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3 years ago

6

When 2/3 is added to a certain number, the sum is 3 greater than twice the number. part 1: set up an equation using n to represe

nt the number. part 2: solve the equation in part 1 for n.?

1 answer:

Gennadij [26K]3 years ago

7 0

2/3 + n = 2n + 3 <== ur equation
2/3 - 3 = 2n - n
2/3 - 9/3 = n
-7/3 = n <== ur solution

or
2/3 + n = 2n + 3...multiply everything by common denominator of 3
2 + 3n = 6n + 9
2 - 9 = 6n - 3n
-7 = 3n
-7/3 = n

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Which is equivalent to V180x11 after it has been simplified completely?

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Question:

Which is equivalent to $\sqrt{180x^{11}}$ after it has been simplified completely?

Answer:

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

Step-by-step explanation:

Given

$\sqrt{180x^{11}}$

Required

Simplify

We start by splitting the square root

$\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}$

Replace 180 with 36 * 5

$\sqrt{180x^{11}} = \sqrt{36 * 5} * \sqrt{x^{11}}$

Further split the square roots

$\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} * \sqrt{x^{11}}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{11}}$

Replace power of x; 11 with 10 + 1

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10 + 1}}$

From laws of indices; $a^{m+n} = a^m * a^n$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x^1}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x}$

Further split the square roots

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10}} * \sqrt{x}$

From laws of indices; $\sqrt{a} = a^{\frac{1}{2}}$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{10*\frac{1}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{\frac{10}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{5} * \sqrt{x}$

Rearrange Expression

$\sqrt{180x^{11}} = 6 * x^{5} * \sqrt{5} * \sqrt{x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}$

From laws of indices; $\sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}$

So, we have

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}$

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

<em>The expression can no longer be simplified</em>

Hence, $\sqrt{180x^{11}}$ is equivalent to $6x^{5}\sqrt{5x}$

7 0

3 years ago

Read 2 more answers

At a baseball game, the ratio of Barons fans to Blue Sox fans is 8 : 3. If you know that at least 22,000 people are attending th

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3 years ago

Maria took out an unsubsidized Stafford loan of $6,925 to pay for college. She plans to graduate in 4 years. The loan had a dura

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Answer:

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Step-by-step explanation:

Calculation to determine how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization

First step is to determine the Interest only monthly repayments

Using this formula

I=Prt

where,

P=$6925

r=0.05/1

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Let plug in the formula

I=6925*0.05/12

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Second step is to determine the amount she will owe after 4 years

Using this formula

S=P(1+r)n

Let plug in the formula

S=6925*(1+0.05/12)4*12

S=6925*(1+0.05/12)48

S=$8454.70

Third step is to determine the Interest part

Interest =8454.70 - 6925

Interest = $1529.70

Now let determine the how much greater will the amount of interest capitalized be

Interest capitalized=1529.70 - 1385.00

Interest capitalized =$144.70

Therefore how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization is $144.70

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