Pauline orders wristbands from two different companies. • Company 1 sells each wristband for $2 and has free shipping. Company 2 sells each wristband for $1.25 and charges $6 for shipping per order. Write an equation to model the number of wristbands, w, for which the two companies charge the same amount.

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

1 result(s) found

x  

2

−x−3

Step by Step Solution:

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STEP

1

:

Equation at the end of step 1

STEP

2

:

           x3 + 3x2 - 7x - 12

Simplify   ——————————————————

                 x + 4        

Checking for a perfect cube :

2.1    x3 + 3x2 - 7x - 12  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  x3 + 3x2 - 7x - 12  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -7x - 12  

Group 2:  x3 + 3x2  

Pull out from each group separately :

Group 1:   (7x + 12) • (-1)

Group 2:   (x + 3) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(x) = x3 + 3x2 - 7x - 12

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -12.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,4 ,6 ,12

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -3.00      

     -2       1        -2.00        6.00      

     -3       1        -3.00        9.00      

     -4       1        -4.00        0.00      x + 4  

     -6       1        -6.00        -78.00      

     -12       1       -12.00       -1224.00      

     1       1        1.00        -15.00      

     2       1        2.00        -6.00      

     3       1        3.00        21.00      

     4       1        4.00        72.00      

     6       1        6.00        270.00      

     12       1        12.00        2064.00      

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

  x3 + 3x2 - 7x - 12  

can be divided with  x + 4  

Polynomial Long Division :

2.4    Polynomial Long Division

Dividing :  x3 + 3x2 - 7x - 12  

                             ("Dividend")

By         :    x + 4    ("Divisor")

dividend     x3  +  3x2  -  7x  -  12  

- divisor  * x2     x3  +  4x2          

remainder      -  x2  -  7x  -  12  

- divisor  * -x1      -  x2  -  4x      

remainder          -  3x  -  12  

- divisor  * -3x0          -  3x  -  12  

remainder                0

Quotient :  x2-x-3  Remainder:  0  

Trying to factor by splitting the middle term

2.5     Factoring  x2-x-3  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3  

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -1 .

     -3    +    1    =    -2  

     -1    +    3    =    2  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Canceling Out :

2.6    Cancel out  (x+4)  which appears on both sides of the fraction line.

Final result :

 x2 - x - 3

Terms and topics

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Polynomial root calculator

Polynomial long division

Related links

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Root Finder -- Polynomials Calculator

How to factor five term polynomial - Yahoo Answers

Long Polynomial Division

Polynomial long division - Wikipedia

Polynomial Long Division

Polynomials - Long Division

Answer:

[tex]280 \: dollars[/tex]

Step-by-step explanation:

[tex]3500 \times .08 = 280[/tex]

Simple as that ^^^ Just find 8% of 3500

280,00$

8% of 3500$ equals to

(8/100)*3500=

280,00$=

Answer:

x=4

Step-by-step explanation:

5(x-10) = 30- 15x

5x - 50= 30 - 15x

+15x              +15x

20x - 50 = 30

       +50    +50

20x = 80

/20     /20

x = 4

Hope this helps!

Answer:

1/2

Step-by-step explanation:

We have to follow the order of operations. Since there are no parenthesis or exponents, we do multiplication first. to multiple fractions, we multiply the two numerators (top parts), which in this situation would get us 5*1=5. Then, we multiply the two denominators (bottom parts), which would get us 8*2=16. then we put the first result over the second, and we get 5/16. since the two denominators are the same, we don't need to change anything. we can just add the numerator, and get 8/16, which simplifies to 1/2.

Answer:

Infinitely many solutions

Step-by-step explanation:

Equation:

7(y-2)= 7y - 14

1. Simplify each side

7y - 14 = 7y - 14

Infinitely many solutions

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Monthly Payment (PMT) = 200 at the end of each period

interest rate = 2.9% = 0.029/12 = 0.0024166

Period (n) = 43 years x 12 = 516

Using the future value(FV) of an ordinary annuity:

FV = PMT[(1 + r)^n - 1] / r

FV = 200[(1 + 0.0024166)^516 - 1] / 0.0024166

FV = 200[(1.0024166)^516 - 1] / 0.0024166

FV = 200(2.4745372) / 0.0024166

FV = 204,794.93

Amount which will be in saving plan towards retirement = $204,794.93

Interest amount :

$204,794.93 - total monthly deposits

$204,794.93 - (200 * 516)

$204,794.93 - $103,200

= $101,594.93

Answer:

8

Step-by-step explanation:

4x4=16x8=128

Answer:

ok I did this construction about a year ago but I think I can remember something so if it's not correct I hope you won't be mad with me ok so the first step draw a straight line measure the length then make an AC on both sides then stand on one side make an arc upstand on the other side make an arc upthen stand on one AC and make another ARK on top of the other one then stand on the other AC and make another ark on top of the other one then join the lines yeah I think that's the procedure

Answer:

The third one is closest

Step-by-step explanation:

half of the diameter=the radius 14/2 = 7 and the formula for the area of a circle is r^2π so 49 × π is 153.93804

Answer:

Length of the side is 10 for a

Each side for b is 3

Step-by-step explanation:

Answer:

50 and the second one is 3

Step-by-step explanation:

to get the length from each side the area divide the area by 2 and to get the length for each side from the total perimeter then divide by 4

Answer:

the product of the two integers is -80

Answer:

-80

Explanation:

it was on a mathcounts competition

Answer:

3d+5

Step-by-step explanation:

Answer:

(-5, 0.5)

Step-by-step explanation:

-12+2/2= -5

-9+10/2= 0.5

(-5, 0.5)

I’d say option 4

However, one may think option 3 might be possible as well. But that it is not interacting, it’s affecting.

So I’d stick with option 4.

Good luck!

Answer: 2

Step-by-step explanation:

Given:  14 mystery books, 12 science-fiction books, and 8 historical-fiction books needs to b shipped.

If they want to pack one genre of book in each box such that they pack same number of books in each box.

Then, the greatest number of books Barnes and Noble can pack in each box

= GCD(14,12,8)

Since, 14 = 2 x 7

12 = 2 x 2 x 3

8 = 2 x 2 x 2

GCD(14,12,8)=2

Hence, the greatest number of books Barnes and Noble can pack in each box = 2

Answer:

Position = -5

Step-by-step explanation:

The number line is not shown, however the question can still be answered.

Given

Start Point: +2

Left Movement: 3.5cm and 7.9cm

Right Movement: 4.8cm

Required

Determine the Ant's position

To do this, we treat all left movements as negative and all right movements as positive.

So, we have:

Position = 2 - 3.5 - 7.9 + 4.8

Position = -4.6

Since the number line is spaced by 1cm, we have to approximate to the nearest integer.

Position = -5

Answer:

The least number of plates and cups she can buy is 24

She will buy 3 packs of plates

She will buy 2 packs of cup

Step-by-step explanation:

Plates = 8 per pack

Cups = 12 per pack

Find the Lowest common multiple of 8 and 12

8 = 16, 24, 32, 40, 48, 56, 64, 72, 80

12 = 24, 36, 48, 60, 72

What is the least number of plates and cups she can buy?

The Lowest common multiple of 8 and 12 is 24

The least number of plates and cups she can buy is 24

How many packs of plates?

Packs of plates = 24 plates / 8 per pack

= 3 packs

She will buy 3 packs of plates

How many packs of cups?

Packs of cups = 24 / 12 per pack

= 2 packs

She will buy 2 packs of cup

Answer:

5(m+9) = 5m+25

Answer:

5(m+9) = 5m+25

Step-by-step explanation:

durrrrrrrrrrrrrrr

Answer:

-1

Step-by-step explanation:

slope = ΔY  / ΔX  = 5/(-5)=-1

Answer:

C

Step-by-step explanation:

We'll have to use trigonometry for this.

First, note that in right triangle ABC, if we look from the perspective of angle A, the opposite side is x, the adjacent side is y, and the hypotenuse is 18.

In order to find x, then, we must use sine, which is opposite/hypotenuse. So:

sin(A) = sin(60) = opposite/hypotenuse = x/18

sin(60) is equal to (√3)/2, so multiplying both sides by 18 gives:

[(√3)/2] * 18 = 9√3

Already, we can tell that the answer is likely C, but let's find y to make sure.

We will use cosine to find y because cos = adjacent/hypotenuse.

cos(A) = cos(60) = adjacent/hypotenuse = y/18

cos(60) = 0.5, so multiplying both sides by 18 gives:

0.5 * 18 = 9

So, y = 9.

Thus, C is our answer.

~ an aesthetics lover

Answer:

C

Step-by-step explanation:

Using the cosine/ sine ratio in the right triangle and the exact values

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and sin30° = [tex]\frac{1}{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{x}{18}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 18[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 9[tex]\sqrt{3}[/tex]

----------------------------------------------------------

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{y}{18}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2y = 18 ( divide both sides by 2 )

y = 9

Thus

x = 9[tex]\sqrt{3}[/tex] and y = 9 → C

Step-by-step explanation:

20n 20394848484848575

The impulse on the body is 20 kg-m/s, the final speed of the body is 2m/s, and the distance covered within the time interval is 0.5m.

Force is the strength applied on an object with mass to change its state of motion.

The mass of the body is 10kg.

The force applied on the object is 40N.

The time for which the force is applied is 0.5 sec.

The impulse on the body is calculated by,

Impulse =  Force * Time

Impulse = 40 * 0.5

Impulse = 20 kg-m/s

The final speed of the body is given by

v = u + at

Assuming the initial speed = 0

v = at

Acceleration =  Force / mass

Acceleration = 40/10

a = 4 m/s²

v = 4 * 0.5

v = 2 m/s

The distance covered within the time interval is given by,

s = ut + (1/2) at²

s = (1/2) at²

s = (1/2) 4 * 0.5 *0.5

s = 0.5 m

To know more about Force

https://brainly.com/question/13191643

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Answer:

c is the answer

Step-by-step explanation:

Answer:

The answer is 10^24kg. 0.07346.

Answer:

C/8    -k= y

Step-by-step explanation:

C=8(y + k)

Divide each side by 8

C/8 = y+k

Subtract k from each side

C/8  -k = y+k-k

C/8    -k= y

Answer: y  =  C /8 −  k

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

SORRY IF THIS IS WRONG IM NOT GOOD IN MATH BUT I TRY

Answer: Parallel and same slope

Step-by-step explanation: Parallel means that the lines will never cross, which is shown in the picture. Basically they won't intersect.

branliest plssss :)

Answer:

Step-by-step explanation:

I & III look good