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timofeeve [1]
3 years ago
10

Dividing rational expressions

Mathematics
1 answer:
Galina-37 [17]3 years ago
5 0
\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
\cfrac{x+3}{x^2-2x}\cdot \cfrac{(x-2)^2}{x^2-9}\implies \cfrac{x+3}{x^2-2x}\cdot \cfrac{(x-2)(x-2)}{x^2-3^2}
\\\\\\
\cfrac{x+3}{x(x-2)}\cdot \cfrac{(x-2)(x-2)}{x^2-3^2}\implies \cfrac{\underline{x+3}}{x\underline{(x-2)}}\cdot \cfrac{\underline{(x-2)}(x-2)}{(x-3)\underline{(x+3)}}
\\\\\\
\cfrac{x-2}{x(x-3)}\iff\cfrac{x-2}{x^2-3x}
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How many quart is in water bucket
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3 years ago
How many pennies could you have if:
Gelneren [198K]

Answer:

The number of pennies owned is 7 pennies

Step-by-step explanation:

The given parameters are;

The number of pennies left over when we break the pennies into groups of 2s = 1 penny

The number of pennies left over when we break the pennies into groups of 3s = 1 penny

Let the number of pennies owned = c

What we are given are as follows;

2 × a = c - 1

3 × b = c - 1

2 × a = 3 × b

a/b = 3/2

Therefore, if we multiply 2 by 3, and 3 by 2 we get 6

2 × 3 = 6, similarly 3 × 2 = 6

If we put 6 = c - 1, we get;

c = 6 + 1 = 7

c = 7

The number of pennies owned = 7 pennies.

4 0
3 years ago
Which ordered pair (a, b) is the solution to the following system of equations?
Kamila [148]

Answer:

  (-13, -4)

Step-by-step explanation:

It is about as easy to try the solutions as it is to find them from scratch.

__

However, we can determine which one it is by adding twice the second equation to the first.

  (-2a +3b) +2(a -4b) = (14) +2(3)

  -5b = 20

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8 0
3 years ago
The exclamation point (!) on a billboard consists of a circle sector and circle. The radius of the sector is 9 ft, and the radiu
harina [27]

Answer:

  24.0 square feet

Step-by-step explanation:

The area of the sector is given by ...

  A = (1/2)r²θ . . . . . where θ is the angle in radians

The area of the circle is the same, with θ=2π, so is ...

  A = πr²

__

In this problem, the area of the sector is ...

  A = (1/2)(9 ft)²(24π/180) = 27π/5 ft² ≈ 16.9646 ft²

The area of the circle is ...

  A = π(1.5 ft)² = 9π/4 ft² ≈ 7.0686 ft²

Then the total area of the exclamation point is ...

  16.9646 +7.0686 ≈ 24.0 . . . ft²

The area is about 24.0 square feet.

8 0
3 years ago
What is the vertex of the graph of y = x^2+ 4x?
xxTIMURxx [149]

Answer:

(-2, -4)

Step-by-step explanation:

You can complete the square of the equation to get

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y+4 = (x+2)^2

y = (x+2)^2 - 4

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6 0
2 years ago
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