Sonia will go on a 9-day vacation with his grandparents. He will take $57 of his
own money. His grandparents will give him another $78. Sonia will spend all
of the money and he will spend the same amount each day. How many dollars
will Sonia spend each day of the vacation?

A polynomial of degree 4 will have 4 zeros. The zero of 3 with a multiplicity of 2 counts as two of these zeros. You've also been given a zero of -i. So it seems that we only have 3 of the 4 zeros. We need all 4 to be able to form the desired polynomial.

You didn't mention that the polynomial should have real coefficients. But I'm going to assume it because otherwise we can't solve the problem. If a polynomial with real coefficients has a complex zero, then the complex conjugate of that complex zero will also be a zero. This is how we will find the 4th zero.

A complex number in standard form is a + bi. Its complex conjugate is a + (-bi) or a - bi. The complex zero we were given is -i. In standard form this would be 0 + (-i). The complex conjugate of 0 + (-i) would be 0 - (-i) or 0 + i or just i.

So the four zeros of the desired polynomial are 3 (twice), -i and i. If a number "z" is a zero of a polynomial then (x - z) is a factor of that polynomial. Using this fact and the four zeros we can write a factored form of our desired polynomial:

f%28x%29+=+a%28x-3%29%28x-3%29%28x-%28-i%29%29%28x-i%29

Simplifying the 3rd factor we get:

f%28x%29+=+a%28x-3%29%28x-3%29%28x%2Bi%29%28x-i%29

where the "a" is any non-zero number. Since there are an infinite number of non-zero numbers, there will be an infinite number of possible correct solutions to this problem. To make things easy we will choose to make "a" be 1. This makes our factored polynomial:

f%28x%29+=+%28x-3%29%28x-3%29%28x%2Bi%29%28x-i%29

All we have to do now is multiply this out. We can simplify this process if we take advantage of some factoring patterns. The first two factors can be multiplied using:

%28a-b%29%5E2+=+a%5E2-2ab%2Bb%5E2

And the last two factors can be multiplied using:

%28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2

With these patterns we get:

f%28x%29+=+%28%28x%29%5E2-2%28x%29%283%29%2B%283%29%5E2%29%28%28x%29%5E2-%28i%29%5E2%29

Simplifying inside each factor we get:

f%28x%29+=+%28x%5E2-6x%2B9%29%28x%5E2-i%5E2%29

And since i%5E2+=+-1 this becomes:

f%28x%29+=+%28x%5E2-6x%2B9%29%28x%5E2-%28-1%29%29

or

f%28x%29+=+%28x%5E2-6x%2B9%29%28x%5E2%2B1%29

We have one more multiplication. There are no shortcuts for this one. We have to multiply each term of one factor times each term of the other and then add like terms, if any:

f%28x%29+=+x%5E2%2Ax%5E2%2Bx%5E2%2A1%2B%28-6x%29%2Ax%5E2%2B%28-6x%29%2A1%2B9%2Ax%5E2%2B9%2A1

Simplifying...

f%28x%29+=+x%5E4%2Bx%5E2%2B%28-6x%5E3%29%2B%28-6x%29%2B9x%5E2%2B9

f%28x%29+=+x%5E4%2B10x%5E2%2B%28-6x%5E3%29%2B%28-6x%29%2B9

Re-ordering into standard form:

f%28x%29+=+x%5E4%2B%28-6x%5E3%29%2B10x%5E2%2B%28-6x%29%2B9

This is a polynomial function of degree 4 with the given zeros.

P.S. As mentioned earlier, this is not the only possible correct answer. This is the answer when you make "a" equal to 1. Other values for "a" give us different polynomial functions which also have the same zeros. For example, if we had chosen a = 2 we would have gotten f%28x%29+=+2x%5E4%2B%28-12x%5E3%29%2B20x%5E2%2B%28-12x%29%2B18.

The volume of the given pyramid comes to be 64 cubic inches.

Length of the square base a= 8 inches

Slant height l =5 inches

The volume of a pyramid is with base area A and height h is 1/3Ah.

So, base area A= 8*8 =64 square inches.

From Pythagoras theorem

[tex]l^{2} =(\frac{a}{2})^2 +h^{2}[/tex]

[tex]5^{2} =(\frac{8}{2})^2+h^{2}[/tex]

[tex]h=3[/tex] inches

So, volume of the pyramid = 1/3*A*h

=1/3*64*3

=64 cubic inches.

Hence, the volume of the given pyramid comes to be 64 cubic inches.

To get more about pyramids visit:

https://brainly.com/question/218706

Answer:

5, 4, 3, & 64

Step-by-step explanation:

i did it

Answer: Mr. Silberman has to pay $150 more than Ms. Washington.

Step-by-step explanation: First calculate how much tax Mr. Silberman will have to pay off after 9 months. 50x9=450, so $450 is how much tax he will have to pay. Add that to 1,500, which is the total cost of the computer, which equals $1,950.

Ms. Washington only has to pay $1,800. Mr. Silberman has to pay $1,950. So Mr.  Silberman has to pay more. He has to pay $150 more than Ms. Washington.

Answer:

64

Step-by-step explanation:
1. Plug it in:

(2(-4))^2

2 times -4 is -8

(-8)^2 = 64

So there’s your answer

Answer:

2nd one is correct.....

Answer:

x = 2

Step-by-step explanation:

Given :

Add 4 on each side

Subtract 3x from each side

Divide 2 from each side

The value of the function when x = 2 will be 9. The value is obtained by putting the value 2 in the place of x.

A connection between independent variables and the dependent variable.is defined by the function. Functions help to represent graphs and equations.

The given function in the problem is;

[tex]\rm f(x) = 2x^2 - 3x + 7[/tex]

On putting x =2 we get;

[tex]\rm f(2) = 2(2)^2 - 3(2) + 7 \\\\\ f(2) = 2(4) - 3(2) + 7 \\\\ f(2) = 8 - 6 + 7 \\\\ f(2) = 9[/tex]

Hence the value of the function when x = 2 will be 9.

To learn more about the function refer to the link;

https://brainly.com/question/12431044

Answer:

a

Step-by-step explanation:

Answer:

I use app called math

way

Step-by-step explanation:

Answer:

Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.

Answer:

8 quarts

Step-by-step explanation:

1/3 of a gallon ---1/6 of a wall

                x  - 1 (all the wall)

                     x = (1 x 1/3) / 1/6

x = 1/3 / 1/6

                     x = 6/3

                     x = 2 gallons

1 gallons - 4 quarts

                     2 gallons -  x

  x = (2 x 4) / 1

                        x = 8 / 1

                        x = 8 quarts

Answer:

Corresponding

Step-by-step explanation:

Matching angles of two congruent figures are called corresponding angles. The angles that are in the same position will have the same measurement.

Answer:

⁶/11

Step-by-step explanation:

total marbles = 4+6+1

=11

blue marble/total marbles : ⁶/11

Answer:

we can't really answer the question without the pictue, but if the time count stays the say and the distance doen't, it would be (t=time/d=distance) (lets say time was an hour and you traveled 11 miles each hour,) then it would be 11t = d

But, if it is without multiplication, then just add all the numbers in each turn to get your answer.

Hope this saved your time. :)

Answer: 6.4 m

Step-by-step explanation:

Answer:

x = 39

Step-by-step explanation:

Secant and tangent line from a point outside the cirlcle,

(length of th tangent)² = length of the secant * external segment

                   26²          =  (13 + x) * 13

               [tex]\sf (13 +x)*13 = 26 *26\\[/tex]

                           [tex]\sf 13 + x =\dfrac{26*26}{13}[/tex]

                           13 + x   = 2* 26

                           13  + x = 52

                                   x = 52 - 13

                                  x = 39

Answer:

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S.

Step-by-step explanation:

Answer: Taking a Photo of another photo displayed in an art gallery and claiming it as your own

Step-by-step explanation:  Because you are claiming something as your own(when it's not) is considered plagiarism and no other situation is considered plagiarism but this one so really the process of elimination explains the answer to this question

Answer:

C  $56,508

Step-by-step explanation:

You take the property taxes of $3164.45 & divide by the tax rate of .056 & you get $56,508

To double check, $56,508 property value X the tax rate of .056 (5.6%) = $3,164.45

Answer: d

Step-by-step explanation:

The 75 degree angle and angle d are same-side interior angles, meaning that if they were supplementary, the lines would be parallel by the converse of the same-side interior angles theorem.

the answer is D

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The height of the parallelogram for A is 3 units while the length the base is 6 units.

For D it follows this same pattern, the height is 1 which is half of the length of the base, 2.

B also follows this pattern, the height is 2 which is half of the length of the base, 4

C does not follow this pattern and is the odd one out.

I think D at (2,1) will do

hope it helps...!!!

Step-by-step explanation:

I think D at (2,1)

hope it will help

Using it's formula, it is found that the population density of the penguin population was of 134.9 penguins per square acre.

It is given by the population divided by the area.

In this problem:

Hence:
D = 6342/47 = 134.9 penguins per acre.

More can be learned about population density at https://brainly.com/question/26148357

#SPJ1

Answer:

18.8

Step-by-step explanation:

First find the area of the rectangle, which is 4x3 (base x height) the area of the rectangle is 12.

We are given the radius as 2 for the quarter circles, and 2 quarter circles form 1 semicircle, so really we can solve for the area of one semi circle using the formula ( (pi*radius²)/2 ). Plug in the values and you should get 6.28.

Next, you add the area of the figures so 12+6.8 which is equal to 18.8.

Answer:

4 (cooked)

Step-by-step explanation:

2 / 1/2 = 4

Answer:

13 through -infinity

or

13, -infinity

Step-by-step explanation:

Answer:

a = 3 , b = 8 , c = 4

Step-by-step explanation:

the standard form of a quadratic equation is

ax² + bx + c = 0

3x² + 8x + 4 = 0 ← is in standard form

with a = 3, b = 8, c = 4

Answer: N = 5

ok done. Thank to me >:3

Answer:

8/14

Step-by-step explanation:

there are 5 odd numbers and 3 numbers are coloured red