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dsp73
3 years ago
14

Answer question (picture below) and show work please

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
7 0

Answer:

A(x)=7x^2-2x+10

Step-by-step explanation:

Long Division

The polynomial long division implies the sequential division of each term of the dividend polynomial by the terms of the divisor polynomial. The procedure is a well-know sequence of steps from which there are two outputs: the quotient and the remainder.

We have two mathematical models, one for the total number of visitors who went to a theme park:

F(x)=126x^3+279x^2+90x+450

The other for the number of shows played at the theme park in the same period

G(x)=18x+45

Where x is the number of days since October 1. We are required to find the expression for the average number of visitors per show. It comes by dividing F(x) by G(x). We must perform a long division as shown  below.

The average number of visitors per show is

A(x)=7x^2-2x+10

For example, day 5

A(5)=7\ 5^2-2(5)+10=175

There were 175 visitors per show (on average)

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Determine the area of the figure shown. Note that each square unit is one unite in length
liq [111]

Answer:

74 units squared

Step-by-step explanation:

we know that the area of a square or rectangle is A = L × w

so we should just separate the object into it's individual rectangles/squares, solve for their areas, then add them together.

so I'll start with the middle square its length is 8 and width is 8 too.

A = 8 × 8

A = 64

now we'll move on to the other small ones to the side.

the one on the right side it's length is 2 and width is 2.

A = 2 × 2

A = 4

and then the last one on the left, Length is 3, width is 2.

A = 2 × 3

A = 6

now we'll add up all of the areas to get the total area.

Total = 64 + 4 + 6

Total = 74 units squared

6 0
3 years ago
In Problems 23–30, use the given zero to find the remaining zeros of each function
Talja [164]

Answer:

x =  2i, x = -2i and x = 4 are the roots of given polynomial.

Step-by-step explanation:

We are given the following expression in the question:

f(x) = x^3 - 4x^2+ 4x - 16

One of the zeroes of the above polynomial is 2i, that is :

f(x) = x^3 - 4x^2+ 4x - 16\\f(2i) = (2i)^3 - 4(2i)^2+ 4(2i) - 16\\= -8i+ 16+8i-16 = 0

Thus, we can write

(x-2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Now, we check if -2i is a root of the given polynomial:

f(x) = x^3 - 4x^2+ 4x - 16\\f(-2i) = (-2i)^3 - 4(-2i)^2+ 4(-2i) - 16\\= 8i+ 16-8i-16 = 0

Thus, we can write

(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Therefore,

(x-2i)(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16\\(x^2 + 4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Dividing the given polynomial:

\displaystyle\frac{x^3 - 4x^2 + 4x - 16}{x^2+4} = x -4

Thus,

(x-4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

X = 4 is a root of the given polynomial.

f(x) = x^3 - 4x^2+ 4x - 16\\f(4) = (4)^3 - 4(4)^2+ 4(4) - 16\\= 64-64+16-16 = 0

Thus, 2i, -2i and 4 are the roots of given polynomial.

4 0
3 years ago
Maya has 3 times as many dimes as nickels. She has 4 more quarters than nickels. if she has a total of $9.40, how many of each t
puteri [66]

Answer:  nickels = 14, dimes = 42, quarters = 18

<u>Step-by-step explanation:</u>

Let n represent nickels <em>which has a value of $0.05 </em>

Let d represent dimes <em>which has a value of $0.10</em>

Let q represent quarters <em>which has a value of $0.25</em>

It is given that:

                       n = n

                      d = 3n

                      q = n + 4

and their total value is $9.40    ⇒     n + d + q = $9.40

Use substitution to find the quantity of nickels:

.05(n) + .10(3n) + .25(n + 4) = 9.40

 5n    +  10(3n) +   25(n+4)   = 940           <em>multiplied by 100 </em>

 5n    +   30n   +  25n + 100 = 940          <em>distributed</em>

                            60n + 100 = 940          <em>added like terms</em>

                            60n           = 840          <em>subtracted 100</em>

                                 n           = 14            <em>divided by 60</em>

n = 14

                d = 3n

                   = 3(14)

                   = 42

                                       q = n + 4

                                          = (14) + 4

                                           = 18

4 0
3 years ago
Match the proper noun to the common noun.
egoroff_w [7]
Uncle peter-relative

january-month

jesse owens-athlete

william shakespeare-author

sunday-day

chrysler-automobile
3 0
2 years ago
Read 2 more answers
1. Consider the data set 1,2,3,4,5,6,7,8,9.
ivanzaharov [21]

Answer:  a) Mean = 5, Median = 5

b) Mean = 15, Median = 5

c) Due to presence of outlier i.e. 99.

Step-by-step explanation:

Since we have given that

1,2,3,4,5,6,7,8,9

Here, n = 9 which is odd

So, Mean would be

\dfrac{1+2+3+4+5+6+7+8+9}{9}=\dfrac{45}{9}=5

Median = (\dfrac{n+1}{2})^{th}=\dfrac{9+1}{2}=5^{th}=5

If 9 is replaced by 99,

1,2,3,4,5,6,7,8,99

So, mean would be

\dfrac{1+2+3+4+5+6+7+8+99}{9}=\dfrac{135}{9}=15

Median would be same as before i.e. 5

The mean is neither central nor typical for the data due to outlier i.e. 99

Hence, a) Mean = 5, Median = 5

b) Mean = 15, Median = 5

c) Due to presence of outlier i.e. 99.

5 0
3 years ago
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