What are the zeros of the function? f(x)=x3+4x2−12x

Answer:

y = 1/3 x.

Step-by-step explanation:

The slope of the given line is

(4 - (-2) / 2 - 4)

=   -3.

So the slope of the line perpendicular to it = -1 / (-3) = 1/3.

This line also passes through the point (3, 1) so its equation is ( by the point-slope form):

y - 1 = 1/3(x - 3)

y - 1 = 1/3x - 1

y = 1/3 x (answer).

Answer: The answer is y= x/3

Step-by-step explanation:

Given  points =(2,4)  and (4,-2) whose mid point is (3,1)

Let the points be named  as A(2,4) and B(4,-2) and mid point as C(3,1)

So slope of AB = [tex]\frac{4-(-2)}{2-4}[/tex]

=[tex]\frac{6}{-2}[/tex]

= -3

We know that   Product of Slope of perpendicular lines = -1

Now slope of the line perpendicular to AB × slope of AB = -1

-3 × m2 =-1

i.e. m2 =[tex]\frac{1}{3}[/tex]

Now equation of perpendicular bisector of AB passing through C(3,1)  is

[tex]y -1 =\frac{1}{3}(x-3)\\[/tex]

[tex]y= 1+\frac{1}{3}x -1[/tex]

[tex]y=\frac{1}{3}x[/tex]

Hence the equation of line is y =x/3

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\pi \theta r^2}{360}~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=&6\\ \theta =&87 \end{cases}\implies A=\cfrac{\pi (87)(6)^2}{360}\implies A=\cfrac{87\pi }{10} \\\\\\ A\approx 27.332\implies \stackrel{\textit{rounded up}}{A=27.3}[/tex]

Answer: the last one

EXPLAINATION:

The first one follows the rule a+b=c, and when you add all the angles it equals 180

The second one when you add up all of the angles, it is 180

The third one follows a2+b2=c2. 5(5)+12(12)= 169, 13(13)=169

The last one does not follow any of the triangle rules.

Answer:

See attached file

Step-by-step explanation:

Answer:

D. the last graph

Step-by-step explanation:

ANSWER

[tex]x = 5 \: or \: x = - 5[/tex]

EXPLANATION

The given absolute value equation is

[tex] | - 5x| - 5 = 20[/tex]

We add 5 to both sides of the equation to get:

[tex] | - 5x| - 5 + 5 = 20 + 5[/tex]

[tex] | - 5x| = 25[/tex]

This implies that,

[tex] - 5x = - 25 \: or \: - 5x = 25[/tex]

Divide both sides by -5,

[tex]x = 5 \: or \: x = - 5[/tex]

To find the percent of decrease from the original price of a video game, subtract the new price from the original price, divide by the original price, and multiply by 100.

To find the percent of decrease from the original price, we can use the formula:

Percent decrease = [(change in price)/(original price)] × 100

Substituting the given values:

Percent decrease = [(49.95 - 45.50)/(49.95)] × 100 = 4.45/49.95 × 100 = 8.9%

Therefore, the percent of decrease from the original price is 8.9%

Amount spent on vacation=$7920,

Let Mike monthly salary be x,

11% of X= $7920,

[tex] \frac{11}{100} \times x = 7920[/tex]

[tex]11x = 7920 \times 100[/tex]

[tex]x = 792000 \div 11[/tex]

[tex]x = 72000[/tex]

Answer: 720

Step-by-step explanation: divide 7920 into 11 and you will get your answer.

Answer: Jacob ran for half an hour, and walked for the remaining half an hour.  15 km/hr x 0.5 hr = 7.5 km running, and 5km/ hr x 0.5 hr=2.5 km walking

Step-by-step explanation:

Let x hours be the time Jacob ran, and therefore for 1-x hours he walked.

time x speed= distance

we get, 15x + 5*(1-x)=10

15x+5-5x=10,

10x=5,

x=0.5 hours.

Average speed was 10km/h.

HOPE THIS HELPS.

Jacob ran 7.5 km at a speed of 15 km/h. By setting up a system of simultaneous equations, we found the distances for both running and walking that add up to the total distance of 10 km, while also fulfilling the constraint of a 1-hour total journey time.

To solve this problem with simultaneous equations, let's define two variables for the two different parts of the journey: x for the distance Jacob runs at 15 km/h and y for the distance he walks at 5 km/h. We know that Jacob covers a total distance of 10 km and the total time taken for the journey is 1 hour.

Set up the equations:

Equation for the distance: x + y = 10

Equation for the time: (x/15) + (y/5) = 1 (Since time is distance divided by speed)

Solve these equations simultaneously.

Multiply the second equation by 15 to clear the denominators: x + 3y = 15

Subtract the first equation from this new equation to solve for y: 2y = 5, so y = 2.5 km.

Substitute y back into the first equation to find x: x = 10 - 2.5, so x = 7.5 km.

Jacob ran 7.5 km at 15 km/h.

Check the answer:

Is 7.5 km in 1 hour at 15 km/h reasonable? Yes, because 15 km/h means he would run 15 km in 1 hour, so running for less than an hour for 7.5 km is plausible.

Answer:

The smaller number is 11

Step-by-step explanation:

The question is

One number is 3 less than a second number. Twice the second number is 16 less than 4 times the first. Find the smaller of two numbers

Let

x and y the numbers

x=y-3 ----> equation A

2y=4x-16 ----> equation B

Substitute equation A in equation B and solve for y

2y=4(y-3)-16

2y=4y-12-16

4y-2y=12+16

2y=28

y=14

x=14-3=11

Answer:7.C

8.B

9.A

Step-by-step explanation:

Make me the brainliest

The second one is the answer

Answer:

Option B (-0.29)

Step-by-step explanation:

Given are x,y values as

(2,47), (3,2), (5,26)

x y xy x^2 y^2

2 47 94 4 2209

3 2 6 9 4

5 26 130 25 676

Total 10 75 230 38 2889

Cov -6.666666667    

r -0.2907    

Thus we find correlation coefficient is -0.29

Option B is right

Answer:

a. x = −2

Step-by-step explanation:

f(x) = g(x)

Substitute the functions in

3x+12 = -9.5x -13

Add 9.5x to each side

3x+9.5x+12 = -9.5x+9.5x -13

12.5x +12 = -13

Subtract 12 from each side

12.5x+12-12 = -13-12

12.5x = -25

Divide by 12.5

12.5x/12.5 = -25/12.5

x = -2

Answer:

a. x = −2

f(x) = g(x)

Substitute the functions in

3x+12 = -9.5x -13

Add 9.5x to each side

3x+9.5x+12 = -9.5x+9.5x -13

12.5x +12 = -13

Subtract 12 from each side

12.5x+12-12 = -13-12

12.5x = -25

Divide by 12.5

12.5x/12.5 = -25/12.5

x = -2

[tex]b. \: \frac{8}{27} [/tex]

Answer:

25.9

Step-by-step explanation:

That is:

25.9

Hope this helped!

Answer:

C, [tex]5e^{i(5\pi/3)[/tex]

Step-by-step explanation:

Euler's formula:

[tex]e^{ix}=\cos{x}+i\sin{x}[/tex]

Looking at the expression in the parentheses, your x is explicitly given to you as [tex]5\pi/3[/tex], so using Euler's formula:

[tex]5\left(\cos\frac{5\pi}{3}+i\sin{\frac{5\pi}{3} })=5e^{i(5\pi/3)[/tex]

Which is C.

Answer:

-5x^5 -5x^4 +6x^3 -x^2 -7x +20

Step-by-step explanation:

(2x^5+x^3−3x^4−x+8)−(7x^5+2x^4−12+6x−5x^3+x^2)

Distribute the minus sign

(2x^5+x^3−3x^4−x+8)−7x^5-2x^4+12-6x+5x^3-x^2

Put them in order from largest exponent to smallest exponent

2x^5−7x^5−3x^4-2x^4+5x^3+x^3-x^2-6x−x+8+12

Combine like terms

-5x^5 -5x^4 +6x^3 -x^2 -7x +20

Standard form is from largest exponent to smallest exponent

The value of x is 15. When you draw out all three triangles individually, the proportion is 9/x=x/25. X squared equals 225. The square root of 225 is 15

Answer:

Team E appears to have the larger mean weight.

Step-by-step explanation:

After seeing the dot plot of two teams i.e. Team E and Team F the conclusion that can be drawn regarding the larger mean of the team is that:

Team E is expected to have larger mean since the dots are for the higher values of weights  and hence will result in higher mean. whereas for team F the dots or frequencies are for smaller weights and hence will result in a less mean as compared to team E.

Hence, Team E appears to have the larger mean weight.

Answer:

team E

Step-by-step explanation:

Answer:

2/15

Step-by-step explanation:

We need to find the difference between the houses

Peter - Natalie

3/10 - 1/6

Get a common denominator of 30

3/10 * 3/3 - 1/6*5/5

9/30 - 5/30

4/30

Divide top and bottom by 2

2/15

Answer:

its not....

Step-by-step explanation:

-6=4+10

not true

2(4)+(-6)=-2

8-6=-2

Also not true

Given:

Principal amount =P=6000$

Required amount =A=8000$

Rate of compunded interest;r=9%=0.09

Let the number of years be 'n'

So.

A=P(1+r)^t

=> 8000 =6000 (1+0.09)^t

=>8000/6000 =(1.09)^t

=> 8/6 =4/3=1.999.. = (1.09)^t

=> (1.09)^t =1.999≈2

(After using calculator)

(1.09)^3 =1.2950...

(1.09)^9 =2.17189...

So approximately The Time in years required is 9 years... i.e option c.

Hope it helps...

Regards,

Leukonov/Olegion.

Answer:

The answer is approximately 3 years ⇒ answer B

Step-by-step explanation:

* Lets talk about the compound continuous interest  

- Compound continuous interest can be calculated using the formula:  

 A = P e^rt  

# A = the future value of the investment, including interest  

# P = the principal investment amount (the initial amount)

# r = the interest rate  

# t = the time the money is invested for  

- The formula gives you the future value of an investment,  

  which is compound continuous interest plus the

  principal.  

- If you want to calculate the compound interest only, you need  

 to deduct the principal from the result.  

- So, your formula is:

 Compounded interest only = Pe^(rt)  - P

* Now lets solve the problem

∵ P = $ 6000

∵ A = $ 8000

∵ r = 9/100 = 0.09

∵ t = ?  

∵ A = P e^(r t)

∴ 8000 = 6000 e^(0.09 × t) ⇒ divide both sides by 6000

∴ 4/3 = e^(0.09 × t) ⇒ insert ㏑ for both sides

∴ ㏑(4/3) = ㏑ e^(0.09 × t) ⇒ (㏑e = 1)

∴ ㏑(4/3) = 0.09 t ⇒ divide the both sides by 0.09

∴ t = [㏑(4/3)] ÷ 0.09 = 3.196467 ≅ 3 years

Answer:

1. The input is f

2. The input is g

3. The input is h

Step-by-step explanation:

The value inside the bracket of the function is the input given to the function.

1. g(f) = 2f

The input is f

2. h(g) = -4+g

The input is g

3. f(h) = h - 7

The input is h

Answer:

g(f)=2f⇒  f

h(g)=-4+g ⇒ g

f (h) =h-7 ⇒h

Step-by-step explanation:

Hi, to answer this question we have to understand what is the input of a function.

A function has an input and an output. The input is inside the parentheses, next to the name of the function.

The input is the independent variable.

Now, with this information, we can match each function with its input.

So:

g(f)=2f⇒  f

h(g)=-4+g ⇒ g

f (h) =h-7  ⇒h

Feel free to ask for more if it´s necessary or if you did not understand something

It's B.

If [tex]0<x<1[/tex], then it's also the case that [tex]0<x^2<1[/tex], because multiplying any number [tex]x[/tex] by a number (in this case, also [tex]x[/tex]) between 0 and 1 scales that number down.

It's not C, because [tex]2^2=4\neq3[/tex].

It's not D, because [tex]3^2=9\neq3[/tex].

Answer:

Point B

Step-by-step explanation:

The square root of 1 is one, so it must be larger than 1.

The square root of 2 is 4 so it must be smaller than 2.

B would make the most sense

Answer:

Step-by-step explanation:

Answer:

The slope is 5/3. The equation would be, y = 5/3x + 8/-3.

Step-by-step explanation:

Standard form is "Ax  + By = C

5x - 3y = 8

-5x.         -5x

3y  = -5x + 8

now divide both sides by 3

y = 5/3 + 8/-3

Slope is 5/3

Answer: 5 milimeters.

Step-by-step explanation:

The formula for calculate the volume of a rectangular prism is:

[tex]V=lwh[/tex]

Where "V"  is the volume, "l" is the lenght, "w" is the width and "h" is the height.

You know that the volume, the lenght, and the width of this rectangular prism are:

[tex]V=750mm^3\\l=15mm\\w=10mm[/tex]

Substitutute these values into the formula and solve for the the height "h":

[tex]750mm^3=(15mm)(10mm)h\\\\h=\frac{750mm}{(15mm)(10mm)}\\\\h=5mm[/tex]

Final answer:

To find the height of a rectangular prism, you can use the formula V = l x w x h and calculate the missing dimension. In this case, the height of the rectangular prism is 5 millimeters.

Explanation:

A rectangular prism, also known as a rectangular solid or box, is a three-dimensional shape that has six rectangular faces. The formula to find the volume of a rectangular prism is V = l x w x h, where l is the length, w is the width, and h is the height. In this case, the given length is 15 mm, the width is 10 mm, and the volume is 750 cubic mm. To find the height, plug these values into the formula as follows:

750 = 15 x 10 x h

h = 750 / (15 x 10) = 750 / 150 = 5 mm

Therefore, the height of the rectangular prism is 5 millimeters.

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Answer:

Putting money in a bank and earning interest

Step-by-step explanation:

This problem can be used in real life to describe when you put money in a bank, in this case, it could be two dollars, and leave it there for x amount of years, then taking it out after an amount of years and checking what you have. Since this is a linear equation, your money doesn't go up exponentially. It'll keep going up the same rate for the whole time until you decide to take it out. Here's an example of what it'll look like, if it helps:

Your money keeps going up. Hope this helps!

Final answer:

A real world situation for the function f(x) = 3(1.06x) + 2 could be a situation where a person is investing money in a savings account. The function represents the balance in the account after a certain amount of time (x years) with an interest rate of 6%.

Explanation:

A real world situation for the function f(x) = 3(1.06x) + 2 could be a situation where a person is investing money in a savings account. Let's say the initial amount of money deposited in the account is $2. The function represents the balance in the account after a certain amount of time (x years) with an interest rate of 6%. The key features of the function are:

3: This represents the multiplier of the initial investment, indicating that the account balance increases by three times the amount of the initial investment.

1.06: This represents the growth factor due to the 6% interest rate. It is multiplied by the current balance each year.

2: This represents the $2 initial deposit in the account.

Answer:

See below  

Step-by-step explanation:

You order the hundreds digits, then the tens, and finally the ones.

a. 213, 290, 871, 899

b. 213, 291, 871, 899

c.    91, 312, 871, 899

d. 123, 190, 871, 899

Answer:

Step-by-step explanation:

a. 213, 290, 871, 899

b. 213, 291, 871, 899

c.    91, 312, 871, 899

d. 123, 190, 871, 899

i hope this helps u guys

Answer:

You are correct my good sir! 7^5/7^2 expanded is (7x7x7x7x7)/(7x7)! another awesome thing to know for future reference is when dividing exponents with the same base you can simply subtract the exponents from each other! for example, 7^5/7^2=7^3! :D Hope This Helps!

Step-by-step explanation:

Answer:

Option D is the answer.

Step-by-step explanation:

The given expression is [tex]\frac{7^{5}}{7^{2}}[/tex]

We know [tex]7^{5}[/tex] = 7×7×7×7×7

and [tex]7^{2}[/tex] = 7×7

Therefore, we can rewrite the expression as [tex]\frac{7\times 7\times 7\times7 \times 7}{7\times 7}[/tex] which maches with option D.

Answer:

The height of the prism is [tex]7.5\ ft[/tex]

Step-by-step explanation:

we know that

The volume of the prism is equal to

[tex]V=BH[/tex]

where

B is the area of the base of prism

H is the height of the prism

Find the area of the base B

[tex]B=(5)(8)=40\ ft^{2}[/tex]

we have

[tex]V=300\ ft^{3}[/tex]

substitute in the formula and solve for H

[tex]300=40(H)[/tex]

[tex]H=300/40[/tex]

[tex]H=7.5\ ft[/tex]