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WARRIOR [948]
3 years ago
10

Simplify 2x²/x²-7x+12 - x²+9/x²-7x+12

Mathematics
2 answers:
Nina [5.8K]3 years ago
7 0

Answer:

2x²/x² - 7x + 12 - x² + 9/x² - 7x + 12

2x²/x² simplifies to just 2 (the x²s cancel out)

2 - 7x + 12 - x² + 9/x² - 7x + 12

add like terms: (2 + 12 + 12) + (-7x - 7x) - x² + 9/x²

= - x² - 14x + 9/x² + 26

Ivenika [448]3 years ago
5 0

Answer:

(x+3)/(x-4)

Step-by-step explanation:

[2x²/(x-4)(x-3)] - [x²+9/(x-4)(x-3)] =

(x²-9)/(x-4)(x-3) =

(x+3)(x-3)/(x-4)(x-3) =

x+3/x-4

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When grades are expressed as a quantity of 1, such as two feet per second or 5 miles per hour, they are called unit rates.
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Which of the following statements about the mean is false?
Harlamova29_29 [7]

Answer:

The value of the mean reflects both the number and the value of cases. is false

Step-by-step explanation:

8 0
3 years ago
In the diagram at the left, O is the center of the circle, MNOP is a rectangle, and the area of the circle is 100π. What is the
RUDIKE [14]

The length of the diagonal of the rectangle will be 14.142 units.

<h3>What exactly is a rectangle?</h3>

It has four sides and is a polygon. The internal angle total is 360 degrees. The opposing sides of a rectangle are parallel and equal, and each angle is 90 degrees.

Rectangle diagonals are equally equal and meet at the midpoint.

O is the circle's center, MNOP is its rectangle, and the circle's area is 100 in the diagram to the left.

Area of circle=πr²

100 π= πr²

r= 10 units

The length of the rectangle is equal to the radius of the circle is 10 units. The length of the diagonal is √2  times the side of the rectangle;

L=√2 R

L=1.414×10

L=14.14

Hence the length of the diagonal of the rectangle will be 14.142 units.

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4 0
2 years ago
A= x^2 -30x+225 The polynomial represents the area (in square feet) of the square playground. a. Write a polynomial that represe
Setler [38]

Answer:

a) The polynomial is equivalent to A = (x-15)^{2}, and the side length of the playground is x -15 feet.

b) The perimeter of the playground, measured in feet, is p = 4\cdot (x-15).

Step-by-step explanation:

a) By Geometry, we know that area of the square is equal to the square of the side length. If A = x^{2}-30\cdot x +225 is the area of the square, then must be a perfect square trinomial, that is:

(x-a)^{2} = x^{2}-2\cdot a\cdot x + a^{2} (1)

Then, we must observe the following properties:

-2\cdot a = -30 (2)

a = 15

a^{2} = 225 (3)

a = 15

Therefore, the polynomial is equivalent to A = (x-15)^{2}, and the side length of the playground is x -15 feet.

b) The perimeter of a square equals four times the side length. That is:

p = 4\cdot (x-15)

The perimeter of the playground, measured in feet, is p = 4\cdot (x-15).

7 0
3 years ago
Nick has $5, $20, and $100 bills that total 17 bills. He exchanges all his $5 bills for $1 bills, then all his $20 bills for $5
Minchanka [31]

Answer:

8

Step-by-step explanation:

Key to this question is assume that each exchange preserves the total dollar amount of Nick’s money.

If He exchanges all his $5 bills for $1 bills, it means that a $5 bill will result in 5 $1 bills as such, if he had x number of $5 bill, after the exchange, he would have 5x $1 bills.

then all his $20 bills for $5 bills, it means that for each $20 bill, he gets 4 $5 bills which means that if he had y number of $5 bills, after the exchange, he would have 4y $5 bills.

and finally all his $100 bills for $20 bills, then he must have received 5 $20 bills for each $100 such that if he had z number of $100 bills before the exchange, he would have 5z number of $20 bills after the exchange. Given that originally he had 17 bills and later 77 bills then

x + y + z  = 17

5x + 4y + 5z = 77

Multiplying the first equation by 5,

5x + 5y + 5z = 85

5x + 4y + 5z = 77

subtract 2 from 1

y = 8

5 0
3 years ago
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