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Use the properties of operations to determine if each pair of expressions is equivalent

SIZIF [17.4K]

Using the properties of operations the given pair of expressions are not equivalent

Solution:

Given that, we have to use the properties of operations to determine if each pair of expressions is equivalent

And the two expressions are:

$\frac{1}{2}(4-2 x) \text { and } 2-2 x$

Now, we know that, there are four (4) basic properties of operations:

Commutative, Associative, Distributive and Identity. These properties only apply to the operations of addition and multiplication.

So, if we observe we can apply distributive property on 1st expression

The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.

$\begin{array}{l}{\frac{1}{2}(4-2 x) \rightarrow \frac{1}{2}(4)-\frac{1}{2}(2 x)} \\\\ {\rightarrow 2-x}\end{array}$

Here the resulting expression is 2 – x and it is not equivalent to 2 – 2x

Hence, the given two expressions are not equal.

3 0

3 years ago

Fill in the blanks to rewrite the following statement with variables: Given any positive real number, there is a positive real n

sveticcg [70]

Answer:

a) there is s such that r>s and s is positive

b) For any r>0 , there exists s>0 such that s<r

Step-by-step explanation:

a) We are given a positive real number r. We need to wite that there is a positive real number that is smaller. Call that number s. Then r>s (this is equivalent to s<r, s is smaller than r) and s is positive (or s>0 if you prefer). We fill in the blanks using the bold words.

b) The last part claims that s<r, that is, s is smaller than r. We know that this must happen for all posirive real numbers r, that is, for any r>0, there is some positive s such that s<r. In other words, there exists s>0 such that s<r.

3 0

3 years ago

The angles of a triangle are 99??, 3x??, and x + 5??.

Anit [1.1K]

Since we know a triangle only has 180 degrees we can say:

99+3x+x+5=180

Then we can solve for x:

4x+104=180
4x=76

x=19

3 0

3 years ago

To determine a student’s grade, a teacher throws out the lowest grade obtained on 5 tests, averages the remaining grades, and ro

schepotkina [342]

Answer:

85

Step-by-step explanation:

add 4 values, excluding 72 (lowest grade)

total = 339

average = 330/4 = 84.75

84.75 rounding to nearest integer is 85

6 0

3 years ago

Last month John had $240 in his savings account. He got money for his birthday and now he has $320. What is the percent of chang

Elis [28]

Answer:

Should be a 33.33% increase

Step-by-step explanation:

320 divided by 240 to get 1.33, anything above 1 is increase, so its a 33% increase.

4 0

2 years ago