Which of the following is a polynomial with roots 3, 5i, and −5i?f(x) = x3 − 3x2 + 25x − 75
f(x) = x3 − 3x2 + 15x − 25
f(x) = x3 − 15x2 + 25x − 75
f(x) = x3 − 3x2 + 15x − 75

Answers

Answer 1
Answer: x_(1)=3 \n  \n x_(2)=5i \n  \n x_(2)=-5i \n  \n f(x)=(x-x_(1))(x-x_(2))(x-x_(3))=(x-3)(x-5i)(x+5i)= \n  \n =(x-3)(x^(2)+25)=x^(3)+25x-3x^(2)-75=x^(3)-3x^(2)+25x-75

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The figure has been decomposed into three rectangles as shown. A figure is decomposed into 3 rectangles. The rectangles are 4 inches by 2 inches, 6.5 inches by 2 inches, and 4 inches by 1.5 inches. Find the area of each piece of the composite figure. The area of the top rectangle is A = 4 in.(2 in.) = 8 in2. The area of the middle rectangle is A = 2 in.( in.) = in2. The area of the bottom rectangle is A = 4 in.( in.) = in2. The total area of the figure is in2.

Answers

Final answer:

The areas of the three rectangles in the decomposed figure are 8 in², 13 in², and 6 in², respectively, whereas the total area of the composite figure is 27.0 square units.

Explanation:

First, we need to calculate the area of each rectangle separately. The area of a rectangle can be found using the formula Length x Width.

For the first rectangle, with dimensions of 4 units by 2 units, we multiply 4 by 2 which gives us an area of 8 square units.

Similarly, for the second rectangle, having dimensions of 6.5 units by 2 units, multiplying 6.5 by 2 gives us an area of 13.0 square units.

Lastly, for the third rectangle with dimensions 4 units by 1.5 units, multiplying 4 by 1.5 gives us an area of 6.0 square units.

After finding the area of all three rectangles individually, we add them all up to get the total area of the composite figure. Hence, the total area is 8 + 13.0 + 6.0 = 27.0 square units.

Learn more about Area of rectangles here:

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Answer:

27 in³

Step-by-step explanation:

4 × 2 = 8 in²

6.5 × 2 = 13 in²

4 × 1.5 = 6 in²

Total area = 8 + 13 + 6

27 in²

How are rectangular prims, triangle prims, and cubes different? How are they the same

Answers

Answer:

Step-by-step explanation:

a cube is a rectangular prism with all sides equal, and therefore all faces of equal area. A rectangular prism will have 4 faces of equal area and 2 faces of equal area. ... A rectangular prism has four faces that are rectangles and two faces that are squares. A cube has six faces that are squares.

Please HELP me solve: the museum's show for July features 30 oil paintings by different artists. All artists show the same number of paintings and each artist shows more than 1 painting. How many artists could be featured in the show

Answers

if  each artist shows more than 1 painting.so minimum number of painting per artist is 2.
so if every artist show same number of painting so maximum number of artists is 30/2 = 15

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Answers

Answer:

5/3

Step-by-step explanation:

The slope is the coefficient next to the x. Therefore, the slope is 5/3.

Answer:

m= 5/3

Step-by-step explanation:

Math wizzz

Worked it out

And online calculator verified!

Rename the number. 204 thousands=   ---------

Answers

Answer : 20,400

Explanation : The name itself suggests that it is 204 thousands.

Which means it has 20 thousands 400.

As renaming process involves, the ability to flexibly rename numbers starting with a whole numbers and move through tens, hundreds, thousands, ten thousands, and so on.

This helps us to find that 204 thousands is 20400 as it says it is a thousand digit value and has three digits in it. To qualify to be called as a thousand it needs to have at least 4 digits in it. But, it has 5 digits because it falls under the category of ten thousands range; which means it should be in 5 digits.

Therefore, the answer is 2→Ten thousand 0→Thousand, 4→ hundred 00→Tens .

So, the answer is correct 20,400.

What is the average rate of change for (0,80) and (15,10)

Answers

Answer:

-14/3

Step-by-step explanation:

formula: (y₂ - y₁) / (x₂ - x₁)

(10 - 80) / (15 - 0)

(-70) / (15)

simplify

-14/3

Y/X
10-80/15-0
-70/15
=-14/3