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Akimi4 [234]
3 years ago
11

Name the property of equality that justifies the following statement. If p = q, then p - r = q - r A) Multiplication Property .

B) Subtraction Property . C) Symmetric Property . D) Reflexive Property
Mathematics
2 answers:
Sonja [21]3 years ago
6 0

Answer:

Option B is correct.

The property of equality that justifies the following statement is; Subtraction property.

Step-by-step explanation:

Subtraction property of equality states that you subtract the same number from both sides of an equation.

i.e, if a=b then, a-c=b -c

Given the statement:

if p =q  

then, by definition of subtraction Property

Subtract r from both sides of an equation we get,

p-r = q -r

Therefore, the property of equality that justifies the following statement is; Subtraction property.

suter [353]3 years ago
4 0
<span>From the given question : 

If,
p = q
Then,
p - r = q - r

Here,
The commutative property of subtraction has been used.
</span><span>But,
Subtraction is not commutative over real numbers since we can't say that </span><span>a – b = b – a</span><span> for all real numbers </span>a<span> and </span>b<span>.
Hence,
The right answer is : 
</span><span>B) Subtraction Property .</span>
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24x^5-8x^4+12x^3-4x^2 / 4x^2
Margaret [11]

Answer:

The detailed process of simplification is :

Step-by-step explanation:

\frac{24x^{5} - 8x^{4} + 12x^{3} - 4x^{2} }{4x^{2} }

= \frac{24x^{5} }{4x^{2} } - \frac{8x^{4} }{4x^{2} } + \frac{12x^{3} }{4x^{2} } - \frac{4x^{2}  }{4x^{2} } ..........................separate the terms

= 6x^{5-2} - 2x^{4-2} + 3x^{3-2} - 1 ................ subtract the power of x from denominator

= 6x^{3} - 2x^{2} + 3x -1

= 2x^{2}( 3x -1 ) +  (3x -1 )................................... Take  (3x -1 ) common in (6x^{3} - 2x^{2})

=  (3x -1 ) (2x^{2} +1) .......................................Take  (3x -1 ) common in whole equation

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When are the absolute value and the opposite of a rational number equal
natulia [17]
|a| = -a if a < 0

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8 0
3 years ago
-6.4 = z/6<br>what does z =?​
Alecsey [184]

Answer:

-38.4

Step-by-step explanation:

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4 0
3 years ago
Can someone please explain to me how to do this?
OLga [1]

Answer:

  1. (-10x -5) -(-7x -4)

  2. (-10x -5) -(-3x -1)

Step-by-step explanation:

The process of simplifying an expression generally involves eliminating parentheses, collecting terms, simplifying fractions, rationalizing denominators, removing appropriate factors from under radicals, and generally putting expressions into general form.

So, to accomplish what the problem is asking, you can create an expression that requires you accomplish as many or as few of these steps as you may like.

In general, you will want to both "do" and "undo" whatever operation(s) you may choose. For example, consider a couple of expressions "a" and "b". For this example, we want our final result to simplify to "a".

If we choose to add "b", we might have ...

  (a+b) -b . . . . . we have both added and subtracted b, so the simplified result is "a"

If we choose to multiply by "b", we might have ...

  (ab)/b . . . . . . we have both multiplied by b and divided by b, so the simplified result is again "a"

_____

We can solve both these problems at once by using ...

  • a = -3x -1
  • b = -7x -4

If we choose the first approach, we want an expression that is (a+b). That will be ...

  a+b = (-3x -1) +(-7x -4) = -10x -5

By subtracting "b" from this expression, we get "a"--and vice versa. That is ...

  1. (-10x -5) -(-7x -4) . . . simplifies to . . . -3x -1
  2. (-10x -5) -(-3x -1) . . . simplifies to . . . -7x -4

_____

<em>Alternate solution to 2</em>

Suppose we choose to multiply instead. Let "b" be -3x+2. Then, using the template for multiplication above, we can write the expression

  (-7x -4)(-3x +2)/(-3x +2) = (21x^2 -2x -8)/(-3x +2)

and we know this rational expression simplifies to -7x -4.

_____

Of course, we can be as elaborate as we might like in modifying the original expression. Whatever we do, we must also include the "undo" so the original expression is recovered when we simplify. To illustrate the point, we can add and subtract 2x from the above rational expression.

  ((21x^2 -2x -8)/(-3x +2) + 2x) - 2x = (21x^2 -2x -8 +2x(-3x +2))/(-3x +2) - 2x

  = (21x^2 -2x -8 -6x^2 +4x)/(-3x +2) -2x

  = (15x^2 +2x -8)/(-3x +2) -2x . . . . . . another alternate solution to #2.

If we're not careful, we can create an expression that is extremely difficult to simplify. The one we have here can be factored to be ...

  (-5x -4)(-3x +2)/(-3x +2) -2x = -5x -4 -2x = -7x -4 . . . our original #2 expression

Knowing that it <em>can</em> be factored is a big help.

6 0
3 years ago
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