Easy math problems!!!

The roots of the polynomial function f(x) = x³ - 3x² + 2 are [tex]\frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, \ and \ 1[/tex].

Given the polynomial function in the question:

f(x) = x³ - 3x² + 2

To find the roots of the polynomial function f(x) = x³ - 3x² + 2, we need to solve for values of x that make the function equal to zero.

f(x) = x³ - 3x² + 2

x³ - 3x² + 2 = 0

Factor the equation using the rational root test:
( x - 1 )( x² - 2x - 2 ) = 0

Equate each factor zero and solve for x:

( x - 1 ) = 0

x - 1 = 0

x = 1

( x² - 2x - 2 ) = 0

x² - 2x - 2 = 0

Using the quadratic formula:

[tex]x = \frac{-b\±\sqrt{b^2 - 4(ac)} }{2a} \\\\x = \frac{-(-2)\±\sqrt{(-2)^2 - 4(1*-2)} }{2*1} \\\\x = \frac{2\±\sqrt{4 + 8} }{2} \\\\x = \frac{2\±\sqrt{12} }{2}\\\\Hence:\\\\x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}[/tex]

Therefore, the roots are [tex]x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, 1[/tex].

Options A, B and D are the correct answers.

Learn more about quadratic equations here: brainly.com/question/1863222

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Answer:

$ 30

$ 20

Step-by-step explanation:

Sea el costo fijo xy el costo por km sea y suponiendo que es el mismo para ambos taxis.

De la pregunta obtenemos las dos ecuaciones

[tex]x+8y=190\quad ...(i)[/tex]

[tex]x+5y=130\quad ...(ii)[/tex]

Aplicando [tex](i)-(ii)[/tex]

[tex]8y-5y=190-130\\\Rightarrow 3y=60\\\Rightarrow y=\dfrac{60}{3}\\\Rightarrow y=20[/tex]

Sustituyendo en [tex](ii)[/tex]

[tex]x+5y=130\\\Rightarrow x+5\times 20=130\\\Rightarrow x=130-100\\\Rightarrow x=30[/tex]

Entonces, el costo fijo es de $ 30 y el costo por km es de $ 20.

Answer:c

Step-by-step explanation:

Answer:

C forsure i just did it just trying to help

Step-by-step explanation:

Step-by-step explanation:

Total Surface area of a pyramid is given as

= Lateral surface area + area of base.

Lateral surface area = 1/2×perimeter of base×slant height

given the base is square with side 9 in , and slant height of 12 inches.

therefore, LSA = 1/2(9*4)×12 = 216 in^2

Now, TSA = LSA + Base area = 216+9^2 = 297 in^2

a) It is given that the pyramid is smaller therefore, it will require lesser paint than the original pyramid ( The TSA of the smaller pyramid cannot be calculated as its dimentions are not given).

b) It can not be solved as dimensions are missing in the question.

However, the logic has been explained in the soluion one easily put values to find the solution.

Answer:

I think they are all always.

Step-by-step explanation:

They are called rational because they are the ratio, or quotient, of two integers

numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end and does not repeat a pattern.

Part 1) The surface that is shared by the two solids is the top of the cube that is the same that the square base of the pyramid

Part 2) The dimensions of this surface are 6 in x 6 in

Part 3) Molly needs to paint 228 square inches

Step-by-step explanation:

The picture of the question in the attached figure

Part 1) Which surface is shared by the two solids?

we know that

The surface that is shared by the two solids is the top of the cube that is the same that the square base of the pyramid

Part 2)  What are the dimensions of this surface?

The surface is a square with side length 6 inches

so

The dimensions of this surface are 6 in x 6 in

Part 3) what is the area molly needs to paint?

we know that

The area that Molly needs to paint is equal to the surface area of the cube plus the surface area of the pyramid minus two times the area of the surface that is shared by the two solids

so

therefore

Molly needs to paint 228 square inches

i hope this helps you

Answer:

c^2 = a^2 + b^2 - 2ab cos(C)

Step-by-step explanation:

The angle at A is named A, the angle at B is named B, and the angle at C is named C

Answer;

he missed 4 of his shots

Step-by-step explanation:

Answer:

C) y= -3, D) x= -1, E y= -5/4x +2

Step-by-step explanation:

Answer:

I think 9.25

Step-by-step explanation:

Answer:

9 dollar

Step-by-step explanation:

it is now 9 dollar because the increase was 3.00

[tex]y=3x[/tex]

The input is classified as x term

The output is classified as y term.

If the input is -4 then

Substitute x = -4 in y = 3x

[tex]y=3(-4)\\y=-12[/tex]

Therefore, the answer is -12 aka the first choice.

Answer:

its b for the both of them

Answer:

81

Step-by-step explanation:

y= x²

if x= 9 substitute x with 9 in the equation

y= 9² = 81

Answer:

Step-by-step explanation:

i=prt

your p=30 dollars

rate is 10%

t=1 year

i=(30*0.01*1)=3

3 dollars

Answer: 8.75

Step-by-step explanation:

Let walking rate = x

Riding rate = x + 10

Time taken to ride 30km = time taken to walk 14 km

Time = distance / speed

Hence,

30/ (x + 10) = 14 / x

Cross multiply :

30x = 14( x + 10)

30x = 14x + 140

30x - 14x = 140

16x = 140

x = 140 / 16

x = 8.75

Walking rate = 8.75 kph

Answer:

-2/3

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

f(t) = t^2 – 2t – 2

To find f(0), replace t with 0 in the expression and evaluate the expression.

f(0) = 0^2 – 2(0) – 2

f(0) = -2

0 = t

We know this because 0 replaced t in the parenthesis next to F !

The question is just asking you to plug in 0 where ever t is!

Let's do it

[tex]f(0) = 0^{2} - 2(0) - 2[/tex]

solve

[tex]0^{2} = 0 \\2 ( 0 ) = 0[/tex]

so, this is what we have left!

[tex]f(0) = 0 - 0 - 2[/tex]

We have our answer!

[tex]f (0) = -2[/tex]

1. Write the equation that represents the data set for Crew A using the variables E for earnings and h for hours.

120e/1h

2. Write the equation that represents the data set for Crew B using the variables E for earnings and h for hours.

105e/1h

Answer:

n<30

Step-by-step explanation:

have a great day

Answer:

a) The equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]

b) The equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]

Step-by-step explanation:

We are given the line: [tex]y=-\frac{2}{7}x-7[/tex]

The slope of the above equation is: [tex]m=-\frac{2}{7}[/tex] (By comparing with general form [tex]y=mx+b[/tex] where m is slope)

a) Find equation of line perpendicular to above line and passes through point (-7,-4)

If two lines are perpendicular there slopes are opposite reciprocal i.e [tex]m_1=-\frac{1}{m_2}[/tex]

The slope of new line will be: [tex]m = \frac{7}{2}[/tex]

Now finding y-intercept using slope and point (-7,-4)

[tex]y=mx+b\\-4=\frac{7}{2}(-7)+b \\-4=\frac{-49}{2}+b \\b=-4+\frac{49}{2}\\b=\frac{-8+49}{2}\\b=\frac{41}{2}[/tex]

So, the equation of line perpendicular to above line and passes through point (-7,-4) will be:

[tex]y=mx+b\\y=\frac{7}{2}x+\frac{41}{2}[/tex]

So, the equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]

b) Find equation of line parallel to above line and passes through point (-7,-4)

If two lines are parallel there slopes are same i.e [tex]m_1=m_2[/tex]

The slope of new line will be: [tex]m = -\frac{2}{7}[/tex]

Now finding y-intercept using slope and point (-7,-4)

[tex]y=mx+b\\-4=-\frac{2}{7}(-7)+b \\-4=-2(-1)+b\\-4=+2+b \\b=-4-2\\b=-6[/tex]

So, the equation of line parallel to above line and passes through point (-7,-4) will be:

[tex]y=mx+b\\y=-\frac{2}{7}x-6[/tex]

So, the equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]

Answer:

4.072

Step-by-step explanation:

Answer:

Step-by-step explanation:

Brainliest? Thanks!

Answer:

5

Step-by-step explanation:

16÷3=5r1. Hope this helps

Answer:

this answer will be b

Step-by-step explanation:

Answer:

The variance is doubled; C

Step-by-step explanation:

Here, we want to select what will be wrong if every number in the dataset is doubled

A. This is correct

The mean is the average of the numbers which is calculated by dividing the sum of the numbers by the count of the numbers

By doubling the numbers, we have simply doubled the sum while the count is same

So what we have as the result of the division will be 2 times what we had initially making the mean doubled

B. The mode is doubled

Yes, this is correct

The mode is the highest in frequency

Doubling all numbers will not double their frequencies but their values. So the number that was the mode in the previous case will be the same but now doubled

D. The median is doubled

This is correct

The median deals with the middle number.

Since all numbers are doubled in the present case, the median to is also doubled along side as the numbers are now twice what they were evenly

C. This is wrong

The variance has to do with the spread of data

We are actually subtracting values

Since we are doubling across board, the difference between the numbers is the same as this, the variance cannot change

We can look at this from the angle that all others are measures of central tendency looking at having a central figure while the variance is a measure of spread.

Answer:

step 2

Step-by-step explanation:

Mark didnt do 5×5

Answer:

f(x)=-0.25x+4.75

Step-by-step explanation:

-0.25x+4.75

-0.25(-1)+4.75=5

-0.25(3)+4.75=4

Hope this helps!

Answer:

8 Days with 6 ounces of Dog Food left Over

Step-by-step explanation:

12 Cans per Case x 12.5 ounces per can = 150 Ounces Total

150 Ounces/18 ounces per day= 8.3333333333333 Days

.3333333333333 Days x 18 ounces = 6 remaining ounces.

Answer:

The customer bought 4 hats, and 6 scarves.

Step-by-step explanation:

$4.50x4 = $18

$3.00x6 = $18

$18 + $18 = $36!

Please mark "Brainliest"!?

- Pricespidey