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storchak [24]
2 years ago
6

do you agree that the equation (x-4)²=9 can be solved both by factoring and extracting square roots? ​

Mathematics
1 answer:
zvonat [6]2 years ago
7 0

Given parameters:

  Equation:

          (x-4)²=9

Problem, solve the equation by factoring and extracting the root

<u>Solution:</u>

    Given equation:

                  (x-4)²=9

         subtract 9 from both sides to equate to zero;

                (x-4)² - 9 = 0

                (x -4)² - 3² = 0

  Now, this is similar to the concept of difference of two squares;

          x² - y² = <em>(x + y)(x-y)</em>

                     

Here x  = x-4 and y = -3

  So input and solve;

              (x - 4 -3)(x - 4 -(-3)) = 0

              (x - 7)(x - 4+3) = 0

              (x -7)(x -1) = 0

S0,

             x - 7 = 0 or x-1 = 0

             x = 7 or 1

If we extract the square roots;

          (x-4)² = 9

         √(x-4)² = √9

              x - 4 = 3

              x  = 4 + 3 = 7; this is not the only solution to the problem

So we cannot solve it by extracting the square root.

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702.50 = 5.5x + 70

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-----------------------------

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7 0
1 year ago
The owners of an amusement park selected a random sample of 200 days and recorded the number of park patrons with annual passes
allochka39001 [22]
<h2>Answer with explanation:</h2><h2></h2>

The x% confidence interval interval interprets that we are x% confident that the true population mean falls in it.

Given : The owners of an amusement park computed a 90% confidence interval for the number of patrons with annual passes who visit the park daily.

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6 0
2 years ago
At the band's peak of popularity, a personally signed Black Diamond poster sold for $500. Three years later the band was almost
maw [93]

Answer:

The annual multiplier is 0.27 and Annual Percent in decrease is 73%.

Step-by-step explanation:

Given:

Initial Value a_i = \$500

Elapsed time n= 3\ years

Final Value a_3 = \$10

We need to find the annual multiplier and annual percent of decrease.

Solution:

Now we know that;

The Final value after n years is equal to Initial value multiplied by the multiplier raise to number of elapsed years.

framing in equation form we get;

a_n=a_i\times (m)^n

m⇒ annual multiplier

Substituting the values we get;

10=500\times (m)^3\\\\m^3=\frac{10}{500}\\\\m^3=\frac{1}{50}

Taking cube root we get;

\sqrt[3]{m^3}=\sqrt[3]{\frac{1}{50}}  \\\\m=0.27

Hence the annual multiplier is 0.27.

Now We will find the annual percent of decrease.

Now we know that;

annual multiplier is equal to 1 minus the depreciation rate.

m=1-r

r ⇒ annual percent in decrease.

0.27 =1-r\\\\r = 0.73\ \ Or \ \ 73\%

Hence Annual Percent in decrease is 73%.

5 0
2 years ago
The distance between two piers on a river is 45 miles. It takes a motorboat, moving downriver, 2 hr 15 min to complete the journ
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3 0
2 years ago
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