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NikAS [45]
3 years ago
9

Simplify completely 14x^5y^4 +21x^3y^2/ 7x^3y

Mathematics
2 answers:
Studentka2010 [4]3 years ago
6 0

Answer:

C.2x^{2}y^{3}+3y

Step-by-step explanation:

We have the expression:

\frac{14x^5y^4+21x^3y^2}{7x^3y}

which can be separeded in two terms, like this:

\frac{14x^5y^4}{7x^3y} +\frac{21x^3y^2}{7x^3y}

and now we can simplify each term, dividing the coefficients and using the exponent law \frac{x^m}{x^n} =x^{m-n} (when we divide a variable we substract the exponts) and we get the following:

2x^{5-3}y^{4-1}+3x^{3-3}y^{2-1}

simplifying the exponents:

2x^{2}y^{3}+3y

which is option C.

ss7ja [257]3 years ago
3 0

C is the answer you have to divide 21 by 3 first which gives you 3. The x cubed cancels out because when dividing exponents you have to subtracting. The y squared minus y gives you just y. This explains the 3y

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Cot 2 2x – 4cot2x + 3 = 0
jeyben [28]

x = 9.21° or x = 22.5°

cot²2x – 4cot2x + 3 = 0

Let cot2x = y

y² - 4y + 3 = 0

Factorizing, we have

y² - y - 3y + 3 = 0

y(y - 1) -3(y - 1) = 0

(y - 1)(y - 3) = 0

y - 1 = 0 or y - 3 = 0

y = 1 or y = 3

Since cot2x = y

cot2x = 1 or cot2x = 3

1/tan2x = 1 or 1/tan2x = 3

tan2x = 1 or tan2x = 1/3

2x = tan⁻¹(1) or 2x = tan⁻¹(1/3)

2x = 45° or 2x = 18.43°

x = 45°/2 or x = 18.43°/2

x = 22.5° or x = 9.21°

So, x = 9.21° or x = 22.5°

Learn more about cotx here:

brainly.com/question/15546709

4 0
3 years ago
Nika rolls an 8-sided cube with faces numbered 1 through 8. Which of the following statements is true?
andreyandreev [35.5K]

Answer: Statement 2 (P(odd number) = 1/2) is true

Step-by-step explanation:

Statement 1: there are 4 even numbers (2, 4, 6, 8) so therefore a 1/2 chance, not a 1/8. [FALSE]

Statement 2: there are 4 odd numbers (1, 3, 5, 7) so therefore a 1/2 chance, so this is true. [TRUE]

Statement 3: 8 is the biggest number, so there are 7, not 1, numbers less than it. [FALSE]

Statement 4: there is no 9 on an 8 sided cube. [FALSE]

8 0
3 years ago
Name two coordinates that are on the line: <img src="https://tex.z-dn.net/?f=y%20%3D%2012" id="TexFormula1" title="y = 12" alt="
Eva8 [605]

Answer:

(1,12) and (2,12).

(- 5,1) and (- 5, 2).

Step-by-step explanation:

y = 12 is a line that is parallel to the x-axis and at a constant distance of 12 units above the x-axis. Therefore, the points on the line will have any x-coordinate but have a constant y-coordinate i.e. 12.

Therefore, the two points on the line y = 12 can be (1,12) and (2,12).  

x = - 5 is a line that is parallel to the y-axis and at a constant distance of 5 units left of the y-axis. Therefore, the points on the line will have any y-coordinate but have a constant x-coordinate i.e. - 5.

Therefore, the two points on the line x = - 5 can be (- 5,1) and (- 5, 2).  (Answer)

3 0
3 years ago
How many cubic blocks of side length of 173 inch would it take to fill a rectangular prism with a length width and height of 3/7
bulgar [2K]

Complete question :

How many cubic blocks of side length of 17 inch would it take to fill a rectangular prism with a length width and height of 3/7 inch 1/7 inch and 3/7 inch

Answer:

9 cubic blocks

Step-by-step explanation:

The volume of a rectangular prism is given as :

V = Length * width * height

V = 3/7 * 1/7 * 3/7 = 9 / 343 in³

The volume of block clube:

Take the cube of the side length :

(1/7)^3 = 1 / 343 in³

Number of cubic blocks required :

Volume of prism / volume of cube

9 / 343 ÷ 1 / 343

9 / 343 * 343 /1 = 9

Hence, 9 cubic cubes are needed to fill the rectangular prism

4 0
4 years ago
Architects make scale models of buildings to present their ideas to clients. If an
MaRussiya [10]

The area of the model is 80 square foot

Step-by-step explanation:

Let the area of the house model be 'a'

The scale = 1:50

The area of the house= 4000 square foot

Area of the model =4000/50

a = 80 square foot

The area of the model is 80 square foot

5 0
4 years ago
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