - 2)

n² - 5n - 14
n² + 5n - 14
n² - 5n + 14

Answers

The answer is n^2 + 5n - 14.


[tex](n+7)(n-2)\\\\n*n+(-2)*n+7*n+7*(-2)\\\\n^{2}-2n+7n-14\\\\n^{2}+5n-14[/tex]
(n+7)(n-2)
=n•n+(-2)•n+7•n+7•(-2)
=n²-2n+7n-14
=n²+5n-14. In conclusion, the product of (n+7) and (n-2) or (n+7)(n-2)=n²+5n-14. Hope it help!

At a sandwich shop they offer 3 kinds of bread, 5 kinds of meat, and 3 kinds of cheese. Each type of sandwich has a combination of exactly 3 ingredients: 1 bread, 1 meat, and 1 cheese. How many types of sandwiches are possible?

Answers

Final answer:

The sandwich shop could yield a total of 45 types of sandwiches based on the three categories provided; namely, bread, meat, and cheese. According to the counting principle in mathematics, you multiply the amount of options available from each category to get the total combinations possible.

Explanation:

In the scenario described, to determine the possible number of sandwiches, we need to analyze the provided combinations. We have 3 types of bread, 5 kinds of meat, and 3 kinds of cheese. Each sandwich exactly contains one item from each category.

To find out all possible sandwich combinations, we multiply the number of choices in each category. This is known as the counting principle.

So, the formula would be:
Number of sandwich combinations = Types of Bread * Types of Meat * Types of Cheese

Plugging the given numbers into this formula, we get:
Number of sandwich combinations = 3 * 5 * 3 = 45

So, there are 45 possible sandwich combinations available in this sandwich shop.

Learn more about Counting Principle here:

https://brainly.com/question/29594564

#SPJ12

Two numbers are in the ratio of 3 to 4. If nine is subtracted from each, they are in the ratio of 3 to 5. Find the numbers.

Answers

12:16= 3:4 when simplified
12-9=3
16-9=5
When subtracting 9 from each the new ratio is 3:5

Hope this helps!

A quiz has 4 multiple-choice questions with 4 possible answer choices each. for each question, there is only 1 correct answer.a student guesses each answer at random. what is the probability of getting exactly 3 questions correct, to the nearest percent?(3 correct and 1 incorrect)

Answers

There are 4C3 ways of getting 3 out of 4 correct. This = 4.

The probability of getting  3 correct and 1 wrong in one of these ways is 
1/4 * 1/4 * 1/4 * 3/4  =  3/256

So required probability = 4 * 3/256  = 12/256  =  4.69 %   
5% to nearest percent.

Answer:    (quartered spinner)     (4)     (1/256)

If BC=5.3, CD=8.8, and AD= 14.3, find AB to the nearest tenth.

Answers

The picture above shows us that triangle ABC and triangle ACD are similar triangles by showing us that then have congruent angles. This tells us that each side of the triangle is bigger/smaller than the other triangle by the same factor. To find this out, we use two corresponding sides of the two triangles. In this case, two corresponding lengths that are given to us are BC and CD. If we divide CD by BC, this tell us that triangle ACD is approximately 5/3 bigger than triangle ABC. Using this, we can figure out the length of AB. We simply take 14.3 and divide it by 5/3. We divide because we are trying to mind the magnitude of the length of the smaller triangle. If we were looking for the length of the larger triangle, we would have multiplied. After dividing 14.2 by 5/3, we find that the length of AB is about 8.6.

Step-by-step explanation:

8.6 is the answer to the equation

Solve 2x + 5y = −13
3x − 4y = −8

Answers

2x+5y=-13
3x-4y=-8

Rearrange the first equation to solve for x in terms of y. This will be needed to apply the substition method.

2x+5y=-13
2x=-5y-13
x=-5/2y-13/2

Now plug this in for x in the second equation.

3(-5/2y-13/2)-4y=-8
-15/2y-39/2-4y=-8
-23/2y-39/2=-8
-23/2y=11.5
y=-1

Now plug this y value in to one of the original equations.
2x+5(-1)=-13
2x-5=-13
2x=-8
x=-4

Final answer: (-4,-1). <=============

To check:

2(-4)+5(-1)=-13
-8+5(-1)=-13
-8-5=-13
-13=-13
True

3(-4)-4(-1)=-8
-12-4(-1)=-8
-12+4=-8
-8=-8
True

Write an equation for the translation of the function. y = cos x; translated 6 units up

Answers

it's just y= cos(x)+6

Answer:

[tex]y=cos(x)+6[/tex].

Step-by-step explanation:

We are asked to write an equation for the translation of the function [tex]y=cos(x)[/tex] to 6 units upwards.

Let us recall transformation rules.

[tex]f(x)\rightarrow f(x+a)=\text{Graph shifted to left by a units}[/tex]

[tex]f(x)\rightarrow f(x-a)=\text{Graph shifted to right by a units}[/tex]

[tex]f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by a units}[/tex]

[tex]f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by a units}[/tex]

Since we need to shift our given function 6 units upwards, so we will add 6 to our given function outside the parenthesis as:

[tex]y=cos(x)+6[/tex]

Therefore, our required equation would be [tex]y=cos(x)+6[/tex].

Someone help me please !!!

Answers

Answer:

1. 10

2. 12

3. Sqrt 130

4. Sqrt 45

Step-by-step explanation:

To find the missing side of a right triangle, use the Pythagorean Theorem. The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where a and b are the legs with a being the smallest and c is the hypotenuse.

1. a=6, b=8, c=?

[tex]6^2+8^2=c^2\\36+64=c^2\\100=c^2\\10=c[/tex]

2. a=5, b=?, c=13

[tex]5^2+b^2=13^2\\25+b^2=169\\169-25=b^2\\144=b^2\\12=b[/tex]

3. a=7, b=9, c=?

[tex]7^2+9^2=c^2\\49+81=c^2\\130=c^2\\\sqrt{130}=c[/tex]

4. a=2, b=?, c=7

[tex]2^2+b^2=7^2\\4+b^2=49\\49-4=b^2\\45=b^2\\\sqrt{45}=b[/tex]

A tea bag is shaped like a regular square pyramid. Each leg of the base is 4 cm, and the slant height is 5 cm. Find the VOLUME of the tea bag.

Answers

(16[tex] \sqrt{21} [/tex])/3
The volume of a pyramid is V=1/3Bh (One-third the area of the base times height). Since your pyramid has a square base, you have to find the area of the base, multiply it by the height, and then divide it by 3.

So, the area of the base is 4x4, which is 16, then you multiply it by the height, 5, and 16x5 is 80, and 80/3 is approximately 26.6

The answer would be 26.6 cm^3

Evaluate 9 - b when b = 8

Answers

9 - b = ?
9 - 8 = 1
So, your answer is 1. Hope this helps, please mark brainliest and have an amazing day!

Equations are expressions separated by an equal sign. The value of the expression 9-b is b is 8 is given as 1

Equations and expressions

Equations are expressions separated by an equal sign

Given the expression  9 - b

If b = 8, we will have to substitute the value of 8 into the expression to have:

f(b) = 9 - b

f(8) = 9 - 8

f(8) = 1

Hence the value of the expression 9-b is b is 8 is given as 1

Learn more on function and values here: https://brainly.com/question/2284360

The sum of two numbers is 54 . the smaller number is 12 less than the larger number. what are the numbers?

Answers

Let x=one number and x+12= the other number.  Together the numbers=54.  Set up the equation:  x+x+12=54;  Combine the variables;  2x+12=54;  Subtract 12 from both sides of the equation;  2x=42; Divide both sides of the equation by 2;  x=21 is one number and 21+12=33 is the other number.  Check:  2(21) +12=54;  42+12=54;  54=54.

Twenty times the square of a non-zero number is equal to 15 times the number

Answers

i think that the answer is 5

20x^2 = 15x
20x^2 - 15x = 0
5x(4x - 3) = 0 
5x = 0, x =0
4x -3 = 0, x = 3/4

answer
non-zero number is 3/4

A and b are complementary angles find a and b a=3/4x-13 b=3x-17

Answers

3/4x-13+3x-17=90

3 3/4x-30=90

3 3/4x = 120

x=32

A=11
B=79
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