What does AB congruent symbol CD mean? AB and CD here have lines over them How is it different than AB=CD?

I like to think of myself as the most lucky person out there. 'Why?' you may ask. My reasoning is quite simple, really. The reas

dusya [7]

That’s really nice man. I’m sure she’ll love it

5 0

3 years ago

Which expression is equivalent to StartFraction (3 m Superscript negative 2 Baseline n) Superscript negative 3 Baseline Over 6 m

Dovator [93]

Option a: $\frac{m^{5} }{162n}$ is the equivalent expression.

Explanation:

The expression is $\frac{(3m^{-2} n)^{-3}}{6mn^{-2} }$ where $m\neq 0, n\neq 0$

Let us simplify the expression, to determine which expression is equivalent from the four options.

Multiplying the powers, we get,

$\frac{3^{-3}m^{6} n^{-3}}{6mn^{-2} }$

Cancelling the like terms, we have,

$\frac{3^{-3}m^{5} n^{-1}}{6 }$

This equation can also be written as,

$\frac{m^{5}}{3^{3}6 n^{1} }$

Multiplying the terms in denominator, we have,

$\frac{m^{5} }{162n}$

Thus, the expression which is equivalent to $\frac{(3m^{-2} n)^{-3}}{6mn^{-2} }$ is $\frac{m^{5} }{162n}$

Hence, Option a is the correct answer.

8 0

3 years ago

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Which is equivalent to sqrt x^10<br> A. X-5<br> B. X -1/5<br> C. X sqrt 10<br> D. X 1/5<br> E. X^5

Lesechka [4]

<h3>Answer: E) x^5</h3>

$\sqrt{x^{10}} = x^5$

=====================================================

Explanation:

We simply take half of the exponent 10 to get 5. This applies to square roots only.

So the rule is $\sqrt{a^b} = a^{b/2}$

A more general rule is

$\sqrt[n]{a^b} = a^{b/n}$

If n = 2, then we're dealing with square roots like with this problem. In this case, a = x and b = 10.

5 0

3 years ago

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Match each question to the correct problem.

Maslowich

<h2>Answer:</h2>

<em>(Check attached images).</em>

<h2>Step-by-step explanation:</h2>

<h3>Exercise 1.</h3>

a. Convert to decimals.

To order the numbers from least to greaters, convert them to decimals and compare.

$5.2(percent)=0.052\\ \\\frac{1}{7} =0.1429\\\\ -0.8=-0.8000\\ \\\frac{-11}{5} =-2.2$

b. Select the second least number.

-0.8.

<h3>Exercise 2.</h3>

a. Convert to decimals.

$-3.4(percent)=-0.034\\ \\-0.031\\\\ -0.2\\ \\-\sqrt{0.8}= -0.8944$

b. Select the correct number.

$-\frac{1}{5}$ .

<h3>Exercise 3.</h3>

a. Convert to decimals.

<em>After seeing that there are negative and positive numbers, and with the premise that negative numbers are </em><u><em>always</em></u><em> lesser than positive numbers, we'll only compare the positive numbers.</em>

<em />

b. Select the correct number.

3/5.

<h3>Exercise 4.</h3>

a. Convert to decimals.

-0.35

-3.5%= -0.035

b. Conclude.

Seeing that -3.5% is less than -0.35, the symbol that makes the statement true is ">".

<h3>Exercise 5.</h3>

a. Try to visually estimate b.

B appears to have a value of -0.9.

b. Convert the numbers to decimals.

-3.4%= -0.034

-0.031

-1/5= -0.2

$-\sqrt{0.8}= -0.8944$

c. Select the correct answer.

<em>Since we estimated the value of b as -0.9, the number that best adequates to its value is </em> $-\sqrt{0.8}$ .

<h3>Exercise 6.</h3>

a. Convert to decimals.

<em>After seeing that there are negative and positive numbers, and with the premise that negative numbers are </em><u><em>always</em></u><em> lesser than positive numbers, we'll only compare the positive numbers.</em>

5.2%= 0.052

1/7= 0.1429

b. Select the correct number.

5.2% is the second largest.

<h3>Exercise 7.</h3>

a. Convert to decimals.

6/7= 0.857143

0.857

b. Select the correct answer.

Seeing that 0.857 is marked as an approximate by the

ellipsis, and considering that 6/7 is an irrational numbers, we can conclude that the number that better fits the situation and makes the statement true is "=".

<h3>Exercise 8.</h3>

a. Convert to decimals.

<em>After seeing that there are negative and positive numbers, and with the premise that negative numbers are </em><u><em>always</em></u><em> lesser than positive numbers, we'll only compare the negative numbers.</em>

<em /> $-\sqrt{21} =-4.5826$