What are all of the real roots of the following polynomial? f(x) = x^4 - x^3 - 13x^2 + x + 12
a) -1 and 1
b) -3, -1, 1, and 3
c) -3 and 3
d) -3, -1, 1, and 4
​

Answer:

3 hours

Step-by-step explanation:

Speed is the ratio of distance traveled to time taken, it is given as:

Speed = distance / time

An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. He then took the helicopter and flew to the corporate offices at an average speed of 78 mph. Given that the executive spent the same amount of time in the car as he did the helicopter how long did it take the executive to get to work.

Let the amount of time the executive spent in the car be t hours, therefore the amount of time spent in the helicopter = t hours.

For car:

Speed = distance / time

35 = distance ([tex]d_1[/tex]) / t

[tex]d_1=35t[/tex]

For helicopter:

Speed = distance / time

78 = distance ([tex]d_2[/tex]) / t

[tex]d_2=78t[/tex]

The total distance traveled = 169.5 miles

[tex]d_1+d_2=169.5\\35t+78t=169.5\\113t=169.5\\t=169.5/113\\t=1.5\ hours[/tex]

The time taken for the executive to get to work = time spent on car + time spent on helicopter = 1.5 + 1.5 = 3 hours

Answer:

40%

Step-by-step explanation:

total cupcakes: 14+21 = 35

Percentage with sprinkles = sprinkles / total

                                           = 14/35

                                           =.4

                                          = 40 %

Answer:

40%

Step-by-step explanation:

14 + 21 = 35

14/35 × 100 = 40

Therefore 40% of the cupcakes had sprinkles

Answer:

x = - 20, h = 34

Step-by-step explanation:

i can't tell ypou what the class period is, but for -x = 20, multiply each side by -1, then you get x = -20

-32 = 2-h

+32 .  +32

0=34-h

+h .   +h

34=h

flip

h=34

Answer:

16$ per shirt

Step-by-step explanation:

60% of 10 is 6

10 + 6 = 16

Since there is two negative signs in the original equation, you need two negative signs in the equivalent one as well.

Because one of the negatives if before the fraction, it doesn't matter if the second negative is on the 13 or on the 12.

The answer is A.

Answer:

the answer is "B" (thank me later) ;))

Answer:

Given:- [tex]f(x)=\frac{x-3}{x+2}[/tex]

Solution:- [tex]\left(-\infty \:,\:-2\right)\cup \left(-2,\:\infty \:\right)[/tex]

So, Answer:- [tex]All \: real\: value \: of x\: such \; that \: \neq -2[/tex]

OAmalOHopeO

Answer:

29

Step-by-step explanation:

The amounts greater than 40 cents can be formed.

After dividing one number by another, the modulo operation yields the remainder or signed remainder of the division.

Given:

According to the situation the equation can be

C = 5x + 11y, where x and y are non negative integers.

Now, We will fix y-values first, because there are fewer indices modulo 5:

y = 0 --> 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,... 5y

y = 1 --> 11, 16, 21, 26, 31, 36, 41, 46, 51, 56,... 5y + 11

y = 2 --> 22, 27, 32, 37, 42, 47, 52, 57, ...5y + 22

y = 3 --> 33, 38, 43, 48, 53, 58, ...5y + 33

y = 4 --> 44, 49, 54, 59, ...5y + 44

Then, 39 may be verified to be the smallest number that is impossible to obtain.

By examining each index (0, 1,..., 4), we may demonstrate this by observing that for y = 1, 6 is the largest positive integer congruent to 1 mod 5 that cannot be made, 17 is the largest positive number congruent to 2 mod 5, etc.

The largest of these improbable numbers is 39.

We could say that since 40, 41, ..., 44 are all obtainable, then we can induct by adding a multiple of 5 (i.e. if k is possible, so is k+5),

Hence, all amounts greater than 40 cents can be formed.

Learn more about Modulo here:

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Answer:

y=x+2

Step-by-step explanation:

Since 1 up, 1 down, 1 left, and 1 right would all cancel out so you would still get y=x+2

Answer:

see below

Step-by-step explanation:

will make it simple.

1 unit up : y = |x+2| + 1

1 unit down : y = |x+2| - 1

1 unit to the left : y = |x + 3|

1 unit to the right : y = |x+1|

hope it helps.  if its wrong, then please report it wo we can delete of correct it.

Answer:

a.ans=(1,3)

b.ans=(1,2,3,4,5,6,7,9,11,12)

c.ans=(1,3,5,7,9,11)

Step-by-step explanation:

Between A and C (1,3) are common.So it is the intersection.

(1,2,3,4,5,6,7,9,11,12) are all the number belongs to set A and set C.So it is called the union of both sets.

C denotes the complement and the number except set b belong to the complement.

Answer:

a rectangular prism

Step-by-step explanation:

consists of 6 faces which are rectangles

Answer:

[tex]\boxed{5}[/tex]

Step-by-step explanation:

[tex](p-q)(2)[/tex]

[tex]p(2)-q(2)[/tex]

[tex]\sf When \ x \ is \ 2, \ p(x) \ is \ 3 \ and \ q(x) \ is \ -2.[/tex]

[tex](3)-(-2)[/tex]

[tex]3+2=5[/tex]

Answer:

1. [1,-8,-7]

2.[4,-3,-2]

3.[9,-7,-2]

srry if wrong

Answer:

$180

Step-by-step explanation:

what is 45 20% of? This is what we need to find! To do this we have to take 45 and divide it by .2 which will give us 225. To check that this is the answer we take 45 and divide it by 225. This brings us back to 20%. He wouldve paid $225 for the desk, but there was a $45 discount, and after subtracting the discount we are left with $180

Answer:

A) 24+24+120+160+200

Step-by-step explanation:

The two ends are 24 (1/2bh= 1/2(8*6)).

One side (the back) is 6x20=120

One side (the bottom) is 8x20=160

One side (the top) is 10x20=200

So the equation is 24+24+120+160+200

Answer:

-3

Step-by-step explanation:

8x+28=12-20-4x

8x+4x=-8-28

12x=-36

x=-3

PLS MARK AS BRAINLIEST

Answer:

140

Step-by-step explanation:

The prism shown is a rectangular prism

Volume of a rectangular prism = length * width * height

Given length: 3 1/2

Given width: 5

Given height: 8

Volume = 3.5 * 5 * 8 = 140

Answer:

[tex]A=140[/tex]

Step-by-step explanation:

The volume of a three-dimensional object is the amount of space the object takes up. In this case, the prism is a rectangular  prism, its volume can be found using the following formula,

[tex]A=l*w*h[/tex]

Substitute the given values into this formula,

[tex]A=l*w*h[/tex]

[tex]A=8*5*3\frac{1}{2}[/tex]

Simplify,

[tex]A=8*5*3\frac{1}{2}[/tex]

[tex]A=40*3\frac{1}{2}[/tex]

Convert the mixed number into an improper fraction, this can be done by multiplying the "number" part of the mixed number by the denominator (number under the fraction bar). Then one adds the result to the numerator (number over the fraction bar).

[tex]A=40*3\frac{1}{2}[/tex]

[tex]A=40*\frac{(3*2)+1}{2}[/tex]

[tex]A=40*\frac{6+1}{2}[/tex]

[tex]A=40*\frac{7}{2}[/tex]

To simplify further, one must divide the number the fraction is being multiplied by the denominator of the fraction,

[tex]A=40*\frac{7}{2}[/tex]

[tex]A=20*7[/tex]

Multiply to finish simplifying and get the answer,

[tex]A=20*7[/tex]

[tex]A=140[/tex]

[tex]\dfrac{\dfrac{1}{p-2}}{\dfrac{4p^2}{p^2+p-6}}=\\\\\\\dfrac{1}{p-2}\cdot\dfrac{p^2+p-6}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{p^2+3p-2p-6}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{p(p+3)-2(p+3)}{4p^2}=\\\\\dfrac{1}{p-2}\cdot\dfrac{(p-2)(p+3)}{4p^2}=\\\\\dfrac{p+3}{4p^2}[/tex]

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

[tex]\dfrac{6n}{3n+2}-\dfrac{2}{2n-2}=\\\\\dfrac{6n(2n-2)}{(3n+2)(2n-2)}-\dfrac{2(3n+2)}{(3n+2)(2n-2)}=\\\\\dfrac{12n^2-12n-(6n+4)}{6n^2-6n+4n-4}=\\\\\dfrac{12n^2-12n-6n-4}{6n^2-2n-4}=\\\\\dfrac{12n^2-18n-4}{6n^2-2n-4}=\\\\\dfrac{2(6n^2-9n-2)}{2(3n^2-n-2)}=\\\\\dfrac{6n^2-9n-2}{3n^2-n-2}[/tex]

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

[tex]\dfrac{2x}{3x^2+18x}+\dfrac{3}{2}=\\\\\dfrac{2}{3x+18}+\dfrac{3}{2}=\\\\\dfrac{2\cdot2}{2(3x+18)}+\dfrac{3(3x+18)}{2(3x+18)}=\\\\\dfrac{4+9x+54}{6x+36}=\\\\\dfrac{9x+58}{6x+36}[/tex]

Answer:

p^3−10p^2+1

——————        We find roots of zeros  F(p) = p^3 - 10p^2 + 1 and see there

      p^2                                             are no rational roots

Step-by-step explanation:

                 p^2

Simplify   ——

                 p^2

1.1    Canceling out p^2 as it appears on both sides of the fraction line

   Equation at the end of step 1

:1

 ((————-(4•1))+p)-6

   (p^2)

STEP 2: working left to right

                  1

Simplify   ——

                 p^2

Equation at the end of step 2:    

1 /p^2 ((—— -  4) +  p) -  6

STEP 3:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  p^2  as the denominator :

          4         4 • p^2

   4 =  —  =  ——————

           1             p^2  

Equivalent fraction

: The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

             1 - (4 • p^2)                 1 - 4p^2

————————————  =  ———————

                    p^2                             p^2  

Equation at the end of step 3:

        (1 - 4p^2)          

 (————————— +  p) -  6

             p^2              

STEP 4:

Rewriting the whole as an Equivalent Fraction

4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  p2  as the denominator :

           p         p • p^2

   p =  —  =  ——————

           1             p^2  

Trying to factor as a Difference of Squares:

4.2      Factoring:  1 - 4p^2

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  1  is the square of  1

Check : 4 is the square of 2

Check :  p^2  is the square of  p^1

Factorization is :       (1 + 2p)  •  (1 - 2p)

Adding fractions that have a common denominator :

4.3       Adding up the two equivalent fractions

                (2p+1) • (1-2p) + p • p^2                                   p^3 - 4p^2 + 1

————————————————————————  =  ————————————

                               p^2                                                            p^2    

Equation at the end of step

4:

        (p^3 - 4p^2 + 1)    

 —————————————— -  6

                 p^2          

STEP 5:

Rewriting the whole as an Equivalent Fraction

5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  p^2  as the denominator :

           6         6 • p^2

   6 =  —  =  ——————

           1             p^2  

Polynomial Roots Calculator :

5.2    Find roots (zeroes) of :       F(p) = p^3 - 4p^2 + 1

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

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  p  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  1.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -4.00    

     1       1        1.00        -2.00    

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

5.3       Adding up the two equivalent fractions

(p3-4p2+1) - (6 • p2)     p3 - 10p2 + 1

—————————————————————  =  —————————————

         p2                    p2      

Polynomial Roots Calculator :

5.4    Find roots (zeroes) of :       F(p) = p3 - 10p2 + 1

    See theory in step 5.2

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

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1

Let us test ....

  P       Q    P/Q       F(P/Q)  Divisor

     -1      1        -1.00       -10.00    

       1      1    1.00       -8.00    

Polynomial Roots Calculator found no rational roots

Final result :

             p3 - 10p2 + 1

 —————————————

                 p2      

Answer:

approximately 5.36

Step-by-step explanation

20 - 9.28 = 10.72

BD = EC

10.72/2 = 5.36

Answer:

[tex]f^{-1}(6) = 2[/tex]

Step-by-step explanation:

Given

[tex]f(2) = 6[/tex]

[tex]f(3) = 7[/tex]

Required

[tex]f^{-1}(6)[/tex]

First, we need to determine the slope of the function using;

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

From the given parameters;

In [tex]f(2) = 6[/tex]

x = 2; y =6 --- Take this as x1 and y1

In [tex]f(3) = 7[/tex]

x = 3; y = 7 --- Take this as x2 and y2

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex] becomes

[tex]m = \frac{6 - 7}{2 - 3}[/tex]

[tex]m = \frac{- 1}{ - 1}[/tex]

[tex]m = 1[/tex]

Next, we determine the equation of the function using

[tex]y - y_1 = m(x - x_1)[/tex]

Substitute the values of x1,y1 and m

[tex]y - 6 = 1(x - 2)[/tex]

Open bracket

[tex]y - 6 = x - 2[/tex]

Add 6 to both sides

[tex]y - 6 + 6 = x -2 +6[/tex]

[tex]y = x + 4[/tex]

Next is to determine the inverse function by swapping the positions of x and y

[tex]x = y + 4[/tex]

Make y the subject of formula;

[tex]y = x - 4[/tex]

Replace y with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x) = x - 4[/tex]

Now, we can solve for [tex]f^{-1}(6)[/tex]

Substitute 6 for x

[tex]f^{-1}(6) = 6 - 4[/tex]

[tex]f^{-1}(6) = 2[/tex]

Answer:

6

Step-by-step explanation:

Function A

y = 9x + 4

Function B

y = max+b

m = 3 and b = 4

y = 3x+4

The difference in the slopes is 9-3 = 6

Answer:

6

Step-by-step explanation:

The two functions are A and B.

A's equation is khown

● y =9x + 4

B is also khown. We should only gather tge information.

● the rate of change is 3

●the y-intercept is 4

So B's equation is:

● y = 3x + 4

3 is the rate of change wich is khown as the slope.

Divide A's slope by B's slope to khow how much A's slope is bigger than B's.

● 9/3 = 3

Substract 3 from 9 and you get the difference 9-3= 6

Answer:

Point : ( -2, 15 )

Step-by-step explanation:

A point that would make this relation not a function would be one that shares a common x - value with the other points. One common domain values for two range values would, when graphed, not follow the vertical test, hence making the relation not a function.

Let's say that the point is ( -2, 15 ). It has a common x - value with respect to the first point, ( -2, 8 ), and therefore would make this set not a function.

Answer:

Point : ( -2, 15 )

Step-by-step explanation:

if you have 88 tablespoons and you convert them into cups you would have 5.5 then you would convert that into a fraction which would be 5 1/2

The inequality that describes the scenario will be; 35  +  12C  ≥  100.

The minimum number of classes a customer can take for Rebekah to meet her goal is 6

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

One-time initial fee = $35

Additional fee per class = $12

Minimum target = $100

Number of classes = C

One-time initial fee  +  (Additional fee per class) x (Number of classes) ≥ Minimum target

The inequality that describes the scenario will be;

35  +  12C  ≥  100

Then Solve for C to know the minimum number of classes a customer can take for Rebekah to meet her goal,

12C  ≥  100 - 35

12C  ≥  65

C   ≥   65 / 12

C  ≥  5.42

Thus, The minimum number of classes a customer can take for Rebekah to meet her goal is 6

Learn more about inequality ;

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Answer:

a₁= -34

aₙ = 13n - 47

Step-by-step explanation:

This is an AP with the first term of -34 and the common difference of 13.

The nth term is:

This is the required formula.

Answer:

c) 6

Step-by-step explanation:

18 divided by 3 is 6

30 divided by 5 is 6

Answer:

C: 6

Step-by-step explanation:

Answer:

£17.50

Step-by-step explanation:

30 punnets /  £20

= 30 / 20

= 1.5

1 punnet costs £1.5

30 strawberries * (1/6 punnets)

= 30 * (1/6)

= 30/6

= 5

5 punnets were rotten.

5 rotten punnets * £1.5

= 5 * 1.5

= 7.5

Sandeep lost £7.5 in profits.

6/6 punnets - 1/6 rotten punnets

= 6/6 - 1/6

= 5/6

5/6 punnets are good

30 punnets * 5/6 good punnets

= 30 * 5/6

= 150/6

= 25

Sandeep has 25 punnets left to sell

25 punnets to sell *  £1.50

= 25 * 1.5

= 37.50

Sandeep will get £37.50 from selling the punnets.  However, you must take into account that he lost £20 when he bought the strawberies.  THat money while be added back with some extra money left over:

£37.50 - £20

= 37.50 - 20

= 17.50

Put all into 1 equation:

{[30 * (5/6)] * 1.50} - 20

= {(150/6) * 1.50} - 20

= {25 * 1.50} - 20

= 37.50 -20

= 17.50

Overall, Sandeep's actual profits are equal to 17.50

I hope this is correct!  Please tell me if the answer or info I gave was wrong!

Answer:You cant get someone to do all of this try doing a few or getting help from someone older that's what I did

I asked help for one problem and the explanation and now I understand how they did it so the other problems I can do now

It's better to make an effort and try doing some of them instead of asking someone to do all of it

Because when the test comes it won't be that easy so next time just try putting a few so that way you can try understanding it and you can apply it to similar problems

Answer:

Don't ask someone to do this if your question is a test

Step-by-step explanation:

Answer:

[tex]\boxed{\sf A, \ B \ and \ E}[/tex]

Step-by-step explanation:

[tex]\sf Exterior \ angles \ are \ the \ angles \ located \ outside \ of \ the \ triangle.[/tex]